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

The initial forward price of the stock when entering a forward contract with a stock price of $40 and a risk-free rate of 10% with continuous compounding is approximately $44.02, with its initial value being $0. Six months later, with the stock price at $45, there exists an arbitrage opportunity if the actual forward price is $46.

Step-by-step explanation:

The initial forward price, F, of the contract can be found using the formula F = S0 * e^(rt), where S0 is the current stock price, r is the risk-free rate, and t is the time in years. Thus, with S0 = $40, r = 0.10, and t = 1, the calculation is F = $40 * e^(0.10 * 1), which results in a forward price of approximately $44.02. The initial value of a forward contract at initiation is $0 because no cash exchanges hands at this point.

Six months into the contract, we would expect the forward price to be the stock price at that time compounded for the remaining time of the contract. However, if the actual forward price is higher than the no-arbitrage forward price, then an arbitrage opportunity exists. The arbitrage strategy would involve selling the forward contract at its current price of $46, simultaneously borrowing the current stock price ($45) at the risk-free rate, buying the stock, and then delivering it at the contract expiration.