AAD and Least-Square Monte Carlo: Fast Bermudan-Style Options and XVA Greeks

27 Pages Posted: 26 Sep 2016 Last revised: 23 Aug 2017

See all articles by Luca Capriotti

Luca Capriotti

University College London; NYU Polytechnic School of Engineering - Department of Finance and Risk Engineering

Yupeng Jiang

University College London

Andrea Macrina

University College London; University of Cape Town (UCT)

Date Written: September 23, 2016

Abstract

We show how Adjoint Algorithmic Differentiation (AAD) can be used to calculate price sensitivities in regression-based Monte Carlo methods reliably and orders of magnitude faster than with standard finite-difference approaches. We present the AAD version of the celebrated least-square algorithms of Tsitsiklis and Van Roy (2001) and Longstaff and Schwartz (2001). By discussing in detail examples of practical relevance, we demonstrate how accounting for the contributions associated with the regression functions is crucial to obtain accurate estimates of the Greeks, especially in XVA applications.

Keywords: Adjoint Algorithmic Differentiation (AAD), Monte Carlo, Bermudan-style options, valuation adjustments (XVA)

Suggested Citation

Capriotti, Luca and Jiang, Yupeng and Macrina, Andrea, AAD and Least-Square Monte Carlo: Fast Bermudan-Style Options and XVA Greeks (September 23, 2016). Available at SSRN: https://ssrn.com/abstract=2842631 or http://dx.doi.org/10.2139/ssrn.2842631

Luca Capriotti

University College London ( email )

Gower Street
London, WC1E 6BT
United Kingdom

NYU Polytechnic School of Engineering - Department of Finance and Risk Engineering ( email )

Brooklyn, NY 11201
United States

Yupeng Jiang

University College London ( email )

Gower Street
London, WC1E 6BT
United Kingdom

Andrea Macrina (Contact Author)

University College London ( email )

Gower Street
London, WC1E 6BT
United Kingdom

University of Cape Town (UCT) ( email )

Private Bag X3
Rondebosch, 7701
South Africa

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