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Monte Carlo Sensitivities Using the Absolute Measure-Valued Derivative Method

Author

Listed:
  • Mark Joshi

    (Centre for Actuarial Studies, University of Melbourne, Parkville, VIC 3010, Australia
    This paper is dedicated to the memory of Mark Joshi who passed away unexpectedly.)

  • 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
    Trinity College, University of Cambridge, Cambridge CB2 1TQ, UK)

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.

Suggested Citation

  • Mark Joshi & Oh Kang Kwon & Stephen Satchell, 2023. "Monte Carlo Sensitivities Using the Absolute Measure-Valued Derivative Method," JRFM, MDPI, vol. 16(12), pages 1-24, December.
    • Handle: RePEc:gam:jjrfmx:v:16:y:2023:i:12:p:509-:d:1296230
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    References listed on IDEAS

    as
    1. Jiun Hong Chan & Mark Joshi, 2015. "Optimal limit methods for computing sensitivities of discontinuous integrals including triggerable derivative securities," IISE Transactions, Taylor & Francis Journals, vol. 47(9), pages 978-997, September.
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