d13 01 introduction - ulb 01... · 2013-02-04 · february 4, 2013 additional references chance,...

Derivatives Introduction

Professor André Farber Solvay Brussels School of Economics and Management Université Libre de Bruxelles

February 4, 2013

Course outline

PART ONE: Forwards, Futures and Swaps 1. Introduction 2. Pricing a forward/futures contract 3. Hedging with futures 4.IR derivatives 5. IR and currency Swaps

PART TWO: Options 6. Introduction to option pricing 7. Inside Black-Scholes 8. Greeks and strategies 9.Exotic options 10. Options on bonds and interest rates (1) 11. Options on bonds and interest rates (2)

Derivatives Summary |2

February 4, 2013 Derivatives 01 Introduction |3

References

•  Reference: John HULL Options, Futures and Other Derivatives, Eighth edition,

Pearson Prentice Hall 2012 John HULL Options, Futures and Other Derivatives, Seventh edition,

Pearson Prentice Hall 2008 John HULL Options, Futures and Other Derivatives, Sixth edition,

Pearson Prentice Hall 2006 Probably the best reference in this field. Widely used by practioners.

•  Copies of my slides will be available on my website: www.ulb.ac.be/cours/solvay/farber

•  Grades: –  Cases: 30% –  Final exam: 70%

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5 ECTS = 125 hours!!!

•  Classes 22 h (11 × 2h) •  Reading 22 h (11 × 2h) •  Review cases 11 h (11 × 1h) •  Graded cases 32 h (2 × 16h) •  Prep exam 40 h (5 x 8h) •  Exam 3 h •  Total 130 h


February 4, 2013

Additional references

Chance, Don, Analysis of Derivatives for the CFA Program, AIMR 2003 Cox, John and Mark Rubinstein, Options Markets, Prentice-Hall 1985 Duffie, Darrell, Futures Markets, Prentice Hall 1989 Hull, John, Risk Management and Financial Institutions, Pearson Education 2007 Jarrow, Robert and Stewart Turnbull, Derivative Securities, South-Western College Publishing 1994 Jorion, Philippe, Financial Risk Manager Handbook, 2d edition, Wiley Finance 2003 McDonal, Robert, Derivatives Markets, 3d edition, Pearson 2013 Neftci, Salih, An Introduction to the Mathematics of Financial Derivatives, 2d ed., Academic Press 2000 Neftci, Salih, Principles of Financial Engineering, Elsevier Academic Press 2004 Portait, Roland et Patrice Poncet, Finance de marché: instruments de base, produits dérivés, portefeuilles et

risques, Dalloz 2008 Siegel, Daniel and Diane Siegel, The Futures Markets, McGraw-Hill 1990 Stulz, René, Risk Management and Derivatives, South-Western Thomson 2003 Veronesi, P., Fixed Income Securities, Wiley 2010 Wilmott, Paul, Derivatives: The Theory of Practice of Financial Engineering, John Wiley 1998

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February 4, 2013

What have you learned so far..

•  Definition of basic derivatives: forward, options (call, put) –  Contracts concluded between a buyer and a seller

concerning a future transaction –  Used to protect against and manage risk, for arbitrage,

speculation and investment –  Value derives from that of underlying product or market

variable –  Valuation based on no arbitrage

•  Forward = SpotPrice – PV(DeliveryPrice) •  Options: Binomial / Black Scholes

•  There is more to come in Derivatives!

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Derivatives: a revolution..

7

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…littered with victims

•  1993 Procter and Gamble (JH p.745) – OTC interest rate derivatives •  1993 Metallgesellschaft (JH p.67) – Futures on oil and gaz •  1995 Barings Bank (JH p.17) – Futures & options on Nikkei225 •  1995 Gibson Greeting Cards (JH p.781) – OTC interest rate derivatives •  1995 Orange County (JH p.87) – OTC interest rate derivatives •  1996 Belgian Treasury – Currency swaps •  1998 Long Term Capital Management (JH p.31) – Russia’s default •  2001 Enron (JH p.537) – credit risk, downgrade triggers •  2006 Amaranth (JH p.780) – Derivatives on natural gas •  2008 Société Générale (JH p.17) – Futures on equity indices •  2008 Lehman Brother (JH p.550) - CDS contract •  2008 AIG (JH p.32) – Credit risk (CDS) related to subprime mortgages •  2008 Madoff – Ponzi scheme hidden by phoney derivatives strategy •  2011 UBS – Futures on equity indices •  2011 Dexia – Interest rate swaps •  2012 Monte dei Paschi di Sienna – Repo on Italian gov. bonds

8

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How to Tame the Derivatives Beast?

