Study Session 16, Reading 48

Value of a Forward Contract at Initiation

valuation of a forward contracts - the amount that one party will have to pay the other party in the future

Value:

The price of the forward contract is set at zero at the time of initiation.

Study Session 16, Reading 48

Value of a Forward Contract at Initiation (cont.)

Value of the forward contract (long position) at any time (t):

Value of a forward contract(short position) at any time (t):

Value of the forward contract (long position) at expiration:

Value of a forward contract (short position) at expiration:

Study Session 16, Reading 48

Price and Valuation of Equity Forward Contracts with Dividends

equity forward contract - a forward contract on a stock, portfolio or equity index

Formula: valuation of a forward to incorporate dividends:

or

Where: PVD - the present value of dividends FVD - future value of dividends.

Study Session 16, Reading 48

Price and Valuation of Equity Forward Contracts with Dividends (cont.)

The forward price should not be interpreted as the forecasted price.

Formula: stocks assuming continuous dividends :

or

Study Session 16, Reading 48

Price and Valuation of Equity Forward Contracts with Dividends (cont.)

Formula: value of a dividend:

Study Session 16, Reading 48

Forward Contract on a Fixed Income Security

forward rate agreement (FRA) -forward contracts on interest rate . The buyer of a FRA is the borrower and the seller is the lender.

Formula:

or

Study Session 16, Reading 48

Forward Contract on a Fixed Income Security (cont.)

Formula: calculate the value of a fixed income security forward contract during the life of the contract:

Study Session 16, Reading 48

Forward Contract on CurrencyThe currency forward rate is calculated by the concept of

covered interest rate parity.

Formula:

Study Session 16, Reading 48

Credit Risk and Market Value as a Measure of Exposure

Credit risk exists in forward contracts.Credit risk arises when the party owing the money is unable to

pay the other party. Party can either declare bankruptcy or inform the other party

of their inability to pay the money owed.

Study Session 16, Reading 49

Convergence of Futures Price to Spot Price at Expiration

long - The party in the futures contract that agrees to buy the asset in the future is called the.

short - The party agreeing to sell the asset is called the. futures price - the price today for the delivery of an asset in the future. spot price - the price for immediate delivery.

The spot price at expiration must equal to the futures price.If the prices are not the same, there will be an arbitrage

opportunity.

Study Session 16, Reading 49

Determining the Value of a Futures Contract

Value for a futures contract is simply the observable price change since the last marked to market.

Value of futures contract at expiration=0Value of the futures contract at expiration is = -F(0,T)

cash and carry arbitrage and reverse cash and carry arbitrage - arbitrage profit can be made by selling the asset short or buying the asset and selling the futures contract, depending on the futures price

Study Session 16, Reading 49

Difference between Forward and Futures Prices

Forwards and futures value at the time of initiation is zero. Credit risk is the major determinant of the prices. Prices of futures and forwards will differ due to the credit risk

involved in the forwards contract. Futures contracts are daily settled.

Study Session 16, Reading 49

Benefits and Costs of Holding Underlying Assets, and their Effect on Futures Price

There is no storage cost for financial assets. There is opportunity cost for financial assets.Formula: Futures price if holding an asset results in a monetary

cost or benefit:

Where: FV(NC) - future value of net costs of holding assets

Formula: Net CostsNet costs(NC) = Storage Costs - Convenience Yield

Study Session 16, Reading 49

Benefits and Costs of Holding Underlying Assets, and their Effect on Futures Price (cont.)

Formula: Futures price if the non-monetary benefits are provided by holding an asset

Where: FV(NB) - the future value of net benefit

Formula: Net BenefitNet benefit = Yield on asset + Convenience Yield

Study Session 16, Reading 49

Normal Backwardation

backwardation - when the futures price is less than the spot price in the market. In backwardation the benefits are more than the costs plus interest.

normal backwardation theory - the markets are lead by hedgers who hold short positions. This theory states that the futures price is less than the expected future spot price.

Study Session 16, Reading 49

Normal Contango

contango - when the futures price is greater than the spot price in the market. In contango, the benefits are less than the cost plus interest.

normal contango theory - the markets are lead by hedgers who hold long positions. This theory implies that the futures price is greater than the expected future spot price.

Study Session 16, Reading 49

Difficulties in Pricing Eurodollar Futures

Eurodollar futures are priced as a discount yield.LIBOR is an add on rate and the LIBOR based deposits are

priced on an add in basis.No combination of a Eurodollar time deposit and Eurodollar

futures contract can be built.There is no arbitrage opportunity in the Eurodollar futures

contract .

Study Session 16, Reading 49

Pricing of Treasury Bond Futures

A T-Bond futures contract involves the delivery of any bond which has 15 years to maturity or first call.

Formula:or

value of a tick - the minimum price change defined in the T-bond contract

Study Session 16, Reading 49

Pricing of Index FuturesFormula:

or

Value: futures price on a stock index discounted at dividend yield, compounded at risk free rate

or

Study Session 16, Reading 49

Pricing of Currency Futures365 days should be used for foreign currency if the maturity is

given in days.

Formula: