ccbshb17 financial derivatives

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Centre for Central Banking StudiesBank of England

Financial Derivatives

Simon Gray and Joanna Place

Handbooks in Central Bankingno.17


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Handbooks in Central Banking

No. 17

FINANCIAL DERIVATIVES


Series editor: Robert Heath

Issued by the Centre for Central Banking Studies,Bank of England, London EC2R 8AH

Telephone 0171 601 5857, Fax 0171 601 5860March 1999

© Bank of England 1999

ISBN 1 85730 141 2


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Foreword

The series of Handbooks in Central Banking has grown out of the activities of the Bank of England’s Centre for Central Banking Studies in arranging and delivering trainingcourses, seminars, workshops and technical assistance for central banks and centralbankers of countries across the globe.

Drawing upon that experience, the Handbooks are therefore targeted primarily at centralbankers, or people in related agencies or ministries. The aim is to present particulartopics that concern them in a concise, balanced and accessible manner, and in a practicalcontext. This should, we hope, enable someone taking up new responsibilities within acentral bank, whether at senior or junior level, and whether transferring from otherduties within the bank or arriving fresh from outside, quickly to assimilate the keyaspects of a subject, although the depth of treatment may vary from one Handbook toanother. We hope they will also be helpful to those with some experience, but who arefacing new problems as the economy and markets develop. While acknowledging that asound analytical framework must be the basis for any thorough discussion of centralbanking policies or operations, we have generally tried to avoid too theoretical anapproach. The Handbooks are not intended as a channel for new research.

We have aimed to make each Handbook reasonably self-contained, but

recommendations for further reading may be included, for the benefit of those with aparticular specialist interest. The views expressed in the Handbooks are those of theauthors and not necessarily those of the Bank of England.

We hope that our central banking colleagues around the world will continue to find the Handbooks useful. If others with an interest in central banking enjoy them too, we shallbe doubly pleased.

We would welcome any comments on this Handbook or on the series more generally.

Robert Heath

Series Editor


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DERIVATIVES


Contents

Page

Abstract....................................................................................................... 3

1 Introduction................................................................................................ 5

2 Policy aspects of derivatives ..................................................................... 6a) Monetary policy ..................................................................................... 6b) Supervision of banks’ derivative risks ................................................... 8

3 Overview of derivative products and arbitrage ..................................... 12

4 Forwards..................................................................................................... 16a) Foreign exchange forwards ..................................................................... 16b) Interest rate forwards............................................................................... 18c) Futures ..................................................................................................... 19

5 Swaps........................................................................................................... 21

i) Interest rate swaps .................................................................................. 23ii) Currency swaps ...................................................................................... 26iii) Credit swaps........................................................................................... 27

6 Options ........................................................................................................ 27

7 Institutional arrangements ....................................................................... 36

8 Accounting standards................................................................................ 39

9 Statistical measurement ............................................................................ 39

Annex 1 The size of global derivatives markets: Survey data fromthe Bank for International Settlements.............................................. 43

Annex 2 Forward exchange rate calculations................................................... 45Annex 3 Forward interest rate calculations ...................................................... 46Annex 4 Swap spreads and government bond yields ....................................... 47Annex 5 Cash flow and margining ................................................................... 49

Glossary............................................................................................................ 51Further Reading.............................................................................................. 58


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ABSTRACT

Derivatives, ranging from relatively simple forward contracts to complicated options

products, are an increasingly important feature of financial markets worldwide. They

are already being used in many emerging markets, and as the financial sector becomes

deeper and more stable, their use is certain to grow. This Handbook provides a basic

guide to the different types of derivatives traded, including the pricing and valuation of

the products, and accounting and statistical treatment. Also, it aims to highlight the main

areas in which derivatives matter to central banks, notably those of monetary policy and

banking supervision. It is not intended as a manual for traders, nor to describe in depth

the current state of world markets, where changes can happen so rapidly that any

description must soon become outdated. But we do hope to provide a clear enough

description of derivatives and their relevance to central banks for central bankers to be

confident in tackling the issues that arise. Most derivatives traded are, in fact, fairly

simple, and well within the grasp of our intended readership.


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DERIVATIVES

1. Introduction

Derivatives are useful for risk management: they can reduce costs, enhance returns and

allow investors to manage risks with greater certainty and precision. But, used

speculatively, they can be very risky instruments as they are highly leveraged and are

often more volatile than the underlying instrument. This can mean that, as markets in

underlying assets move, speculative derivatives positions can show even greater

movements, resulting in large swings to profits and losses. Recent attention has

focused on large losses (such as Barings, Sumitomo) and has underlined the need to

have good management controls in place when dealing with such instruments.

A derivative contract assumes value from the price of an underlying item, such as a

commodity, financial asset or an index. The underlying asset could be a physical good,

such as wheat, copper or pork bellies, where derivatives pricing is affected by

expectations about future supply and demand constraints; or a financial product, such as

equities, fixed-income securities or simply a cash balance. A financial derivative

contract derives a future price for that asset on the basis of its price today (the spot price)

and interest rates (the time value of money).

This Handbook considers financial derivatives. The underlying assets are typically a

short-term or a long-term loan (normally the three-month interbank interest rate and a

long-term government bond yield); foreign currencies; or equities, whether individual

equities or an index. Also, credit risk based derivatives have recently emerged in

financial markets. Derivative contracts can be subdivided into forward contracts, in

which both parties are obliged to conduct the transaction at the specified price and on

the agreed date; swaps, which may be viewed as a subset of forwards and involve the

exchange of one asset (or liability) against another at a future date (or dates); and

options, which give the holder the right but not the obligation to require the other party

to buy or sell an underlying asset at the specified price on or by the agreed date.


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Distinction also needs to be made between exchange-traded contracts, which are

standardised, and OTC (over-the-counter) contracts, which typically are non-standard.

Data on the world’s derivatives markets are available from the Bank for International

Settlements (BIS). The BIS triennial survey of foreign exchange business in major

financial centres around the world was extended in 1995 to include derivatives

transactions, and this was repeated in 1998. Also in 1998, the BIS initiated a semi-

annual survey on open positions in global over-the-counter derivatives markets. The

first data - for end-June 1998 - are presented in Annex 1.

The next section discusses the policy issues raised by derivatives. However, as a good

understanding of the instruments is necessary to an appropriate central banking

response, those readers who are wholly unfamiliar with derivatives will need to return to

this section after reading through sections 3-9.

2. Policy Aspects of Derivatives

a) Monetary Policy

There are three main areas in which derivatives may impact monetary policy. These

relate to the informational content of the market; any effects on the transmission

mechanism; and the possible use of derivatives as monetary policy instruments.

Informational content

Even if derivatives are not traded, the same processes as used for calculating derivative

prices such as forward interest and exchange rates can be used to extract information

from market prices. For instance, the central bank may calculate implied forward rates to

judge whether the market expects interest rates to increase, or whether market


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expectations of the timing of interest rate changes has altered; or perhaps to estimate a

term premium. In interpreting these estimates, the central bank has to remember that the

markets will be making (possibly wrong) guesses about future changes in the central

bank’s own intervention rates.

If an exchange rate target is being used, the calculation of forward rates can give the

central bank a measure of the credibility of the policy. If forward rates are outside a

targeted band, this implies the market does not have full confidence that the band can or

will be sustained.

If options are traded, then options prices can give an indication not only of the market’s

central expectation of future price moves, but also of the distribution of risk. So-called

kurtosis analysis can be used to analyse the distribution of expected outcomes (is it

normal? Skewed? fat-tailed?).

