Graduation Year
2019
Date of Submission
5-2019
Document Type
Campus Only Senior Thesis
Degree Name
Bachelor of Arts
Department
Mathematics
Reader 1
Mark Huber
Terms of Use & License Information
Abstract
This article investigates several variance reduction techniques in Monte Carlo simulation applied in option pricing. It first shows how Monte Carlo simulation could be leveraged in the field of option pricing by demonstrating the quality of Monte Carlo methods and properties of stock options. Then the articles simulate stock price trajectories to infer the optimal option price by averaging the payoff at maturity. The article shows in depth the effect of control variates and antithetic variates, and importance sampling in reducing variance. The last part of the article shows how the same variance reduction techniques could be used in more exotic options such as Asian and Bermuda options. In these cases, their closed-form expressions are more difficult to derive compared to the European options, and thus simulation is widely practiced in the industry.
Recommended Citation
Ye, Haocheng, "Monte Carlo Methods in Option Pricing" (2019). CMC Senior Theses. 2122.
https://scholarship.claremont.edu/cmc_theses/2122
This thesis is restricted to the Claremont Colleges current faculty, students, and staff.
