The value of a forward contract at initiation is zero. Over time, the value depends on the relationship between the forward price and the expected future spot price. Futures prices also converge to the spot price at expiration. Like forwards, futures have value of zero at initiation but are marked to market daily. Factors like storage costs, convenience yields, and interest rates can cause the futures price to be in contango or backwardation relative to the expected future spot price.

1. 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

2. 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

3. 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

4. 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

5. Price and Valuation of Equity
Forward Contracts with Dividends (cont.)
Formula: value of a dividend:
Study Session 16, Reading 48

6. 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

7. 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

8. Forward Contract on Currency
The currency forward rate is calculated by the concept of
covered interest rate parity.
Formula:
Study Session 16, Reading 48

9. 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 48

10. 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

11. 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=0
Value 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

12. 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

13. 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 Costs
Net costs(NC) = Storage Costs - Convenience Yield
Study Session 16, Reading 49

14. 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 Benefit
Net benefit = Yield on asset + Convenience Yield
Study Session 16, Reading 49

15. 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

16. 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

17. 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

18. 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 Tbond contract
Study Session 16, Reading 49

19. Pricing of Index Futures
Formula:
or
Value: futures price on a stock index discounted at dividend
yield, compounded at risk free rate
or
Study Session 16, Reading 49

20. Pricing of Currency Futures
365 days should be used for foreign currency if the maturity is
given in days.
Formula:
Study Session 16, Reading 49