Monte Carlo Sensitivities Using the Absolute Measure-Valued Derivative Method

Mark Joshi, Oh Kang Kwon () and Stephen Satchell
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Mark Joshi: Centre for Actuarial Studies, University of Melbourne, Parkville, VIC 3010, Australia
Oh Kang Kwon: Discipline of Finance, Codrington Building (H69), The University of Sydney, Sydney, NSW 2006, Australia
Stephen Satchell: Discipline of Finance, Codrington Building (H69), The University of Sydney, Sydney, NSW 2006, Australia

JRFM, 2023, vol. 16, issue 12, 1-24

Abstract: Measure-valued differentiation (MVD) is a relatively new method for computing Monte Carlo sensitivities, relying on a decomposition of the derivative of transition densities of the underlying process into a linear combination of probability measures. In computing the sensitivities, additional paths are generated for each constituent distribution and the payoffs from these paths are combined to produce sample estimates. The method generally produces sensitivity estimates with lower variance than the finite difference and likelihood ratio methods, and can be applied to discontinuous payoffs in contrast to the pathwise differentiation method. However, these benefits come at the expense of an additional computational burden. In this paper, we propose an alternative approach, called the absolute measure-valued differentiation (AMVD) method, which expresses the derivative of the transition density at each simulation step as a single density rather than a linear combination. It is computationally more efficient than the MVD method and can result in sensitivity estimates with lower variance. Analytic and numerical examples are provided to compare the variance in the sensitivity estimates of the AMVD method against alternative methods.

Keywords: measure-valued differentiation; sensitivities; Greeks; Monte Carlo simulation (search for similar items in EconPapers)
JEL-codes: C E F2 F3 G (search for similar items in EconPapers)
Date: 2023
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