Stochastic Automatic Differentiation - AAD for Monte-Carlo Simulations (Presentation at the 13th Fixed Income Conference) (Presentation Slides)

129 Pages Posted: 29 Nov 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: October 20, 2017

Abstract

The presentation illustrates the theory and application of a Stochastic Automatic Differentiation (Stochastic Algorithmic Differentiation).

The Stochastic Automatic Differentiation allows to improve performance and reduce the memory requirements of an AD algorithm by exploiting the stochastic nature of the random variables.

Considering an Expected Stochastic Automatic Differentiation we can give a modified AD algorithm which allows efficient adjoint (backward) automatic differentiation of evaluations containing non-pathwise operators like the conditional expectation operator.

The algorithm can be applied to calculate forward sensitivities, i.e.~differentiation with respect to stochastic intermediate (future) values. This can be used for the efficient calculation of MVAs in finance.

The implementation can be performed using only few additional lines of code. We provide source code and numerical examples.

Keywords: Monte-Carlo Simulation, Automatic Differentiation, Adjoint Automatic Differentiation, American Monte-Carlo, Bermudan Callables, Conditional Expectation, Forward Sensitivities, Initial Margin, MVA

JEL Classification: C15, G13

Suggested Citation

Fries, Christian P., Stochastic Automatic Differentiation - AAD for Monte-Carlo Simulations (Presentation at the 13th Fixed Income Conference) (Presentation Slides) (October 20, 2017). Available at SSRN: https://ssrn.com/abstract=3077197 or http://dx.doi.org/10.2139/ssrn.3077197

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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