Question

A one-year long forward contract on a non-dividend-paying stock is entered into when the stock price is $56 and the risk-free rate (with continuous compounding) is 8%.` (1) What are the forward price and the initial value of the forward contract?

(2) Five months later, the price of the stock is $60 and the risk-free rate is still 8%. What are the forward price and the value of the forward contract?

Answer 1

Value of the forward contract can be given by the below formula

$^{F}0=^{S}0_{e}rT$

where S = Stock price

r= continuously compunded risk free rate

T = Time to maturity

Forward price = 56*e^0.08*1

= 56*1.083287068

= 60.6640

Forward price = $60.66

Initial value of the contract = Spot price - present value of the forward contract = 56 -56 = 0

Revised forward price = 60*e^0.08*7/12

= 60*e^0.04666667

= 60* 1.047772694

= 62.87

Value of the forward contract = 60 - present value of 62.87

= 60 - 60 = 0