CHAPTER 11 Forwards and Futures Valuation

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

(11.1) numbered Display Equation

with X set at the start so that the present value of (PTX) 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 ...

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