Financial Mathematics

QUESTION 3 (a) What is the difference between the forward price and the value of a forward contract? [2] (b) A one-year long forward contract on a non-dividend-paying stock is entered into when the stock price is R40 and the risk-free rate of interest is 10% per annum with continuous compounding. i. What are the forward price and the initial value of the forward contract? [2] ii. Six months later, the price of the stock is R45 and the riskfree interest rate is still 10%. What are the forward price and the value of the forward contract? (c) Suppose that the risk-free interest rate is 10% per annum with continuous compounding and that the dividend yield on a stock index is 4% per annum. The index is standing at 400 , and the futures price for a contract deliverable in four months is 405 . What arbitrage opportunities does this create? [3] (d) The spot price of silver is R25 per ounce. The storage costs are R0.24 per ounce per year payable quarterly in advance. Assuming that interest rates are 5\% per annum for all maturities, calculate the futures price of silver for delivery in nine months. [3]