AAD and Least-Square Monte Carlo: Fast Bermudan-Style Options and XVA Greeks
27 Pages Posted: 26 Sep 2016 Last revised: 23 Aug 2017
Date Written: September 23, 2016
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)
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