You hold a portfolio of (vanilla, European-style) options written on the same stock share, whose price follows a geometric Brownian motion with drift 9% and volatility 25%. At present, the stock price is \($30,\) and the risk-free rate, with continuous compounding, is 3%. The portfolio consists of:

1-A short position in 1000 put options, strike \($27,\) maturing in three months 2-A long position in 500 call options, strike \($30,\) maturing in four months 3-A short position in 1500 call options, strike \($28,\) maturing in two months How many stock shares do you need to make the portfolio delta-neutral? Can you also make the portfolio gamma-neutral by using stock shares? If so, explain how. Otherwise, how should you change the position in the last call to make the portfolio gamma neutral?