Transmission mechanism

Since the trading of derivatives allows risk, or market exposure, to be transferred from

one person/institution to another, a BIS committee (called the Hannoun committee, after

its chairman) studied whether the trading of derivatives affected the transmission

mechanism, and concluded that there was no significant effect in the markets studied . A

similar conclusion was reached in an IMF paper (“Derivatives Effect on Monetary

Policy Transmission”, dated September 1997): “Theoretically, derivatives trading speeds

up transmission to financial asset prices, but changes in transmission to the real

economy are ambiguous. [In] a study of the UK economy...no definitive empirical

support for a change in the transmission mechanism is found.”


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Use of derivatives as monetary policy instruments

A number of central banks use foreign exchange swaps as a monetary policy instrument;

and some will use a broader range of derivatives in managing their foreign exchange

reserves, but not for monetary policy purposes. While a theoretical case can be made for

using derivatives, including options, to defend a monetary policy stance, they do not

have a direct impact on monetary base, and their use is normally considered to be risky

and uncertain. We would in general argue that, with the exception of foreign exchange

swaps, derivatives should not be used by central banks for monetary policy purposes.

b) Supervision of banks’ derivative risks

Derivative instruments give rise to few completely new risks in themselves. Like most

products they generate exposures to market risk and to counterparty credit risk, as well

as the usual range of operational risks. However, derivatives sometimes can repackage

risks in complex ways. This can result in a misunderstanding of the exposure to these

risks and to mis-pricing. Derivatives can enable banks to take on large exposures to

market risks for relatively small initial cash outlays. This is known as leveraging.

In the UK, banking supervisors tend not to focus specifically on banks’ derivatives

activities - because they pose few new risks - but consider them instead as part of banks’

wider treasury and trading activities. When assessing a bank’s treasury and trading

activities, supervisors focus on two main areas: the adequacy of internal risk

management and control, and capital adequacy.

Internal risk management and control

Supervisors undertake on-site visits to the whole range of banks which have treasury and

trading operations - whether they are engaged in balance sheet hedging, or trading for


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own account or customers - including to banks which use internal pricing and risk

aggregation models to calculate market risk capital requirements (see below). These

visits, which typically last 1-3 days, focus very much on internal controls and risk

management in the treasury and/or trading area, as well as on the technical aspects of

pricing and risk models. Internal controls and risk management are judged against

supervisors’ assessment of market best practice, with the onus on banks to justify any

divergence.

Managing the market risk of derivatives can be more challenging than managing the

underlying assets because of the sometimes complex relationship between changes in the

value of derivatives and changes in the underlying asset price. This is particularly true

for options: as the price of the underlying asset changes, option values change in a non-

linear way, making them sometimes very sensitive to small changes in the price of the

underlying asset. For some products, e.g. barrier or digital options1, there are also

discontinuities in the relationship between an options’ value and the price of the

underlying asset. And discontinuities are not confined to exotic products, since a

portfolio of “vanilla” options can closely approximate exotic options: sudden changes in

the value of a portfolio of vanilla options are therefore quite possible. Risk

identification and timely measurement of exposures are therefore crucial to effective risk

management. Typically, many banks use Value-at Risk (VaR) models to manage their

market risk exposure. These VaR models estimate the potential loss of a portfolio over a

given time interval at a given confidence interval; normal market conditions are usually

assumed.

Independent valuation of positions is an important aspect of internal control in any

trading area, including one that uses derivatives. Where a bank is marking to market,

valuing any OTC product can be difficult if market prices are not readily available, e.g.

from brokers’ screens. OTC derivatives are no exception and, in fact, the problem can

be greater for OTC options, whose value depends on implied volatilities that are hard to


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estimate, particularly for options that are away from the money. Losses can therefore

easily be concealed in a portfolio (deliberately or otherwise) and so it is important for

middle and back office staff to be as familiar with derivatives risks and pricing issues as

traders, and to undertake a rigorous comparison of profit and loss against risks taken.

Capital requirements

Both the EU and BIS have established capital requirements for market and credit risks

for on- and off-balance sheet items, including derivatives. Capital requirements for

foreign-exchange and commodity price risk on all positions, and interest rate and equity

risk on trading positions, are set out in the EU Capital Adequacy Directive (1993) (as

subsequently amended) and the BIS Amendment to the Capital Accord to incorporate

market risks (1996). Capital requirements for counterparty credit risks are set out in the

EU Capital Adequacy and Solvency Ratio Directives (as subsequently amended) and the

Basle Capital Accord (as subsequently amended). None of these make special

provisions for derivatives except where the risks differ from those on the underlying

assets. So, capital is charged for options risks to capture their non-linearity (gamma)

and sensitivity to changes in volatility (vega), and a special calculation is made for

counterparty risk. Banks’ internal models may be used to calculate options’ risk

requirements, with their supervisor’s prior agreement.

The counterparty risk on a derivative contract depends on the size of the exposure, the

probability of the counterparty defaulting, and the recovery value in the event of default.

The size of the exposure is typically only a small proportion of the notional amount

underlying the contract but can change quite substantially over the life of the contract as

the underlying asset price changes. For capital adequacy purposes, the size of the

exposure is measured as the current value of a contract - how much it would cost to

replace a contract today if the bank’s counterparty defaulted today - plus an “add-on” to

capture potential future exposure. To see the need for this add-on consider an interest

1 A glossary of terms is provided at the end of this Handbook.


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rate swap. At the time the contract is entered into, its market value is usually zero. But

clearly a bank has an exposure to its counterparty because it expects the counterparty to

make payments to it over the life of the contract. So, its counterparty exposure is not

zero and an “add-on” is required to capture the full exposure (note that there is no

counterparty exposure of this sort arising on written options, as the holder will not

exercise an out-of-the money option). The net value to a bank of the payments which

are payable and receivable over the life of a swap are uncertain at the outset and will

depend upon the path of interest and exchange rates over the swap’s life. The add-on

must therefore reflect the expected path of the underlying interest and exchange rates

over the life of the contract.

The EU and BIS capital requirements distinguish between contracts of different

maturities, and contracts with different underlying asset prices, with larger amounts of

capital (larger add-ons) held against contracts where the underlying price is more

volatile, e.g. more for options based on commodity prices than on interest rates. Capital

requirements for derivatives are finally calculated using the usual counterparty credit

risk weights, but with the maximum risk weight reduced from 100% to 50%.

Derivatives clearing houses reduce their counterparty exposures through initial and daily

margining. There are a number of ways to reduce counterparty exposures on OTC

contracts, including bilateral netting, collateralisation, margining, guarantees or letters

of credit, but these will only be effective if the arrangements are legally enforceable in

relevant jurisdictions.

A number of other risks should also be considered in relation to derivatives 2:

2

In September 1998, the Basle Committee on Banking Supervision and the Technical Committee of theInternational Organisation of Securities Commission (IOSCO) published Framework for Supervisory

Information about Derivatives and Trading Activities, a document that provides a framework for thecollection of data for supervisory purposes.


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Liquidity - Derivatives can give rise to large and unpredictable cashflows, particularly

margin calls for exchange-traded products, and this should be considered as part of a

bank’s overall liquidity position, if material.

Legal and settlement risks - For exchange-traded products, provided the exchange is

well set up, the legal and settlement risks may be small. But, for OTC contracts, where

there is not usually a clearing house, and where legal contract documentation may not be

standardised, risks may be considerably greater.

For banks selling OTC derivatives to clients, there is also a need to take account of

suitability. There have been a number of court cases in the UK and the USA where non-

financial clients have entered into derivatives transactions, lost money and subsequently

sued the bank in question for selling them an inappropriate product. Banks need not only

to take account of the sophistication of the client and ensure that derivative products are

properly explained, but also to be able to demonstrate that they have done so in the event

of a subsequent dispute.

