Question

Problem 3: A one-year-long forward contract on a non-dividend-paying stock is entered into when the stock price is $50 and the risk-free interest rate is 5% per annum (continuous compounding).

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

(b) Six months after the signing of the forward contract, the price of the stock is $55 and the risk-free interest rate is still 5%. What is the new market forward price for the same contract (which will now mature in 6 months)? What is the value of the forward contract signed 6 months ago?

Answer 1

a) Price of the Stock = $50

Risk Free Rate = 5%

Forward Price of the Stock = Price of the stock * e^ number of years* rate of interest

Or, Forward Price of the Stock = $50* e ^ 0.05*1 = $52.55

The initial value of the forward contract is zero.

b) The forward Price of one-year stock is $52.55 but after six months the new price of the stock is $55, so the new market price of the same contract would be;

New Forward Price of the Stock = Price of the stock * e^ number of years* rate of interest

Or, New Forward Price of the stock = $55* e ^ (6/12)* 0.05 = $56.39

Value of the Forward contract signed 6-months ago would be: Current Price – Forward Price of 1-year contract * e^ - (no. of years remain * rate of interest)

Or, $55 - $52.55 * e^ - (0.05*0.5) =

Or, $55 – $52.55* (1/1.025315)

Or, $55 - $47.65 = $7.35