Automatic Differentiation for Diffusion Operator Integral Variance Reduction

26 Pages Posted: 4 Dec 2020 Last revised: 12 Jul 2021

See all articles by Johan Auster

Johan Auster

University of Copenhagen - Department of Mathematical Sciences

Date Written: November 18, 2020

Abstract

This paper demonstrates applications of automatic differentiation with nested dual numbers in the diffusion operator integral variance reduction framework originally proposed by Heath and Platen. Combining this estimator with automatic differentiation techniques for computing value function sensitivities allows for a flexible implementation without trade-offs in numerical stability or accuracy. This fully mitigates a key practical shortcoming of the original estimator, as we remove the dependency on error-prone and problem-specific manual calculations. We perform a relative error analysis of the estimator and standard Monte Carlo estimation against the numerical integration solution of the European call option in the Heston model and find computational time savings in excess of three orders of magnitude for the same expected relative errors for an at-the-money option. The implementation is further extended to the valuation of discrete down-and-out barrier call options and floating-strike lookback put options, demonstrating the relative ease of applying the automatic differentiation approach to path-dependent options with monitoring bias corrections.

Keywords: Monte Carlo, Automatic Differentiation, Variance Reduction, Heston Model, Barrier Options, Lookback Options, Monitoring Bias

JEL Classification: C63, C65, G12

Suggested Citation

Auster, Johan, Automatic Differentiation for Diffusion Operator Integral Variance Reduction (November 18, 2020). Available at SSRN: https://ssrn.com/abstract=3733041 or http://dx.doi.org/10.2139/ssrn.3733041

Johan Auster (Contact Author)

University of Copenhagen - Department of Mathematical Sciences ( email )

Universitetsparken 5
Copenhagen, DK-2100
Denmark

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