Floating lookback put, MC vs analytic

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.

• Hi there and welcome. In order for us to help you, please provide a reproducible example. Also, please copy the code into the question body (instead of the screenshots), and please provide the 'main' as well, i.e. the input and output to your testing. Commented May 27, 2021 at 6:20
• Sorry for the lack of details and bad formatting. I will follow the guidelines for my next post. I believe the comment by @AkhiCTropChaud below has guided me to a potential solution. Commented May 27, 2021 at 12:49
• OK, good luck :) Commented May 27, 2021 at 14:36

1 Answer

You can simulate the maximum using the brownian bridge as explained in the chapter 8 of this course https://www.lpsm.paris/documents/71/probnum_gilp_pf17_wCJtiAO.pdf

• Thank you, I will have a look. Would you mind explaining why my approach does not work (i.e why there is a discrepancy between the analytic and mc price)? Commented May 26, 2021 at 15:47
• Plot your result vs number of simulations - has it converged yet? Calculate standard errors too, is your answer within 1stderr? Commented May 26, 2021 at 20:54
• basically you underestimate the max since you discretize, you can correct the bias by taking a finer discretization and/or by simulating the max between two instants with a Brownian bridge Commented May 27, 2021 at 7:56
• Thank you very much, this was very useful! Commented May 30, 2021 at 16:23