When answering each question, state any additional assumptions you may need to make. Show all working/calculations.

(a) Consider the following two strategies:

• Strategy 1: Go long one call option with strike price K + 2C, go long one call option with strike price K - 2C, and go short 2 call options with strike price K.

• Strategy 2: Go short two put options with strike price K, go long one put option with strike price K - 2C, and go long one put option with strike price K + 2C.

Both strategies are based on the same underlying non-dividend-paying stock and all options are European and have the same maturity date, T. Both K and C are positive constants,

K - 2C > 0 and the stock price today is equal to K.

Which strategy has the higher cost to implement today? You must use a payoff table at maturity to comprehensively justify your answer, stating any assumptions. Why would a trader use these strategies?

(b) Consider a three-period binomial model (t = {0,1, 2, 3}), with a risky non-dividend paying stock, Prudential, which is currently trading for £1,350. In each period the stock can go up by 30% or down by 20%. The risk-free rate is 2% in the first period, 3% in the second period, and 1% in the third period.

Using the risk-neutral pricing method, what is the no-arbitrage value today of an at-the-money European put option on Prudential stock with maturity date t = 3? Would the value of the option change if it was American? Explain.

(c) You work as a commodities trader and are trying to calculate the no-arbitrage price of a forward contract on gold. The current spot price of gold is £1,325 per kg and the annual risk-free rate is 3% per year, constant over time. The storage cost of gold is £50 per year per kg and is paid at the beginning of each year the gold is stored. Assume the convenience yield for gold is zero. What is the 10-year forward price if the forward contract species 250kg of gold?

(d) Explain intuitively how volatility in the underlying stock price affects the prices of both call and put options written on the underlying stock.