Monte Carlo Simulation With Machine Learning For Pricing American Options And Convertible Bonds

Monte Carlo Simulation with Machine Learning for Pricing American Options and Convertible Bonds

Li, Szepesvari and Schuurmans (2009) show that reinforcement learning (RL) algorithms are superior to the classical methods (such as Longstaff and Schwartz (2001)) in pricing American options using Monte Carlo simulation. We extend their techniques to the problem of pricing convertible bonds and show that RL outperforms LS on this task. Additionally, we propose a new method, based on the random forest algorithm from machine learning [Breiman (2001)], that can be used for pricing both American options and convertible bonds with Monte Carlo simulation. We show that this algorithm outperforms LS and is also superior to RL in most cases. We demonstrate how to use Monte Carlo simulation with the methods described above for pricing a complex convertible bond trading at the Tel Aviv stock exchange. Like many Israeli convertibles, this bond exhibits the "gradually diminishing principal" feature, meaning that instead of one payment of the principal at maturity, there are multiple principal payments during the lifetime of the bond. This feature presents a challenge to existing models. We also model other exotic features of this bond, such as path-dependent conversion ratio and exchange rate indexation. The prices that we obtain using this model are close to the market prices of the bond.

American-style Option Pricing and Improvement of Regression-based Monte Carlo Methods by Machine Learning Techniques

Monte Carlo Methods for American Option Pricing

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 book 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). The author first presents the mathematical descriptions underlying these numerical methods. Then the selected algorithms are tested on a common set of problems in order 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.