Understanding derivatives requires expertise in many areas outside the scope of this course: •  Economic theory •  Statistics •  Management •  Communication •  Accounting •  Mathematics •  Programming

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1. Today

1.  Course organization 2.  Derivatives: definition (forward/futures), options + brief history 3.  Derivatives markets: evolution + BIS statistics 4.  Why use derivatives 5.  Forward contracts: cash flows + credit risk 6.  Futures: marking to market, clearing house 7.  Valuing a forward contract: key idea (no arbitrage)



Derivatives

•  A derivative is an instrument whose value depends on the value of other more basic underlying variables

•  2 main families: •  Forward, Futures, Swaps •  Options

•  = DERIVATIVE INSTRUMENTS •  value depends on some underlying asset

•  Why derivatives? For risk management

February 4, 2013

(Very) Brief History of Derivatives

•  Genesis 29: Jacob buys option to marry Rachel •  580 B.C.: Thales the Milesian buys option on olive press •  1550-1650: Antwerp Amsterdam forward market on grains,

herrings, tulip bulbs •  1650: rice futures market in Osaka •  1848: creation of the Chicago Board of Trade futures market •  1972: creation of the first financial currency futures •  1973: creation of the Chicago Board Option Exchange •  1977: T-bond futures •  1982: Interest Rate Futures •  1980’s: Currency and IR swaps •  1990’s: Credit derivatives

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Derivatives and price variability



Forward contract: Definition

•  Contract whereby parties are committed: –  to buy (sell) –  an underlying asset –  at some future date (maturity) –  at a delivery price (forward price) set in advance

•  The forward price for a contract is the delivery price that would be applicable to the contract if were negotiated today (i.e., it is the delivery price that would make the contract worth exactly zero)

•  The forward price may be different for contracts of different maturities

•  Buying forward = "LONG" position •  Selling forward = "SHORT" position •  When contract initiated: No cash flow •  Obligation to transact


Forward contract: example

•  Underlying asset: Gold •  Spot price: $1,750 / troy ounce •  Maturity: 6-month •  Size of contract: 100 troy ounces (2,835 grams) •  Forward price: $1,760 / troy ounce

Spot price 1,560 1,660 1,760 1,860 1,960 Buyer (long) -20,000 -10,000 0 +10,000 +20,000 Seller (short) +20,000 +10,000 0 -10,000 -20,000

Profit/Loss at maturity

ST ST

Gain/Loss

1,760 1,760

Gain/Loss Long Short


Options: definitions

•  A call (put) contract gives to the owner –  the right : –  to buy (sell) –  an underlying asset (stocks, bonds, portfolios,..) –  on or before some future date (maturity)

•  on : "European" option •  before: "American" option

•  at a price set in advance (the exercise price or striking price) •  Buyer pays a premium to the seller (writer)


Option contract: examples •  Underlying asset: Gold •  Spot price: $1,750 / troy ounce •  Maturity: 6-month² •  Size of contract: 100 troy ounces (2,835 grams) •  Exercise price: $1,760 / troy ounce •  Premium: Call $148/oz Put: $148/oz

Spot price 1,460 1,560 1,760 1,860 1,960 Call (long) -14,80 -14,800 -14,800 -4,800 +5,200 Put (long) +5,200 -4,800 -14,800 -14,800 -14,800

Profit/Loss at maturity

ST ST

Gain/Loss

1,760 1,760

Gain/Loss Call Put

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Components of a forward contract: put-call parity

Spot price

Forward = Call - Put

Forward Call

- Put

Terminal value

Delivery price Exercise price

Notes: European options

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Forward vs Options


Fwd > Call

Call > Fwd

-Fwd>Put

Put>-Fwd


Derivatives Markets

•  Exchange traded –  Traditionally exchanges have used the open-outcry system, but

increasingly they are switching to electronic trading –  Contracts are standard there is virtually no credit risk

•  Europe Eurex: http://www.eurexchange.com/ NYSE Euronext Liffe: http://www.liffe.com

•  United States –  CME Group http://www.cme.com

•  Over-the-counter (OTC) –  A computer- and telephone-linked network of dealers at financial

institutions, corporations, and fund managers –  Contracts can be non-standard and there is some small amount of credit

risk

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Global financial markets

Source: McKinsey Institute, Mapping global financial markets, August 2011

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Derivatives Markets

Source: Own calculations

February 4, 2013 Source: BIS Quarterly Review December 2012

February 4, 2013 Derivatives 01 Introduction |26 26

Credit Default Swaps

•  A huge market •  Buyer of the instrument acquires protection from the seller

against a default by a particular company or country (the reference entity)

•  Example: Buyer pays a premium of 90 bps per year for $100 million of 5-year protection against company X

•  Premium is known as the credit default spread. It is paid for life of contract or until default

•  If there is a default, the buyer has the right to sell bonds with a face value of $100 million issued by company X for $100 million (Several bonds are typically deliverable)

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Using derivatives

•  Who? –  Commercial banks –  Large corporates –  Central banks –  Government –  Fund managers –  Pension funds

•  Why? –  To hedge risks –  To speculate –  To lock in an arbitrage

profit –  To change the nature of a

liability –  To change the nature of

an investment



Forward contract: Cash flows

•  Notations ST Price of underlying asset at maturity Ft Forward price (delivery price) set at time t<T

Initiation Maturity T Long 0 ST - Ft Short 0 Ft - ST

•  Initial cash flow = 0 :delivery price equals forward price.

