The Mathematics of Financial Modelingand Investment Management

2-Financial Markets Page 60 Wednesday, February 4, 2004 1:15 PM

60 The Mathematics of Financial Modeling and Investment Management

However, the pricing of futures contracts does not require any high level

mathematical analysis. Rather it is based on simple arbitrage arguments

discussed in Chapter 14. To see this, let’s derive the theoretical price of a

futures contract using simple algebra. All we need to know is the fol-

lowing:

■ The price that the underlying asset for the futures contract is selling for

in the cash market.

■ The cash yield earned on the underlying asset until the settlement date.

■ The interest rate for borrowing and lending until the settlement date.

Let

r = financing cost

y = cash yield on underlying asset

P = cash market price ($) of the underlying asset

F = futures price ($)

Now consider the following strategy, referred to as a cash and carry

trade:

■ Sell the futures contract at F

■ Purchase the underlying asset in the cash market for P

■ Borrow P until the settlement date at the financing cost of r

The outcome at the settlement date then is:

1. From Settlement of the Futures Contract

Proceeds from sale of the underlying asset to settle the = F

futures contract

Payment received from investing in the underlying asset for = yP

3 months

Total proceeds = F + yP

2. From the Loan

Repayment of the principal of loan = P

Interest on loan = rP

Total outlay = P + rP

The profit will equal: