Peter has just sold a European call option on 10,000 shares of a stock. The exercise price is $50; the stock price is $50; the continuously compounded interest rate is 5% per annum; the volatility is 20% per annum; and the time to maturity is 3 months.

(a) Use the Black-Scholes-Merton model to compute the price of the European call option. (7 marks)

(b) Find the value of a European put option with the same exercise price and expiration as the call option above. (6 marks)

(c) What position should Peter take in the stock for delta neutrality? (3 marks)

(d) Suppose that Peter does set up a delta neutral position as soon as the option has been sold and the stock price jumps to $55 within the first hour of trading. What trade is necessary to maintain delta neutrality? (4 marks)