The price of one share of BIOGEM, the hedge fund of hot biotechnology stocks, is currently $100. The volatility of returns on BIOGEM is 30% per annum. The risk-free rate is 2%. Suppose that put and call options on BIOGEM are traded on CBOE. The exercise price of the put option is $98 and the exercise price of the call option is $102.

a. Use the Black Scholes model to price the put option on BIOGEM;

b. Use the Black Scholes model to price the call option on BIOGEM;

c. Use the Black Scholes model to find deltas and gammas for both options;

d. Construct a gamma-delta neutral portfolio of BIOGEM shares, and call and put options mentioned above.