#### Subject 3. Pricing and Valuation of Forward Contracts

Pricing and Valuation at Expiration

At expiration T, the value of a forward contract to the long position is:

VT(T) = ST - F0(T)
where ST is the spot price of the underlying at T and F0(T) is the forward price.

The forward price is the price that a long will pay the short at expiration and expect the short to deliver the asset.

Pricing and Valuation at Initiation Date

There is no cash exchange at the beginning of the contract and hence the value of the contract at initiation is zero.

V0(T) = 0
The forward price at initiation is:

F0(T) = S0(1 + r)T
Example

Consider a forward contract on a non-dividend paying stock that matures in 6 months. The current stock price is \$50 and the 6-month interest rate is 4% per annum. Compute the forward price, F. Solution: Assuming semi-annual compounding, F = 50 x 1.02 = 51.0.

If we add benefits ʇ (dividends, interest, and convenience yield), and costs θ the forward price of an asset at initiation becomes

F0(T) = S0(1 + r)T - (ʇ - θ) (1 + r)T
Consider a forward contract on a 4-year bond with 1 year maturity. The current value of the bond is \$1018.86. It has a face value of \$1000 and a coupon rate of 10% per annum. A coupon has just been paid on the bond and further coupons will be paid after 6 months and after 1 year, just prior to delivery. Interest rates for 1 year out are flat at 8%. Compute the forward price of the bond.

F = 1018.86 x 1.042 - 50 x 1.04 - 50 = \$1,000

Pricing and Valuation during the Life of the Contract

The value of a forward contract after initiation and during the term of the contract change as the price of the underlying asset (S) changes. The value (profit/loss) of a forward contract between initiation and expiration is the current price of the asset less the present value of the forward price (at expiration).