3. Overview of derivative products and arbitrage

Forwards may be related to interest rates, bond prices, foreign currency, a basket of

equities, a commodity or, more recently, credit risk. For instance, a forward rate

agreement (FRA) fixes the interest rate for a deposit or loan transaction commencing on

an agreed future date. Futures3 are exchange traded forwards, and consequently are

traded in a standardised format e.g. traded in predetermined bundles for settlement only

on certain fixed dates, and settled through a clearing house. Some traders use the futures

market as a proxy for the market in the underlying asset. Forwards are bilateral contracts

whose terms can be decided by the parties involved. As OTC contracts, forwards may

provide a more exact match of the needs of the parties involved than is possible with a

3 In this Handbook, we will refer to an OTC forward simply as a "forward" and an exchange tradedforward as a "future".


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standardised exchange-traded product, but with this flexibility comes potentially greater

counterparty risk 4 because of the lack of a clearing house arrangement (although some

clearing houses are discussing the possibility of clearing some OTC contracts). While

the OTC market is bigger than that for exchange-traded products, it is often thought of

as less liquid in that there is less trading in each contract.

Options can be either exchange traded (like futures) or OTC. A call option gives the

holder the right (but not the obligation) to buy an underlying item - an interest rate,

foreign exchange, a security or other assets - at a predetermined price on or before the

agreed expiry date of the option. A put option gives the holder the right (but not the

obligation) to sell an underlying item.

Swaps are almost exclusively traded OTC; they are virtually never exchange-traded.

They can be related to interest rates, exchange rates, commodities, equities or credit risk.

A swap is an agreement to exchange cash flows based on a given principal amount

(usually notional) for a given time period.

Interest rate swaps represent an agreement to exchange cash flows related to interest

rates - normally at least one of which is on a floating basis - at a future date, based on a

notional principal amount. Foreign exchange swaps are in effect a spot transaction

coupled with a reverse forward transaction (an agreement to transact at a fixed price at a

future date). These instruments may also involve an exchange of interest payments

during the life of the contract, if the underlying assets involved are loans (liabilities)

rather than cash balances (assets).

“Long” and “short” positions can be measured in different ways. A “long” position is

associated with an obligation to purchase an asset (foreign exchange, securities,

commodities, and loans), and a “short” position an obligation to sell. The position is

usually looked at on a net basis by type of risk category e.g a net forward foreign

4 The risk that a counterparty fails to make all of the payments over the life of the contract.


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exchange position will take into account future obligations to purchase sterling against

obligations to sell it (including swaps). But it could be divided by time periods, or added

to an underlying cash position. Traders will tend to take a long position if they expect

asset prices to rise, and a short position if they expect prices to fall.

The table below summaries the different derivative types and how they are traded.

Exchange -Traded(= standardised contracts)

Over-the-Counter (OTC)(= non-standardisedcontracts)

Purchase/Sale of Asset at specified price on

agreed future date

Future Forward

Exchange of assetsat specified prices andon agreed date(s)

- Swap

Right but not theobligation to conductone of the above

transactions

Option OTC OptionSwaption5

Pricing

In order to value a financial derivative it is essential to have an active market in the

underlying item. The market pricing of derivatives also assumes a well-arbitraged

market. If this is not the case, perhaps because of segmentation in the market or an

inefficient payments system, it may prove difficult for the market to price derivatives;

and market liquidity will consequently be reduced.

If the market is well arbitraged, participants in the markets should be indifferent between

comparable transactions. For instance, a borrower needing finance for six months could

borrow for 6 months, or could borrow for three months and roll over the finance for a

5 An option to transact in a swap.


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further 3 months, or any other combination of periods which totalled the required 6

months. Ex ante, the expected cost of any of these options should be the same.

Derivatives allow traders to take advantage of different expectations of forward interest

rates from that implied in the yield curve. For instance if one trader thought that interest

rates were likely to remain flat but the yield curve implied a sharp rise, the trader could

take a position in a forward contract such that he would profit if his expectation turned

out to be correct. For instance, if the three month interest rate is 10%6 and the six month

rate 12%, implying that the three months rate in three months’ time will rise to 14% (see

Annex 2 for forward yield calculations), a trader who thought interest rates would not

rise might borrow for three months and lend for six. He could then refinance after three

months at a rate lower than 14% to lock in a profit.

Assets Liabilities

Loan 100 Borrowing 100

Interest rate 12% for

six months

100 * 12% * 182/365 = 6 Interest rate:

10% for 3 months10% for 3 months

100*10%*91/3657

= 2.5100*10%*91/365 = 2.5

Profit 1.0

Total 106 Total 106

But this would tend to increase demand for three month money, pushing up that interest

rate, and increase supply of six month money, pulling that rate down. If enough tradersor other market participants took this position, then as traders positioned themselves to

take advantage of the perceived anomalies, they would shift the pattern of supply and

demand in a way that would tend to remove those anomalies. The yield curve would

flatten out until the implied futures rates reflected market opinion. Any trader can take a

6

Annualised basis.7 The market convention for money market calculations in the UK is actual/365. However, othercountries may have different conventions e.g. for the Euro area countries the recommended marketconvention in actual/360.


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different view to the market, but the market as a whole can only have internally

inconsistent pricing if arbitrage is weak.

4. Forwards

A forward agreement is an agreement made between two counterparties to sell/buy an

underlying item at a certain future time for a certain price. The price agreed is referred

to as the delivery price. It allows both the buyer and seller to lock in a certain price and

therefore protects them from price movements in the period ahead of delivery. The

reason for entering into such an agreement may be to ensure certainty of price. For

example, if a manufacturer has agreed a certain price for his products with his

customers, he may want to guard against increases in the price of raw materials for the

period in which his output prices are set. It may also be used as a speculative instrument,

where the buyer/seller anticipates future price movements and hopes to gain from them;

or as an arbitrage against other markets where an opportunity exists.

An OTC forward agreement can be for any size, amount and period. It will be bilaterally

negotiated between two counterparties and credit risk will remain with the

counterparties themselves.

a) Foreign Exchange forwards

“A contract for the exchange of one currency against another, at an

agreed rate, for a specified settlement date in the future”

Foreign exchange forwards are often the first derivatives to be traded in an emerging

market, as it tends to be the forex market that develops first. In some cases, capital

controls mean that there are problems, particularly for non- residents, in taking or

providing delivery of the underlying currency. Sometimes foreign markets will trade

“non-deliverable forwards” (NDFs), allowing non-residents to take or hedge exposures

against the currency in question, but settling the contract in another currency such as the


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US dollar. The bank or other entity which trades in such NDFs cannot always hedge its

own net position easily in the cash market, however. This will tend to mean that spreads

are relatively wide, and pricing may reflect localised demand and supply rather than

being a good proxy for the domestic market.

Forward rates are based on the spot exchange rate and the interest rate differential

between the two countries in question. The calculation is detailed in Annex 2. The

calculation of foreign exchange forwards can be shown pictorially:

times spot

FX rate

times impliedforward FX

rate

plus foreign interest rate, If ‘X’ units of FXat future date

(1 + Id ) * (implied) forward rate = Spot rate * (1 + If );

(implied) forward rate = Spot rate * (1 + If ) / (1 + Id )

This can be approximated as :

(Implied) forward rate = Spot rate * (1 +( If - Id ))

‘Y’ units of domestic currency

plus domestic interest rate, Id


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b) Interest rate forwards

The pricing of interest rate forwards is taken from the forward yield curve. The forward

yield curve can, in turn, be derived from the yield curve as follows:

Current interest rates Implied 3 month forward

No. ofdays

(i) annualrate

(ii) periodrate

(iii) periodrate

(iv)annual

rate

A B C D E

3 month 91 10% 2.4% now 2.4% 10.0%6 month 182 12% 5.8% in 3 months’ time 3.3% 14.0%

Strictly speaking, the longer-term rate should be divided by the shorter term, rather than

the latter subtracted from the former. For example, using the number in the example

above, the forward rate of 14% - column E - is 1.058 / 1.024, annualised (i.e. figures

from col. C) - rather than 1.058 - 1.024, annualised (see Annex 3). The difference

becomes significant if the annualised rate is much over 10%.

