Question

QUESTION FOUR

A. The price of oil is K100 per barrel. Oil prices are expected to grow at 4% per year. The one-year risk-free rate of interest is 2% in simple terms. It costs K1 to store a barrel of oil for one year. If oil has no costs or benefits of carry, what is the theoretical one-year forward price of oil?

B. A non-interest-bearing asset has a spot price of K100. It costs 1% per annum (on a simple rate basis) to store the asset. Simple interest rates are 5% per annum. What is the fair one-year forward price?

C. Consider a forward start option which, 1 year from today, will give its owner a 1-year European call option with a strike price equal to the stock price at that time. You are given: (i) The European call option is on a stock that pays no dividends.

(ii) The stock’s volatility is 30%.

(iii) The forward price for delivery of 1 share of the stock 1 year from today is 100.

(iv) The continuously compounded risk-free interest rate is 8%. Required: Under the Black-Scholes framework, determine the price today of the forward start option.

Answer 1

A.

B.

fair one-year forward price = spot price*e(r+q)*T
r = interest rate; q = storage cost; T = time period
fair one-year forward price = K100*e(0.05+0.01)*1 = K100*e0.06 =K100*1.0618 =K106.18

C.

We will now use the Black Scholes Model to solve for the price of the call option.

The forward price for delivery of 1 share of the stock 1 year from today is 100.
Hence, its no arbitrage current stock price will be = Fe-rt = 100 x e-8% x 1 = 92.31 Consider follwings ;