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Optimal Limit Methods for Computing Sensitivities of

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  • Jiun Hong Chan and Mark Joshi

Abstract

We introduce a new approach to computing sensitivities of discontinuous integrals.The methodology is generic in that it only requires knowledge of the simulation scheme and the location of the integrand's singularities. The methodology is proven to be optimal in terms of minimizing the variance of the measure changes caused by the elimination of the discontinuities for finite bump sizes. An efficient adjoint implementation of the small bump-size limit is discussed, and the method is shown to be effective for a number of natural examples involving triggerable interest rate derivative securities.

Suggested Citation

  • Jiun Hong Chan and Mark Joshi, 2012. "Optimal Limit Methods for Computing Sensitivities of," Department of Economics - Working Papers Series 1142, The University of Melbourne.
    • Handle: RePEc:mlb:wpaper:1142
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    File URL: http://fbe.unimelb.edu.au/economics/research/workingpapers
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    References listed on IDEAS

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    1. Joshi, Mark & Yang, Chao, 2011. "Fast delta computations in the swap-rate market model," Journal of Economic Dynamics and Control, Elsevier, vol. 35(5), pages 764-775, May.
    2. Mark Broadie & Paul Glasserman, 1996. "Estimating Security Price Derivatives Using Simulation," Management Science, INFORMS, vol. 42(2), pages 269-285, February.
    3. Eric Benhamou, 2003. "Optimal Malliavin Weighting Function for the Computation of the Greeks," Mathematical Finance, Wiley Blackwell, vol. 13(1), pages 37-53, January.
    4. Christian P. Fries & Mark S. Joshi, 2011. "Perturbation Stable Conditional Analytic Monte-Carlo Pricing Scheme For Auto-Callable Products," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 14(02), pages 197-219.
    5. Heidergott, Bernd & Vazquez-Abad, Felisa J. & Volk-Makarewicz, Warren, 2008. "Sensitivity estimation for Gaussian systems," European Journal of Operational Research, Elsevier, vol. 187(1), pages 193-207, May.
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    Cited by:

    1. Frazier, David T. & Oka, Tatsushi & Zhu, Dan, 2019. "Indirect inference with a non-smooth criterion function," Journal of Econometrics, Elsevier, vol. 212(2), pages 623-645.
    2. Christian P. Fries, 2018. "Stochastic Algorithmic Differentiation of (Expectations of) Discontinuous Functions (Indicator Functions)," Papers 1811.05741, arXiv.org, revised Nov 2019.

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    Keywords

    Price Sensitivities; Monte-Carlo Greeks; Partial Proxy Simulation Scheme; Minimal Partial;
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