A hedge fund with net asset value of $101 per share currently has a high water mark of $108. Suppose it is January 1, the standard deviation of the fund's annual returns is 35%, and the risk-free rate is 3%. The fund has an incentive fee of 18%.

a. What is the value of the annual incentive fee according to the Black-Scholes formula? (Treat the risk-free rate as a continuously compounded value to maintain consistency with the Black-Scholes formula.)
 b. What would the annual incentive fee be worth if the fund had no high water mark and it earned its incentive fee on its total return?
 c. What would the annual incentive fee be worth if the fund had no high water mark and it earned its incentive fee on its return in excess of the risk-free rate?
d. Recalculate the incentive fee value for part (b) assuming that an increase in fund leverage increases volatility to 45%.