•  Credit risk during the whole life of forward contract. •  Use of collateral to mitigate credit risk


Forward contract: Locking in the result before maturity

•  Enter a new forward contract in opposite direction.

•  Ex: at time t1 : long forward at forward price F1

•  At time t2 (<T): short forward at new forward price F2

•  Gain/loss at maturity :

•  (ST - F1) + (F2 - ST ) = F2 - F1 no remaining uncertainty


Futures contract: Definition

•  Institutionalized forward contract with daily settlement of gains and losses

•  Forward contract –  Buy ⇔ long –  sell ⇔ short

•  Standardized –  Maturity, Face value of contract

•  Traded on an organized exchange –  Clearing house

•  Daily settlement of gains and losses (Marked to market)

Example: Gold futures Trading unit: 100 troy ounces (2,835 grams)


Futures: Daily settlement and the clearing house

•  In a forward contract: –  Buyer and seller face each other during the life of the contract –  Gains and losses are realized when the contract expires –  Credit risk

BUYER ⇔ SELLER •  In a futures contract

–  Gains and losses are realized daily (Marking to market) –  The clearinghouse garantees contract performance : steps in to take a

position opposite each party BUYER ⇔ CH ⇔ SELLER


Futures: Margin requirements

•  INITIAL MARGIN : deposit to put up in a margin account •  MAINTENANCE MARGIN : minimum level of the margin account •  MARKING TO MARKET : balance in margin account adjusted daily

•  Equivalent to writing a new futures contract every day at new futures price •  (Remember how to close of position on a forward) •  Note: timing of cash flows different

+ Size x (Ft+1 -Ft)

-Size x (Ft+1 -Ft)

LONG(buyer)

SHORT(seller)

Time

Margin

IM

MM

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Margin - example


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Basic Structure of Futures Market

Exchange corporation

Clearing house

Exchange members

Nonclearing members

Clearing members

Customers Orders Margin

Broker?

Order: Buy/Sell # contracts Delivery month Counterparty

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Who are the members?

Cantillon, Estelle and Pai-Ling Yin, How and when market tip? Lessons from the Battle of the Bund, ECB Working paper 766, June 2007


Valuing forward contracts: Key ideas

•  Two different ways to own a unit of the underlying asset at maturity: –  1.Buy spot (SPOT PRICE: S0) and borrow

=> Interest and inventory costs –  2. Buy forward (AT FORWARD PRICE F0)

•  VALUATION PRINCIPLE: NO ARBITRAGE •  In perfect markets, no free lunch: the 2 methods should cost the same.

You can think of a derivative as a mixture of its constituent underliers, much as a cake is a mixture of eggs, flour and milk in carefully specified proportions. The derivative’s model provide a recipe for the mixture, one whose ingredients’ quantity vary with time. Emanuel Derman, Market and models, Risk July 2001


Discount factors and interest rates

•  Review: Present value of Ct •  PV(Ct) = Ct × Discount factor

•  With annual compounding:

•  Discount factor = 1 / (1+r)t

•  With continuous compounding: •  Discount factor = 1 / ert = e-rt


Forward contract valuation : No income on underlying asset

•  Example: Gold (provides no income + no storage cost) •  Current spot price S0 = $1,340/oz •  Interest rate (with continuous compounding) r = 3% •  Time until delivery (maturity of forward contract) T = 1

•  Forward price F0 ?

Strategy 2: buy spot and borrow

Buy spot -1,340 + ST

Borrow +1,340 -1,381

0 ST -1,381

Strategy 1: buy forward

0 ST –F0

t = 0 t = 1

Should be

equal


Forward price and value of forward contract

•  Forward price:

•  Remember: the forward price is the delivery price which sets the value of a forward contract equal to zero.

•  Value of forward contract with delivery price K

•  You can check that f = 0 for K = S0 e r T

rTeSF 00 =

rTKeSf −−= 0


Arbitrage

•  If F0 ≠ S0 e rT : arbitrage opportunity

•  Cash and carry arbitrage if: F0 > S0 e rT

•  Borrow S0, buy spot and sell forward at forward price F0

•  Reverse cash and carry arbitrage if S0 e rT > F0 •  Short asset, invest and buy forward at forward price F0


Arbitrage: examples

•  Gold – S0 = 1,750, r = 1.14%, T = 1 S0 erT = 1,770

•  If forward price =1,800 •  Buy spot -1,750 +S1

•  Borrow +1,750 -1,770 •  Sell forward 0 +1,800 – S1

•  Total 0 + 30 •  If forward price = 1,700

•  Sell spot +1,750 -S1

•  Invest -1,750 +1,770 •  Buy forward 0 S1 – 1,700 •  Total 0 + 70

d13 01 introduction - ulb 01... · 2013-02-04 · february 4, 2013 additional references chance,...

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