Mixing LSMC and PDE Methods to Price Bermudan Options

TL;DR

This paper introduces a hybrid LSMC-PDE method for pricing Bermudan options with stochastic volatility, demonstrating improved accuracy over classical LSMC in multi-asset models.

Contribution

The paper presents a novel mixed LSMC-PDE algorithm for Bermudan options with stochastic volatility, including convergence proof and computational enhancements.

Findings

Hybrid algorithm outperforms standard LSMC in price estimation.

Effective in single and multi-dimensional Heston models.

Converges almost surely for a broad class of models.

Abstract

We develop a mixed least squares Monte Carlo-partial differential equation (LSMC-PDE) method for pricing Bermudan style options on assets whose volatility is stochastic. 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 discuss two methods 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.