The Manhattan bank in Philadelphia has just sold a call option on 500,000 shares of stock. If the strike price is $40, the stock price is $40, the risk-free rate is 5%, the volatility is 30%, and the time to maturity is 3 months,

a) Suppose the bank does set up a delta-neutral position as soon as the option has been sold and the stock price jumps to $42 within the first hour of trading.

i)What trade is necessary to maintain delta neutrality? (3 marks).

ii) Explain whether the bank has gained or lost money in this situation. (you do not need to calculate the exact amount gained or lost).