Mixing LSMC and PDE Methods to Price Bermudan Options

38 Pages Posted: 18 Nov 2016 Last revised: 10 Jan 2020

See all articles by David Farahany

David Farahany

University of Toronto - Department of Statistics

Kenneth R. Jackson

University of Toronto - Department of Computer Science

Sebastian Jaimungal

University of Toronto - Department of Statistics

Date Written: November 16, 2016

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

Suggested Citation

Farahany, David and Jackson, Kenneth R. and Jaimungal, Sebastian, Mixing LSMC and PDE Methods to Price Bermudan Options (November 16, 2016). Available at SSRN: https://ssrn.com/abstract=2870962 or http://dx.doi.org/10.2139/ssrn.2870962

David Farahany (Contact Author)

University of Toronto - Department of Statistics ( email )

100 St. George St.
Toronto, Ontario M5S 3G3
Canada

Kenneth R. Jackson

University of Toronto - Department of Computer Science ( email )

Sandford Fleming Building
10 King's College Road, Room 3302
Toronto, Ontario M5S 3G4
Canada

Sebastian Jaimungal

University of Toronto - Department of Statistics ( email )

100 St. George St.
Toronto, Ontario M5S 3G3
Canada

HOME PAGE: http://http:/sebastian.statistics.utoronto.ca

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