Assume that the stock price follows a geometric Brownian motion, where the current price S0=100, expected return =0 and volatility =0.80.The risk-free rate r=0.02 p.a.For each of the following scenarios, find the worst-case value of the portfolio in 3 months such that there is only 2.5% chance of the actual value being lower.

a) A short position of 10,000 shares of the stock.

b) A short position of a call option on 100,000 shares of the stock with a strike price of $80 and a maturity of 3 years.

c) A short position of a put option on 100,000 shares of the stock with a strike price of $120 and a maturity of 3 years.