It is vital to remember that forward rates are arithmetical calculations based on the

market yield curve and not an individual trader’s opinion of what the spot rate will be at

the settlement date quoted.

If the yield curve is reasonably robust - i.e. it reflects real transactions in the money

markets - then it should be possible for banks and others to calculate implied forward

rates.


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Upward sloping yield curve

0.00%

5.00%

10.00%

15.00%

20.00%

25.00%

1 2 3 4 5 6 7 8 9 10 11 12

annual rates

one month forward, ar

“Synthetic” forward positions can be created using cash market instruments. For

instance, borrowing for 6 months and lending for 3 results in an exposure to the 3

months interest rate in 3 months time. This gives the same result as using a

forward/future contract to take a “long” position in the three month interest rate. The

opposite could be done to take a short position. As a rule, derivatives are

administratively simpler and cheaper to use than such synthetic positions (which expand

the balance sheet).

c) Futures

A futures contract is an exchange traded forward contract. It is an agreement to deliver

or receive a specified amount of a particular asset on a fixed future date at a price agreed

today. The instruments underlying financial futures contracts are typically government

bonds, money market instruments or foreign exchange. To this extent they are exactly

the same at OTC forwards. Exchange trading is only possible where most of the features

of the asset are standardised. A future will be for a set contract size; a fixed maturity

and a limited number of settlement dates; and the responsibility for credit risk control

will normally rest with a clearing house (see section 7), which is the counterparty to

each outstanding position (counterparty risk is standardised). The exchange also needs


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to specify certain details about the futures contract: i.e. how prices will be quoted, and

when and how delivery will be made.

Because of the liquidity of the futures markets - which is facilitated by the

standardisation and the speed and safety of transactions - it often leads the cash market;

and is used as proxy for the market as a whole. It can therefore be thought of as, and is

often used as, a barometer of market sentiment in the underlying instrument. Many

investors will use futures rather than the cash market in order to e.g., change the

duration8 of their portfolio or their asset allocation or for hedging purposes. Futures are

often more liquid than cash bonds, there are low ‘up-front’ payments (just the initial

margin), and the purchase/sale is very quick. However, although, under ‘normal’

circumstances, derivatives markets are often more liquid than the underlying cash

market, liquidity in derivatives markets is more easily lost at times of crisis, partly as

there are no market makers in derivatives (as there may be in the underlying assets) and

therefore liquidity can not be guaranteed.

It is relatively rare for the futures contract to be held to maturity and for the underlying

asset to be delivered: usually investors/traders buy and sell the contract without wishing

to receive/deliver the underlying asset. They simply want to take on an exposure (or

hedge) for a particular period. If the contract is held to delivery, it is the seller of the

contract who will deliver the underlying asset. In the case of a government bond future,

the seller chooses which specific bond – from a basket of “deliverable” bonds – to

deliver.

When the asset is a short-term interest rate (rather than, say, a long-term bond) the

contract will be cash settled: this is easier than trying to standardise the credit risk of

short-term loans. For example, the three-month “short [i.e. relatively short-term] sterling

future” traded in the London market uses as a reference point the three month LIBOR

8 Weighted average term to maturity. Duration provides a measure of price sensitivity: the longer theduration of the portfolio the more sensitive its value to interest rate changes.


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quote for the relevant day as set by the British Bankers Association. Interest futures

prices are usually quoted as “100 minus the annualised interest rate”. If the expected

interest rate at the futures settlement date is 7.5%, the future will trade at 92.5; and the

value of each basis point move in the futures price is fixed in relation to a notional loan

size. If the notional loan is 1 million currency units and a three month interest rate is

being traded, the value of a one basis point move in the future will be 25 currency units

(1,000,000 * 0.01% * [3/12]; the “3/12” factor is because a three month notional loan is

being traded, but the future is priced as 100 minus the annualised interest rate). It is

assumed that a borrower’s actual costs will move in parallel with the LIBOR quote.

Futures can be used as a proxy for the broader position of a bank or other company . If

I wish to borrow money for a three month period in two months’ time at today’s implied

forward rate, I could sell a three month futures contract for delivery in, say, four months’

time. In two months’ time I buy the equivalent number of contracts, closing out my

position. If the yield curve has moved upwards (interest rates have risen), the price of

the futures contract will fall and I will make a profit on my futures trading which offsets

the higher cost of my borrowing. But if the yield curve changes shape, the hedge will

turn out to be imperfect. In contrast, a forward contract is more flexible and would give

me a perfect hedge, thus reducing market risk, but could be less liquid and potentially

could expose me to potentially greater counterparty risk unless it was settled through a

clearing house.

5. Swaps

A “Swap” can be related to interest rates, foreign exchange rates, equities, commodities

or, more recently, credit risk.

The two most common types of swap are interest rate swaps and currency swaps. The

former typically swaps a floating rate payment for a fixed rate payment; the latter swaps

currency A for currency B. It is also possible to use swaps to change the frequency or

timing of payments, even if interest type or currency remains the same. Swaps can


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change either the net liability or the net asset and are therefore sometimes referred to as

an “asset swap” or “liability swap”. The structure is the same in both cases; it is simply

the motivation behind the swap that gives it this name.

Essentially the swap market provides a means of converting cash flow, changing the

amount of payments and/or the type, frequency or currency. Swaps are used by

investors to match more closely their assets/liabilities (which may change over time); by

traders to exploit arbitrage opportunities; to hedge exposures; to take advantage of better

credit ratings in different markets; to speculate9; and to create certain synthetic products.

For example, if a British company wishes to borrow in Deutschmarks, it does not need

to issue a Deutschmark-denominated security. It may find it cheaper to issue in, say,

sterling – where its name is better known in the market - and then to swap into

Deutschmarks. The company’s borrowing (ie its net liability) will be in DM, but it has

‘tapped’ the investor base in sterling. Similarly, an investor could purchase a fixed-rate

asset, perhaps a government security, and swap into a floating rate asset if he wanted to

change his type of income stream.

The market in swaps has grown over the past few years for a number of reasons. Global

deregulation has meant access to new markets and greater choice for investors and

borrowers; financial innovation has allowed more advanced products to be developed,

so matching borrower and investor needs more closely; interest from traders has helped

boost liquidity; and the attraction of their off-balance-sheet nature, which can free up

capital to be used elsewhere. Banking supervisors will, of course, aim to take account of

the risks involved in swaps, even though they are off balance sheet.

9 For instance, a lender may want to pay floating and receive fixed payments if he expects rates to fall.


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In some developing and transitional economies, the futures market is significantly larger

than the swaps market (ie. the opposite case to developed markets). This may be

because futures, being exchange traded, are likely to have a standard counterparty risk

and a margining mechanism, which helps to protect against the greater uncertainties of

counterparty risk.

(i) Interest rate swaps

An interest rate swap is defined as an agreement between two parties to exchange cash

flows related to interest payments. The most common type of interest rate swap is a

liability swap where the parties swap a stream of future fixed rate payments for floating

rate payments. A counterparty may want to swap fixed for floating payments if he holds

floating rate assets or if, with fixed-rate liabilities, he expects rates to fall and does not

want to be locked in at high rates.

“A” has an existing fixed rate liability and “B” has a floating rate liability. They then

enter into a swap transaction to alter the nature of their net cash flows (ie to alter their

exposure to interest rate movements); the arrows show the direction of the cash

payments under the swap transaction.

A Floating → B

↓

Fixed

← Fixed ↓

Floating

A now makes a net floating rate cash payment and B a net fixed rate cash payment. A’s

original fixed rate loan remains A’s direct liability (eg to its bondholders), regardless of

whether B keeps his side of the agreement. But provided B does so, then A’s net liability

is now in floating rate rather than fixed rate money.


