Question

A 1-year long forward contract on a non-dividend-paying stock is entered into when the stock price is $40 and the risk-free rate of interest is 10% per annum with continuous compounding.

(a) What are the forward price and the initial value of the forward contract?


(b) Six months later, the price of the stock is $45 and the risk-free interest rate is still 10%. What are the forward price and the value of the forward contract?

Answer 1

(a) What are the forward price and the initial value of the forward contract?

Fo= 40ε
`^(0.1*1)` = 44.21

The initial value of the forward contract is zero.

(b) Six months later, the price of the stock is $45 and the risk-free interest rate is still 10%. What are the forward price and the value of the forward contract?

The delivery price K in the contract is $44.21. The value of the contract, f, after six months is given by:

f= 45-44.21ε
`^(-0.1*0.5)`

= $2.95

The forward price is:

45ε
`^(0.1*0.5)` = $47.31