Consider the problem of pricing lookback options for a stock modeled by a geometric Brownian motion with an initial price of $100, a volatility of 40%, and zero interest rate. Let the expiry time be 12 weeks in the future (consider 52 weeks a year), and let the monitoring frequency be weekly.(USING R)

a) Find the fair price of both the put and call options.

b) Does the put or the call have a higher price? What is a possible intuitive explanation?