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The amount of the interest payments exchanged is based on a notional principal amount:

only the interest payments are exchanged; principal is not. (For supervisory purposes,

however, the notional amount is important in providing an indication of the potential

exposure to adverse price movements and is also relevant for determining capital

requirements.)

Using swaps as an arbitrage opportunity will exist if one party has a comparative

advantage and if each party borrows in the market where they have a relative advantage.

An example of this is shown below.

Credit

rating

Cost of 10 year

fixed debt

Cost of 10 year

floating debt

Firm 1 AA 8% Libor + 25bp

Firm 2 BB 10% Libor + 100bp

Credit Differential 200bp 75bp

Arbitrage availablefor a Swap

125bp

An arbitrage will exist if there is a difference in the ‘credit differential’ between

borrowing in fixed or floating. In order to take advantage of this differential, each firmwill have to borrow in the market where it has the comparative advantage. In this

example the difference in credit differentials between the two markets is 125bp and

therefore this is the amount available for arbitrage. Firm 1 can borrow more cheaply -

perhaps because of better credit rating, or perhaps because it is a better known name.

Obviously the comparative advantage of Firm 1 gives it a certain negotiating power.

Sources of comparative advantage include better credit rating, name recognition,regulatory constraints, and currency constraints.


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So: • Firm 1 wants floating rate debt, but issues fixed rate debt at 8%; while Firm 2

wants fixed rate debt, but issues floating debt at Libor + 100bp.

• The two firms enter into an interest rate swap, and (jointly) save 125bp (the

difference between the fixed and floating rate credit differentials): this is divided

up in agreement between them. Say, Firm 1 saves 75bp. In other words, its

costs are 75bp cheaper than if it issued directly into the floating rate market. Its

net interest-related payments will therefore be Libor - 50bp. Firm 2 saves 50bp,

paying a net 9.5%

Payments under the Swap Transaction

8% fixed to Libor + 100bp bondholders floating bondholders

Although the diagram shows the gross payments under the swap transaction, it may be

possible to settle only the net flows, if the interest payment dates coincide. Because of

this, and the fact that no principal is exchanged, the counterparty credit risk is oftenconsidered not as important as the market risk, ie exposure to changes in interest rates.

If the benefit was smaller, it may not be considered worth doing the swap due to the

extra transactions cost, supervisory capital (if a bank) and credit risk which both firms

take on. (A further example on an interest rate swap is contained in Annex 4).

8.50% fixed

Libor

Firm 1 Firm 2


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(ii) Currency swaps

An issuer may find it difficult (or even impossible on account of legal or other

restrictions) to issue in a particular currency. However, it may be important - eg for

hedging purposes or for asset/liability management for the company - to have its liability

in that particular currency. It therefore may choose to borrow in another currency

(currency B) and swap the proceeds; this allows the borrower to raise the necessary

funds and have the net liability in the chosen currency (currency A). The chart sets the

payments under this currency swap transaction.

Borrower

← Currency B

Currency A →

SwapCounterparty

↓

↓

Currency Bto investor

At its simplest, a currency swap is equivalent to a spot forex transaction coupled with a

forward forex agreement. (Forex swap rates are calculated on this basis.) This simple

version is usually referred to as a FX swap; and (unlike an interest rate swap) involves

exchange of principal at the start and at end of the transaction - but no cash flow in

between. Alternatively, the two counterparties may exchange a series of interest flows

throughout the swap; this is usually referred to as a currency swap.

For instance, two counterparties may agree to a swap of DEM150 mn at 6% DEM

(Deutschemark) against USD100 mn at 5% USD (US dollar) for 5 years, with an

exchange of principal at the beginning and end of the period, and annual interest

payments of DEM 9mn and $5mn. There is, therefore, greater risk on a currency swap


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than an interest rate swap, as the principal is exchanged (credit risk and Herstatt risk 10

are both higher).

(iii) Credit Swaps

It is also possible to swap credit risks by exchanging payments received from two

different income streams relating to different credit risks. A ‘credit default swap’ is a

credit derivative in which the counterparties swap the risk premium inherent in an

interest rate on a bond or loan – on an ongoing basis – for a cash payment in the event of

default by the debtor. A total return swap is a credit derivative under which the cash

flows and capital gains/losses related to the liability of a lower rated entity are swapped

for cash flows related to a guaranteed interest rate such as inter-bank rate plus a margin.

6. Options

An options contract confers on the holder the right, but not the obligation, to conduct a

transaction on or by a future date at a pre-determined price. Options may be either puts

or calls. A put gives the holder of the option the right to sell the underlying item at the

specified price, and a call gives him the right to buy the item. As the contract is

asymmetric - the writer of the option is obliged to complete the transaction if the holder

chooses, but not vice versa - the writer will always receive a premium11, for writing it

(whereas for forwards, the contract is symmetric and no premium is paid). This means

that a bank can write options in order to generate “fee” income/cash flows, believing

that the income will more than offset any future losses, on average. By contrast,

forwards/ futures allow a bank to take a position, but do not generate cash flow. Options

contracts can be either exchange-traded or OTC. Exchange – traded options relate to

10

“Herstatt risk” refers to the June 1974 bankruptcy of Herstatt Bank: large losses arose when HerstattBank collapsed after receiving settlement of European currencies in forex transactions but before payingout the dollar counterpart (because of time differences between settlement in Europe and the USA).11 This has some similarities to an insurance premium in concept.


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(exchange-traded) futures contracts; OTC options relate directly to the underlying

financial item.

Call options on some assets - equities and commodities - have, in theory, unlimited

potential for notional profit, as there is no limit to price increases, although there is of

course an expected maximum likely profit. If an investor has a call option to buy crude

oil or Microsoft shares, at a given price, then unexpected events - political problems in

the Middle East, or technological breakthrough - could result in very sharp increases in

the value of the assets involved.

This does not hold true for securities: a zero coupon bond will not trade for more than

nominal/face value, for instance, as investors will hold cash rather than receive a

negative interest rate. A similar argument holds for coupon-bearing bonds. Likewise

with foreign exchange. Assume a bank sells a call option to buy US$100 for Thai baht

4,000. Even if there is a catastrophic collapse in the value of the baht, say to Thai baht 1

million = US$1, the bank’s loss cannot exceed US$100. In baht terms its percentage

loss may be astronomic; but in the face of a currency depreciation of this order, the

bank’s whole balance sheet would have changed substantially. That said, a written

option on a currency can, in extremis, result in a loss equivalent to the notional value (in

terms of the stronger currency) of the option.

There is a maximum profit for all put options, as asset values will not turn negative. A

put option to sell crude oil at $15 per barrel cannot be worth more than $15 (even if the

oil could be obtained free, it could only be sold for $15 pb); whereas a call option to buy

crude oil at a strike price of $15 pb could be worth much more, for instance if spot prices

rose to $50 pb when the option would be worth around $35.

The potential loss for a buyer of options is limited to the premium paid; but the potential

loss for a writer can be much greater (although limited to the price of the underlying

asset).


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Strike Price

The strike price (or exercise price) is the pre-specified price at which the underlying

asset position is taken if the option is exercised: a long position in the case of exercising

a call option, or a short position with a put option. The intrinsic value of the option is

the difference between the underlying futures contract (or the underlying item, in the

case of an OTC option) and the strike price. An option cannot have negative intrinsic

value. The intrinsic value is a measure of the amount by which an option is in-the-

money.

At the money: an option is “at the money” if the strike price of an option is the same as

the spot price, so that exercise of the contract does not imply a gain or a loss to holder of

the option. (This does not include the gain/loss caused by the premium paid, as this is a

sunk cost.) For instance, if in September the short sterling future12 December contract is

trading at 93.00 (i.e. the market is on balance expecting the three month interest rate in

December to be 7% - see page 21 for explanation of futures pricing), an "at the money”

option on the December contract would have a strike-price of 93.00. If on the last

trading day of the life of an option, the futures price were (still) 93.00, the option with

strike price of 93.00 would have no value.

