Forward Contracts

Chapter 2

Forwards

Oldest of all derivatives A forward contract refers to an agreement

between two parties to Exchange (buy/sell) an agreed quantity of an asset

for cash At a certain date in future At a predetermined price specified in that

agreement. The promised asset may be currency, commodity,

instrument etc.

Forward Contract

A user (holder) who promises to buy the specified asset at an agreed price at a fixed future date is said to be in “long position”.

The user (holder) who promises to sell at an agreed price at a future date is said to be in “short position”.

The mutually agreed price in a forward contract is known as “delivery price”.

The value of the contract is determined by the market price of the underlying asset.

Features of Forward Contract

The contract is usually referred to as FRC i:e forward rate contract.

OTC trading: These contracts are purely privately arranged agreements and hence, they are not standardized ones. they are traded OTC not in exchanges. There is much flexibility: can be modified according to the requirements of the parties to the contract.

No down payment Settlement on maturity Linearity: Symmetrical gains and losses due to price

fluctuation of the underlying asset

When spot price > contract price the buyer is the gainer

Gain= spot price – contract price The gain which one get when the price moves in one

direction will be exactly equal to the loss when the price moves in the other direction by the same amount.

No secondary market: Purely private contract Necessity of a third party: Intermediary may be a

financial institution like bank or any other third party Delivery: On the date of maturity of the contract.

Forward Price

A forward price of a contract is the delivery price which would render a zero value to the contract.

Zero value implies that no party is required to pay any amount to other when the contract is entered into.

When forward contracts are entered into forward price and delivery price are identical.

Gradually forward price changes and delivery price remains unchanged.

PAY-OFF

ST-spot price E= delivery price Pay-off for long position: ST- E

ST>E ST=E ST<E gain break-even loss

Pay-off for short position: E- ST

ST>E ST=E ST<E loss break-even gain

Advantages of forward contract

Forward contract can be used to hedge or lock in the price of purchase or sell of commodity or financial asset on the future commitment date.

In forward contracts generally margins are not paid and there is also no up-front premium(service charge), so it does not involve service charge.

Since forward are tailor made price risk exposure can be hedge upto 100% which may not be possible in future and options.

Disadvantages

counter party risk is very much present in a forward since there is no performance guarantee. On due date the possibility of counter party failure to perform his obligation creates another risk.

It does not allow the investor to unwind the transaction once it is entered into. At the most the contract can be cancelled on the terms agreed upon by the counter party.

Since forwards are not exchange traded they have no ready liquidity. Further it is difficult to set counter party on one’s terms.

Pricing Forward Contracts

Forwards are priced using “Cost of Carry Model”

Depending on the nature of the carry costs associated with the asset and carry return principle the model has been modified.

Carry Cost

Carry cost include the holding costs for the underlying assets. For commodities, this may refer to warehousing costs, insurance expenses, transportation cost, etc. For financial products, carry costs include financing cost like interest charges on borrowing the cash to take position in the asset.

Carry Return

Carry return principle refers to the income generated by the asset. For financial product, carry return may include dividends received on shares.

The major assumptions of the model

Markets are perfect i:e.,information flow is instantaneous and freely available, equal borrowing and lending rates and large number of market participants.

The underlying asset are infinitely divisible. No transaction cost and brokerage fees Only one price exists thereby removing the

possibility of bid (buying rate)-ask (selling rate) spread

Absence of any market restrictions such as short selling, margin money, etc.

Continuous Compounding

The calculation of forward prices and option prices is based on the concept of continuous compounding

A=P(1+r)n

A= compounded value P=principal amount r=interest rate per annum n=time period

A=P(1+ r/m)mn

r= per annum rate of interest. m= number of compounding per

annum. n= number of years. For quarterly compounding m=4 For daily compounding, m=365.

A=Pe nr

e is a mathematical constant whose value is 2.7183

r1=interest rate when m compounding are done

r2= equivalent rate when continuous compounding is done

(1+r1/m)mn=e r2

n

r2=m ln ( 1+ r1/m)

r1= m (er2/m-1)

Three situations for pricing forwards depending on underlying assets

Asset with no income

Asset providing a given amount of income

Asset providing a known yield

Asset with no income

The prominent example of this type of asset, giving no income, is an equity share on non-dividend basis and a deep discount bond.

This is the simplest forward contract True price of a forward contract is that

when no arbitrage opportunities exist

F=Ser*t

Asset providing a known cash income

The examples for assets, providing known cash income, are bonds promising known coupon rate, securities with a known dividend, preference shares, etc.

F=(S-I)*ert

Asset providing a known yield

A known yield refers to income expressed as percentage of the asset life, and this yield is assumed to be paid continuously as a constant annual rate of y

In this case forward price is as follows:

F=S*e (r-y)*t