Question

A one-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

A one-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.

c). If actual forward contract price  in month 6 is $46, formulate an arbitrage strategy.

Answer 1

a) Forward Price = Current Spot Price * e^{(risk-free rate of interest * delivery date in years)}

Forward Price = $40 * 2.7183^(0.1*1) = $40*1.105 = $44.21

The initial value of the forward contract is $0 as no money is exchanged in initial agreement of a forward contract.

b and c) Forward Price = Current Spot Price * e^{(risk-free rate of interest * delivery date in years)}

Actual Forward Contract Price in month 6 is $46 but it should be = $45 * 2.7183^(0.1*0.5) = $47.31. So the actual forward contract price is less by $1.31 Buy the forward now and expect to sell it at $47.31 after 6 months.