Monte Carlo Methods for American Option Pricing

Alberto Barola

Student thesis: Master thesis

Abstract

The Monte Carlo approach has proved to be a valuable and flexible computational tool in modern finance. A number of Monte Carlo simulation-based methods have been developed within the past years to address the American option pricing problem. The aim of this thesis is to present and analyze three famous simulation algorithms for pricing American style derivatives: the stochastic tree; the stochastic mesh and the least squares method (LSM). We first present the mathematical descriptions underlying these numerical methods. We then proceed to analyze the impact of efficiency enhancement and variance reduction techniques on the algorithms performance. At the end we test the selected methods on a common set of problems in order to be able to assess the strengths and weaknesses of each approach as a function of the problem characteristics. The results are compared and discussed on the basis of estimates precision and computation time. Overall the simulation framework seems to work considerably well in valuing American style derivative securities. When multi-dimensional problems are considered, simulation based methods seem to be the best solution to estimate prices since the general numerical procedures of finite difference and binomial trees become impractical in these specific situations.

EducationsMSc in Advanced Economics and Finance, (Graduate Programme) Final Thesis
LanguageEnglish
Publication date2013
Number of pages153