A floating strike

A lookback option can be structured as a put or call. The strike can be either fixed
or floating. We now consider two lookback options written on the minimum value
achieved by the underlying index during a fixed time window:

1. A fixed strike lookback put: The payoff is given by the difference, if positive,
   between the strike price and the minimum price over the monitoring period.
2. A floating strike lookback call: The payoff is given by the difference between
   the asset price at the option maturity, which represents the floating strike, and
   the minimum price over the monitoring period.
   a) Assume
   Compute the price for a fixed strike lookback put by Monte Carlo Simulation.
   b) Assume .
   Compute the price for a floating strike lookback call by Monte Carlo Simulation.
   c) Improve the accuracy of the two algorithms by using control variate techniques.