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Optimal limit methods for computing sensitivities of discontinuous integrals including triggerable derivative securities

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  • Jiun Hong Chan
  • Mark Joshi

Abstract

We introduce an 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. For piecewise constant payoffs this minimizes the variance of Monte Carlo sensitivities. An efficient adjoint implementation is discussed, and the method is shown to be effective for a number of natural financial examples including double barrier options and triggerable interest rate derivative securities.

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  • 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.
    • Handle: RePEc:taf:uiiexx:v:47:y:2015:i:9:p:978-997
    DOI: 10.1080/0740817X.2014.998390
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    Cited by:

    1. Roberto Daluiso, 2023. "Fast and Stable Credit Gamma of CVA," Papers 2311.11672, arXiv.org.
    2. Joshi, Mark S. & Zhu, Dan, 2016. "An exact method for the sensitivity analysis of systems simulated by rejection techniques," European Journal of Operational Research, Elsevier, vol. 254(3), pages 875-888.
    3. 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.
    4. 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.

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