In the money: for a call option, if the strike price is lower than the underlying, then the

contract is in-the-money; in other words, a profit is implied for the holder of the option

because he will be able buy the underlying item for a lower price than in the spot market

currently. For example, if the strike price of call was 92.50, then if the contract was

trading at 93.00 it would have positive value, since a exercising the option would allow

a future to be bought for 92.50 and sold immedately for 93.00 (or, as is more likely, the

position could be closed out by selling call options). For a put option, if the strike price

12 The short sterling future relates to the three-month sterling interbank rate. A long position in thiscontract protects the holder who wishes to invest cash at a future date against a fall in interest rates,since a fall in future interest rates will be offset by a rise in the value of the future.


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is above that of the underlying, the option is also in-the-money because the holder can

sell the underlying item for more than in the spot market.

Out of the money: for a call option, if the strike price is higher than the underlying, this

implies a loss for the holder of the option if it were exercised (i.e. no intrinsic value); in

other words, if he exercised the option, the holder would have to buy the underlying

item at a higher price than available in the spot market. In such a case, the holder would

simply allow the option to expire worthless, and the cost would be the option premium

paid in the first place. For a put option, a strike price below the underlying means that

the put would be "out of the money", since there would be no point in exercising a right

to sell the future at 92.50 if the open market price was higher than that. The opposite

would apply if the strike price were 93.50 with the underlying item (the future) still at

93.00. A put would be worth exercising, but a call would expire worthless (‘out of the

money’).

The above does not mean that an out-of-the-money option necessarily means a loss for

the holder. It may still have some value as a hedge. Even if it expires worthless, the

holder has still benefited from the hedge provided during its lifetime, which may have

facilitated treasury management or even reduced capital costs (since regulators of

financial institutions typically require less capital to be held for a well-hedged portfolio).

Types of options

Options can also be divided into American and European style. This does not refer to

the location of trading, but to the period when the option may be exercised. European-

style options can be exercised only on a specific day i.e. the last trading day of the

option’s life. For instance, at the end of September you could buy a European-style

option with an end November expiry date; the option could only be exercised on the last

trading day of November. By contrast, American-style options can be exercised at any

point during their life. In the above example, this would be on any trading day from the


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day the option was purchased until the last trading day of November, at the choice of the

holder.

For call options, it makes little difference whether the option is European or American.

Options have time-value (see below), and it normally makes sense for the call option

holder to realise this value by selling the option (for “intrinsic value plus time value”)

rather than exercising it before the end of its life, as exercise will only ever yield

intrinsic value. The time value of money is also a factor here, since the option gives the

holder the right to purchase an asset at a fixed price in the future. Consider an investor

with 100 of cash and an option to purchase an asset (securities, forex etc) for 100 at any

time in the next three months. It will be more profitable to invest the cash for three

months and then pay 100 for the asset than to exercise the option today and lose three

months interest income.

This is not, however, the case with put options. Again, the time value of money is a

factor here. If an investor can exercise a put option today and invest the cash received

from selling the asset involved, rather than waiting three months to sell the asset at the

same price, he will earn interest income over the period and so be better off. This means

that American style put options do have an advantage over European style, and will

therefore have greater value.

Valuation

Pricing an option is much more complex that pricing a forward or swaps contract. The

value of an option is a function of its intrinsic value, its maturity and market price

volatility. This Handbook does not go into detail on the pricing, but offers an intuitive

guide to the way that an options price behaves.


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Option prices are a function of:

Option price = f (V, T, S p - S t ; 0] ),

where V is volatility, T is time to expiry, S t is strike price, S p is spot price. Since the

value of an option cannot be below zero, the intrinsic value – discussed above - is

shown as the greater of zero or spot minus strike price. (For a put option, it is the

greater of zero or strike minus spot.)

Consider the issue of market price volatility. If the three-month interbank rate is

currently 10% p.a., the central bank has declared its intention to keep market rates at this

level for at least 30 days and there is no expectation whatever that the rate will move

over this period, then an “at-the-money” option with a 30 day maturity would have no

value. No-one would pay a premium for an option to enter into a future transaction if

there was certainty that an equivalent transaction could be undertaken without payment

of the premium. But if market rates were volatile, the picture would change. With the

same spot interest rate, strike rate and maturity, but no central bank commitment to hold

the rate and a history of interest rate volatility, the option would have value. The more

volatile the market - both as regards “historic volatility” (i.e. past performance) and

“expected volatility” (a matter of judgement), the greater the value of the option.

The intuition to this is straightforward. An option may be used to hedge risk exposure.

The greater the perceived risk (expected volatility) the more expensive the hedge; and if

there is no (perceived) risk, then the market value of an option will be zero. If

volatility/risk increases, then the value of an options portfolio increases for the holder;

and a writer of options, facing a greater chance of payout, should hold more capital.


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A similar analysis holds for the time value of an option. For a given underlying price,

strike price and level of volatility, the value of an option will increase with the length of

its life. Again, considering that an option can be used to hedge risk exposure, the longer

the time to maturity, ceteris paribus, the greater the option’s value to the buyer/seller as

there is a greater chance that the option will be exercised. This means that, as a given

options portfolio ages, its value will tend to decrease. The holder will have less value

and the writer less risk (other things being equal).

Time decay - the loss of time value (or theta, see below) as the option ages - is not a

linear function. This is simply because, as the time to expiry approaches, a one-day

change in lifetime represents a greater proportion of the remaining life. If there are 30

days to expiry and one day passes, 1/30th of the time value has eroded. But with two

days left to expiry, when one day passes then 1/2 of the remaining time value has

eroded. Theta is calculated in relation to the remaining time to expiration, rather than the

original maturity of the option; this means that the theta value of two options with

T ime va lue o f a 30 day op t ion

-

1.00

1 2 3 4 5 6 7 8 9 1 0 11 12 13 14 15 1 6 1 7 18 19 20 2 1 22 23 24 25 26 27 2 8 29 30

T i m e

P r i c e


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identical terms and the same expiry date will be the same, even if the original life of one

was longer.

Synthetics

To create a synthetic short position in securities using options, a trader could sell a call

and buy a put at the same (current market) strike price (the net premium should be very

small). If the price rises, the call will be exercised, leaving a short position; if the price

falls, the bought put will be exercised, again leaving a short position. (Vice versa for a

long position). This may allow traders to take the equivalent of a short position even if

short selling itself is not permitted under local trading regulations.

“Greeks”

Certain Greek letters are often used to denote the risk of changes in underlying prices or

market conditions to the value of an options portfolio.

Delta: the delta of an option portfolio is the change in value implied by a one point

move in the price of the underlying asset.

Delta factor = change in the price of the option

change in the price of the underlying

For an option that is at the money, the delta is typically around 50% i.e. if the value of

the underlying moves by £1:00, the value of the option will change by £0.50.


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Delta values range from 0% for deep out-of-the-money options to 100% for deep in-the-

money options. If an option is deeply out-of-the-money - for instance, if the strike price

on a call option is 100 and the spot price for the underlying is 50, the option will havelittle value (unless the market is extremely volatile), since the underlying price would

have to more than double for the option to move into the money. An increase in the

underlying price from 50 to 51 would have little effect on the option value. At the other

extreme, if the strike price were 50 and that of the underlying 100, then an increase in

the price of the underlying from 100 to 101 would be fully reflected in the value of the

option.

An increase in volatility will tend to flatten the delta curve for a given price range. The

delta may be viewed as a probability estimate that the option will expire in-the-money. A

deep in-the-money option is virtually certain to expire in-the-money, and delta is 100%.

