just b and c

3) (ii) An investor buys one call option contract on a stock with a strike price of 38.5 and sells a call option contract on the same stock with a strike price of 40 . The market prices of the options are 2.40 and 1.80 respectively. The options have the same maturity date. Describe the in- vestor's position and the possible gain/loss he will get (taking into account the initial investment). Make a graph of your gain/loss. [6] (b) (i) State the non-arbitrage principle. Suppose that 1 pound is worth 1.3 dollar and 1 dollar is worth 100 yen. If 1 pound is worth 133 yen, an arbitrage opportunity arises. Describe such arbitrage strategy and compute the net gain. [3] (ii) Consider a European call option on a non-dividend paying stock. Suppose that So is the current stock price, K is the strike price, T is the time to maturity and r is the continuously compounded risk-free interest rate. Which are the upper and lower bounds the price c of the European call option must satisfy? Taking into account such bounds, if So = 50, K = 48, r = 3%,T 0.5 and c=2, what arbitrage opportunities would exist? Describe the arbitrage strategy and compute the gain. [6] (c) Suppose that a stock price has an expected return of 4.3% per annum and a volatility of 20% per annum. When the stock price at the end of a certain day is 37 , calculate each of the following: (i) The expected stock price 30 days later; (ii) The standard deviation of the stock price 30 days later; (iii) The 95% confidence interval for the stock price 30 days later