Before our discussion of derivative instruments, we discuss the valuation and analysis of forward and futures contracts. A description of interest-rate futures was given in Chapter 6. Here we develop basic valuation concepts.
A forward contract is an agreement between two parties in which the buyer contracts to purchase from the seller a specified asset, for delivery at a future date, at a price agreed today. The terms are set so that the present value of the contract is zero. For the forthcoming analysis, we use the following notation:
- P is the current price of the underlying asset, also known as the spot price
- PT is the price of the underlying asset at the time of delivery
- X is the delivery price of the forward contract
- T is the term to maturity of the contract in years, also referred to as the time-to-delivery
- r is the risk-free interest rate
- R is the return of the payout or its yield
- F is the current price of the forward contract
The payoff of a forward contract is therefore given by
with X set at the start so that the present value of (PT – X) is zero. The payout yield is calculated by obtaining the percentage of the spot price that is paid out on expiry.
When a forward contract is written, its delivery price is set so that the present value of the payout is zero. This means that the forward ...