Automatic Backward Differentiation for American Monte-Carlo Algorithms - ADD for Conditional Expectations and Indicator Functions

22 Pages Posted: 18 Jul 2017 Last revised: 19 Dec 2017

See all articles by Christian P. Fries

Christian P. Fries

Ludwig Maximilian University of Munich (LMU) - Faculty of Mathematics; DZ Bank AG

Date Written: June 27, 2017

Abstract

In this note we derive a modified backward automatic differentiation (a.k.a. adjoint automatic differentiation, adjoint algorithmic differentiation) for algorithms containing conditional expectation operators and/or indicator functions. Bermudan option and xVA valuation are prototypical examples. We consider the Bermudan product valuation, but the method is applicable in full generality.

Featuring a clean and simple implementation, the method improves accuracy and performance.

For conditional expectation operators it offers the ability to use different estimators in the valuation and the differentiation.

For the indicator function, the method allows to use "per-operator"-differentiation of the indicator function, enabling an accurate treatment of each individual exercise boundary - which is not possible in a classic finite difference applied to the Bermudan valuation.

Keywords: Monte-Carlo Simulation, Automatic Differentiation, Adjoint Automatic Differentiation, Algorithmic Differentiation, AAD American Monte-Carlo, Bermudan Callables, Conditional Expectation, Exercise Boundary

JEL Classification: C15, G13

Suggested Citation

Fries, Christian P., Automatic Backward Differentiation for American Monte-Carlo Algorithms - ADD for Conditional Expectations and Indicator Functions (June 27, 2017). Available at SSRN: https://ssrn.com/abstract=3000822 or http://dx.doi.org/10.2139/ssrn.3000822

Christian P. Fries (Contact Author)

Ludwig Maximilian University of Munich (LMU) - Faculty of Mathematics ( email )

Theresienstrasse 39
Munich
Germany

DZ Bank AG ( email )

60265 Frankfurt am Main
Germany

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