Mixing LSMC and PDE Methods to Price Bermudan Options

Abstract

We develop a mixed least squares Monte Carlo-partial differential equation (LSMC-PDE) method for pricing Bermudan style options on assets under stochastic volatility. The algorithm is formulated for an arbitrary number of assets and volatility processes and we prove the algorithm converges almost surely for a class of models. We also introduce a multi-level Monte-Carlo/multi-grid method to improve the algorithm's computational complexity. Our numerical examples focus on the single (2d) and multi-dimensional (4d) Heston models and we compare our hybrid algorithm with classical LSMC approaches. In each case, we find that the hybrid algorithm outperforms standard LSMC in terms of estimating prices and optimal exercise boundaries.

Keywords: least-squares Monte Carlo, bermudan options, stochastic volatility, variance reduction, dimension reduction