Vice versa for a deep out-of-the-money option. As volatility increases, the probability of

expiring in-the-money tends to 50% (i.e. uncertainty increases with volatility; 50%probability represents the highest level of uncertainty).

Delta of a call option

01 2 3 4 5 6 7 8 9

Value of option

P r i c e

o f u n d e r l y i n g

a s s e t

at the money


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Gamma: denotes the change in the delta for a one-point move in the underlying price.

Since delta is not a linear function, gamma too is non-linear. Gamma decreases as

certainty increases.

Vega: is used to denote the sensitivity of the option price for a 1% change in volatility

(easy to remember because both begin with V). If volatility increases, so does the value

of the option. Vega may vary depending on whether the option is at, in or out of the

money. In major OECD government securities markets, implied volatility for at-the-

money options is usually between 5-10%, but has in recent years jumped to around 15%

in periods of market uncertainty.

Theta (sometimes called zeta or kappa): denotes the time value of an option (easy to

remember because both begin with T). The longer the time period until the strike date,

the greater is Theta: this is because there is more time for the price of the underlying to

move in a direction favourable to the holder.

7. Institutional Arrangements

Clearing Houses

In order to standardise counterparty risk in exchange-traded derivatives, a clearing house

is typically interposed between traders. If a trader belonging to firm “A” sells a contract

to a trader belonging to firm “B”, then at the end of the trading day, the clearing house

will stand in between the two, buying (for future settlement) from “A” and selling (for

future settlement) to “B”. As long as the clearing house is reliable, then neither “A” nor

”B” need worry about credit risk. But the clearing house needs to protect itself against

credit risk of both A and B. If prices rise and “A” defaults, the clearing house will still

need to sell to “B” at the pre-agreed lower price; and vice-versa if prices fall and “B”


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defaults. The clearing house protects itself by margining (see Annex 5 for detailed

description).

The exchange or clearing house will take initial margin at the start of the contracts, and

will call for variation margin each day. The counterparties will realise profits or losses

on the contracts on a daily basis by “marking-to-market” (see below). The clearing

house not only has responsibility for credit risk control (i.e. for ensuring that the

margining system is correctly applied) but also for the administration of closing out

contracts and for the delivery procedures.

Margining Practices

Margin is taken to protect against counterparty exposure. It is regularly used in repo

operations, and by derivatives exchanges. Initial margin is taken by a clearing house at

the start of the agreement, to protect against any sudden price changes or future failure

to provide (daily) variation margin. Variation margin is taken on a daily basis and is

related to the movement in price of the contract each day. Further examples of

margining are found in Annex 5.

Margining in derivative exchanges has the same basic function as with repo, but is

different in some important respects. First, margin is paid by both seller and purchaser of

the futures or options contract, as it is to protect the clearing house, which stands in

between the two parties. Second, the payment of variation margin is different from repo

variation margin in that it is not like “collateral” which is returned at the end of the

period if the “loan” is repaid; rather, the traders’ positions (usually their overall position

on all exchanges served by the relevant clearing house) are marked-to-market daily, with

any losses paid over and any profits withdrawn on a daily basis. Thus on any day,

including the settlement day for cash settled contracts, traders pay/receive their net profit

for that day’s price movements. This daily cash flow minimises the exposure of the


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clearing house to traders, and by putting the clearing house in a strong position, means

that traders’ exposure to the clearing house does not constitute a large risk.

Margining is being increasingly used in OTC markets.

The deliverable basket

Given the homogeneity of government bonds, there needs to be some criteria as to what

bonds could be delivered in a futures contact for bonds and there needs to be some form

of “standardisation” between the bonds that can be delivered.

In deciding which bonds are eligible for delivery, the first criteria to decide is the

maturity of the underlying asset(s) in the contract, for example, if it is a long bond

futures contract the exchange will assign a notional maturity for a deliverable bond (a

real bond will, of course, only have that exact maturity for a single day). The exchange

will provide a “contract specification” as shown below:

Contract specification for long gilt future on LIFFE (London International Financial

Futures Exchange)

Nominal Value £50,000

Notional coupon 7%

Range of deliverable bonds 8.75 to 13 years residual maturity

The notional coupon is set to approximate the yield that is expected to prevail over the

long term.

The fewer deliverable bonds in the contract, then the greater the homogeneity but the

less the liquidity of the basket. Obviously, the exchange could decide to have only one


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deliverable bond but, whilst this would mean homogeneity, it would not provide a very

liquid basket which could cause problems for delivery. In this case, all bonds in the

maturity range are eligible for delivery in the long gilt futures contract on LIFFE.

Having established a basket of deliverable bonds, the exchange must then find a

mechanism by which these securities can all be valued and traded at one unique price

prevailing on the futures exchange. Whilst this Handbook does not go into the details of

this formula, the aim is to “standardise” the pricing of the deliverable bonds. A price

factor system is used to “reprice” all bonds falling within the relevant maturity range –

which will have different maturities, coupons and accrued interest – into a unified scale.

8. Accounting Standards

At the time of writing, international accounting standards are not yet fully agreed. The

general principle that is emerging is that all derivatives should be recognised on the

balance sheet and valued at fair value i.e. marked-to-market. There is an argument that,

where derivatives are being used to hedge a specific risk, then either both sides of the

balance sheet should be marked-to-market, or neither. But while the theoretical case for

this is strong, practical implementation can be difficult.

9. Statistical Measurement

Measurement in Economic Statistics of Activity in Financial Derivatives

Set out below is an outline of the IMF’s recommendations for the measurement of

financial derivatives in the economic accounts. Fuller detail is provided in the IMF

working paper entitled “The Statistical Measurement of Financial Derivatives” (March

1998).


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For economic statistics purposes, financial derivatives are defined as follows:

Financial derivatives are financial instruments that are linked to a specific financial

instrument or indicator or commodity, and through which specific financial risks can be

traded in financial markets in their own right. Transactions in financial derivatives

should be treated as separate transactions rather than as integral parts of the value of

underlying transactions to which they may be linked. The value of a financial derivative

derives from the price of an underlying item, such as an asset or index. Unlike debt

instruments, no principal amount is advanced to be repaid and no investment income

accrues. Financial derivatives are used for a number of purposes including risk

management, hedging, arbitrage between markets, and speculation.

If a financial derivative instrument meets the above definition and there is an observable

market price for the underlying item from which the derivative can acquire value,

transactions in the instrument should be recorded in the financial account and any

positions in the position statement. Among arrangements that are not to be classified as

financial derivatives are fixed price contracts for goods and services, unless standardised

in such a way as to be traded as a futures contract, insurance, which involves the pooling

rather than the trading of risk, contingencies, and embedded derivatives.

Transactions Data

Forwards: At inception, risk exposures of net zero value are exchanged so there are no

transactions to record in the financial account, although any fees associated with the

creation of a forward should be recorded as a service payment. As forwards are not

traded in the sense of ownership changing hands, no transactions are recorded during the

life of the contract. The one exception is for contracts, such as interest rate swaps and

futures, where there is on-going settlement: transactions are to be recorded in the

financial account as either assets or liabilities depending on the net position of the


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contract at the time the transaction occurs, although in the absence of information on the

net position, net payments are recorded as a reduction in financial derivative liabilities

and any net receipts as a reduction in financial derivative assets. The latter is also the

recording practice for a forward that is settled at maturity or through mutual agreement

to extinguish it. If the underlying item is delivered at the time of settlement, such as

with many foreign exchange derivatives, the transaction in the underlying should be

recorded at its prevailing market price, and any difference between the contract and

prevailing market price, times quantity, should be recorded as a transaction in financial

derivatives.

