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
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: Suggested Citation