I am attempting to price a floating lookback put using the analytic formula. (eg. can be found in Shreve's vol II stochastic calculus section 7.4 or on Wikipedia) and wish to confirm the result by using an MC estimator with geometric Brownian motion paths. Unfortunately, I obtain different results (analytic : 0.1429 vs ~ 0.13 using MC simulation) which I don't expect.
My parameters are the following vol: 0.2, T (expiry): 1, r: 0.05, dt: 0.01, t: 0, spot: 1.
Please find below my code:
Thank you very much for any help.