Suppose S = $ 45, r = 9 %, delta (the annualized dividend rate) is 9%, and sigma (the annualized standard deviation of the continuously compounded stock returns) is 47%. Suppose you sell a $ 50-strike call with 75 days to expiration.

a) What is delta, the partial derivative of the call price, with respect to the price of the underlying asset?

b) If the option is on 100 shares, what investment is required for a delta-hedged portfolio?

c) What is your overnight profit if the stock tomorrow is $ 44.35?