Pricing American options by simulation

Abstract

Pricing American options is a di cult problem in mathematical nance as no closed form solution exists. So, many approximations and numerical techniques have been developed. In option pricing, it is advantageous to use Monte Carlo simulation due to its precision and convergence. In this thesis, we implement and analyze the Least Squares Monte Carlo (LSM) algorithm of Longsta and Schwartz (2001), which is a regression-based method for American option pricing. For one-dimensional cases, we o er an alternative method that requires less computational e ort while the accuracy is increased; Simple Regression Approach (SRA), which is based on the LSM algorithm. Moreover, we analyze the options on multi-assets and use the LSM algorithm to price these options. As well as applying variance reduction techniques and reaching a considerable decrease in the estimated variance in multi-dimensional cases, we also investigate how many early exercise opportunities should be considered in the algorithm for the option to be close to American one. Numerical results indicate that the price estimates in the literature are actually low for American options on the maximum of two and ve assets. In addition, we determine a useful set of basis functions for pricing American spread options. For all implementations we use R, which is a programming language and environment for statistical computing and graphics.