Options: The creation of an option involves the payment of a premium that is recorded

as an increase in financial assets by the buyer and an increase in financial derivative

liabilities by the writer of the option. Any trading in an option during its life is recorded

and valued at the price agreed, like any other financial asset. At maturity, the option may

expire worthless in which case no transactions are recorded. If there is a net cash

settlement, or the underlying item is delivered, the treatment in the economic accounts is

the same as described above for forwards.

Margins: Any margin that is paid but remains in the ownership of the depositor is

termed repayable margin. If this margin is in the form of a security, no transactions are

recorded because the depositor still has a claim on the same entity – the issuer of the

security. On the other hand, if the margin is paid in currency then two transactions are

recorded: a reduction in claims on the original depository and an increase in claims on

the new depository. If margin is paid to meet a liability in financial derivatives, that is

ownership of the margin changes hands, a transaction in financial derivative is recorded

in accordance with the recommendations set out above. This type of margin is known as

nonrepayable margin.


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Position Data

Forwards: The value of a forward derives from the discounted net present value of

expected receipts or payments. Because the market price of the item underlying the

derivative contract can change between end reporting periods, so a position in a forward

may switch from a net asset to a net liability position, or vice versa, between end

periods. This change in value is recorded as a revaluation gain or loss in the position

statement.

Options: The value of an option derives from the relationship between the contract and

prevailing market price for the underlying item, the time to maturity of the contract, the

time value of money, and the volatility of the price of the underlying item. The buyer of

the option always has an asset and the writer a liability. If an option expires worthless

but had value at the end of the previous reporting period, the writer records a revaluation

gain and the holder a revaluation loss in the position statement.


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Annex 1

The Size of Global Derivatives Markets: Survey Data from the Bank forInternational Settlements (BIS)

At end-June 1998, the G-10 countries under the auspices of the BIS conducted a surveyof the over-the-counter financial derivatives market. The data include both the notionalamounts and gross market values outstanding of the world-wide consolidated OTCderivatives exposure of 75 large market participants that account for 90% of globalmarket activity in financial derivatives. The survey covered four main categories of market risk: foreign exchange, interest rate, equity and commodity.

After adjustment for double counting resulting from positions between reportinginstitutions the total estimated notional amount 13of outstanding OTC contracts stood at$70 trillion at end-June 1998. This was 47% higher than the estimate for end-March1995, which was obtained from a supplementary survey to the triennial foreign exchangeand derivatives turnover survey. However, adjusting for differences in exchange ratesand the change from locational reporting in 1995 to consolidated reporting in 1998, theBIS estimates the increase between the two dates at about 130%. These data alsoconfirm the predominance of the OTC market over organised exchanges in financialderivatives business. The data show that interest rate instruments are the largest OTCcomponent (67% mainly swaps), followed by foreign exchange products (30%, mostlyoutright forwards and forex swaps) and those based on equities and commodities (with2% and 1% respectively).

At end-June 1998, estimated gross market values 14stood at $2.4 trillion, or 3.5% of thereported notional amounts. The BIS stressed that such values exaggerate actual creditexposure, since they exclude netting and other risk reducing arrangements. Allowing fornetting lowered the derivatives-related credit exposure of reporting institutions to $1.2trillion, or to 11% of on-balance sheet international banking assets. As might beexpected, the ratio of gross market values to notional amounts varied considerablyacross individual market segments, ranging from less than 1% for FRAs to more than15% for equity-linked options. Interestingly, the ratio was of the same order of magnitude in the two major individual market segments: outright forwards and forexswaps (3.9%), and interest rate swaps (3.5%). This stands in sharp contrast to the resultsof the 1995 survey, which had founds a considerably higher value of replacement costsfor foreign exchange contracts.

13 The amount used to calculate payments or receipts – for interest rate contracts, for instance, this amount is not exchanged.14 A measure of the cost of replacing the contract at prevailing market prices.


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Table 1The global over-the-counter (OTC) derivatives markets1

Positions at end-June 1998, in billions of US dollars

Notional amounts

Gross marketvalues

A. Foreign exchange contractsOutright forwards and forex swapsCurrency swapsOptions

18,71912,1491,9474,623

799476208115

B. Interest rate contracts2

FRAsSwapsOptions

42,3685,147

29,3637,858

1,16033

1,018108

C. Equity-linked contractsForwards and swapsOptions

1,274154

1,120

19020

170

D. Commodity ContractsGoldOther Forwards and swaps Options

451192259153106

381028

--

E. Estimated gaps in reporting 7,100 240

GRAND TOTAL 69,912 2,427GROSS CREDIT EXPOSURE3 1,203

Memorandum items:

Credit -linked and other OTC contracts4

Exchange-traded contracts5

98

14,256

3

Source: BIS

1 All figures are adjusted for double-counting. Notional amounts outstanding have been adjusted by halving positions vis-à-vis other reporting dealers. Gross market values have been calculated as the sum of the total gross positive market value of

contracts and the absolute value of the gross negative market value of contracts with non-reporting counterparties.2 Single-currency contracts only3 Gross market values after taking into account legally enforceable bilateral netting agreements.4 Gross market values not adjusted for double-counting5 Sources: Futures Industry Association and various futures and options exchanges


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Annex 2

Forward exchange rate calculations

Forward exchange rates are priced from interest rate differentials. For instance, UKinterest rates less US interest rates determine the forward rate for a £-$ future (or swap).As with interest rate forwards, it is vital to remember that forward rates are arithmeticalcalculations and not an individual trader’s opinion of what the spot rate will be at thesettlement date quoted.

Spot/forwardDM/$exchangerate

Current interestrates

DM Dollar

A B C D E

Spot 1.565One month 1.562 3.08% 0.26% 5.31% 0.44%Three months 1.556 3.00% 0.75% 5.42% 1.36%

Implied forward rate is spot rate plus (spot rate multiplied by the interest ratedifferential)

Column A = One and three month forward rates are

Spot rate (col. A) + [spot rate * (col.C - col. E)]e.g. 1.565 + [1.565 * (0.0026-0.0044)] = 1.565 + [1.565 * -0.0018] = 1.565 - .0028 = 1.562

Columns B and D = Annualised interest rates for relevant currency

Columns C and E = Period rate for relevant currency e.g. 0.26% = 3.08%/12 and 0.75%= 3.00%/4


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Annex 3

Forward interest rate calculations

This table shows the calculation, using compound interest, for forward interest rates.

Current interest rates Implied 3 month forward

No. ofdays

(i) annualrate

(ii) periodrate

(iii) periodrate

(iv)annual

rate

A B C D E

3 month 91 10% 2.4% now 2.4% 10.0%

6 month 182 12% 5.8% in 3 months’ time 3.3% 14.0%9 month 273 14% 10.3% in 6 months’ time 4.2% 18.1%

12 month 365 16% 16.0% in 9 months’ time 5.2% 22.1%

Column B = interest rates from the yield curve

Column C = Col.B to the power of (days in period/365)e.g. 1.024 = 1.10^(91/365)

Column D = Col. C / Col.C T-1 e.g. 1.033 = 1.058/1.024

Column E = Col. D to the power of (365/days in period) e.g. 1.14 = 1.033^ (365/91)

Using simple interest rates, then

If interest rate for period X is A%, and for period Y is B%, then the forward ratefor the period from end of X to end of Y is

Forward rate = B% / (1-[X/Y]) - ([X/Y]*A%)/(1-[X/Y])

This looks difficult; but when Y = 2*X (e.g X is 3 months, Y is 6 months) then [X/Y] is0.5, giving (simplified)

Forward rate = 2*B% - A% (or B% + (B-A)).

e.g. 2 * 12% - 10% = 24% - 10% = 14%

or 12% + (12%-10%) = 12% + 2% = 14%


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Annex 4

Swap spreads and government bond yields

FIXED RATE FLOATING

RATE

Government bond yield +

ccbshb17 financial derivatives

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