Valuing American-style derivatives by simulation : alternative regression-based methods

Abstract

American-style derivatives remain one of the most complex financial instruments to price due to their early-exercise feature. The aim of this dissertation is to effectively price various exotic American-style derivatives with algorithms proposed by Longstaff and Schwartz (2001) and Tsitsklis and Van Roy (2001). The effect of utilising in-themoney paths against all paths for the regression is investigated, and the robustness of the algorithms proposed by Longstaff-Schwartz and Tsitskilis-Roy to a change in polynomial basis functions is analysed. We compute upper and lower bounds for the value of a Bermudan put option using the technique proposed by Andersen and Broadie (2004). We further evaluate the accuracy and efficiency of using nonparametric kernel regression and support vector regression to replace the least-squares regression component of the Longstaff-Schwartz algorithm. Numerical results indicate that nonparametric regression and the Longstaff-Schwartz algorithm are superior. The Tsitsiklis-Roy algorithm produces the least desirable results as it contains a high bias, and support vector regression produces reasonable results at the expense of substantially reduced efficiency.