Mixing LSMC and PDE Methods to Price Bermudan Options
51 Pages Posted: 18 Nov 2016 Last revised: 23 Mar 2018
Date Written: November 16, 2016
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 driving processes and we prove the algorithm converges probabilistically. We also discuss two methods to greatly improve the algorithm's computational complexity. Our numerical examples focus on the single (2d) and multi-dimensional (4d) Heston model and we compare our hybrid algorithm with classical LSMC approaches. In both cases, we demonstrate that the hybrid algorithm has significantly lower variance than traditional LSMC. Moreover, for the 2d example, where it is possible to visualize, we demonstrate that the optimal exercise strategy from the hybrid algorithm is significantly more accurate compared to the one from the full LSMC when using a finite difference approach as a reference.
Keywords: least-squares Monte Carlo, bermudan options, stochastic volatility, variance reduction, dimension reduction
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