# 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.

## INTRODUCTION

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*P*is the price of the underlying asset at the time of delivery_{T}*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 (*P _{T}* –

*X*) is zero. The payout yield is calculated by obtaining the percentage of the spot price that is paid out on expiry.

## FORWARDS

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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