Back to the Future: Comparing Forward and Backward Differentiation for Forward Sensitivities in Monte-Carlo Simulations

12 Pages Posted: 26 Jan 2018 Last revised: 31 Jan 2018

See all articles by Christian P. Fries

Christian P. Fries

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

Date Written: January 16, 2018

Abstract

We derive representations for forward sensitivities (also known as future sensitivities) in a Monte-Carlo simulation suitable for backward and forward differentiation. We compare the performance of the two approaches.

The calculation of all forward sensitivities of a Monte-Carlo simulation with n paths, m time-steps and r risk factors requires in forward mode r valuations ad r×m conditional expectation (given that the value process is Markovian), and in backward mode 1 valuation and m conditional expectation.

There is no additional scaling in the number of path n.

Keywords: Automatic Differentiation, Adjoint Automatic Differentiation, Forward Sensitivities

JEL Classification: C15, G13, C63

Suggested Citation

Fries, Christian P., Back to the Future: Comparing Forward and Backward Differentiation for Forward Sensitivities in Monte-Carlo Simulations (January 16, 2018). Available at SSRN: https://ssrn.com/abstract=3106068 or http://dx.doi.org/10.2139/ssrn.3106068

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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