A fund manager has just sold a call option on 100 shares of a stock. The stock price is $87 and its volatility is 20% per annum. The strike price of the option is $89 and it matures in 6 months. The risk-free rate is 6% per annum (continuously compounded).

a) What position should the fund manager take in the stock to achieve delta neutrality?

b) Suppose after the fund manager sets up the delta neutral position, the stock price suddenly jumps to 80. Should she buy or sell shares to maintain delta neutrality? Why? Did she gain money, lose money or achieve no gain/loss on her position? Why?