Suppose that the current price of a stock is 40. The stock has a volatility of 30% and pays no dividends. The continuously compounded risk-free interest rate is 8%. A customer buys a call option from the market-maker with strike price 40 and time to maturity of 91 days.

(a) Find C (the price of the call) and at the time of the transaction.

(b) Suppose that the market-maker leaves his position unhedged. What is the realized profit if the stock increases to 40.50 the next day?

(c) Suppose that the market maker-hedges his position by buying 0.58240 shares of the stock. What is his profit/loss in the next day when the price increases to 40.50?