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A New Stochastic Derivative Estimator for Discontinuous Payoff Functions with Application to Financial Derivatives

Author

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  • Yongqiang Wang

    (Department of Electrical and Computer Engineering and Institute for Systems Research, University of Maryland, College Park, Maryland 20742)

  • Michael C. Fu

    (The Robert H. Smith School of Business and Institute for Systems Research, University of Maryland, College Park, Maryland 20742)

  • Steven I. Marcus

    (Department of Electrical and Computer Engineering and Institute for Systems Research, University of Maryland, College Park, Maryland 20742)

Abstract

Motivated by infinitesimal perturbation analysis (IPA) and the likelihood ratio (LR) method, we derive a new unbiased stochastic derivative estimator for a class of discontinuous payoff functions that arise in many options pricing settings from finance. Our method includes IPA and the LR method as special cases and can be applied to functions of more general forms containing indicator functions. This new estimator can be computed from a single sample path or simulation, whereas existing estimators generally require additional simulations for the class of discontinuous payoff functions considered here. We apply this method to sensitivity analysis for European call options and American-style call options, and numerical experiments indicate that the estimator is computationally more efficient than other estimators.

Suggested Citation

  • Yongqiang Wang & Michael C. Fu & Steven I. Marcus, 2012. "A New Stochastic Derivative Estimator for Discontinuous Payoff Functions with Application to Financial Derivatives," Operations Research, INFORMS, vol. 60(2), pages 447-460, April.
    • Handle: RePEc:inm:oropre:v:60:y:2012:i:2:p:447-460
    DOI: 10.1287/opre.1110.1018
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    References listed on IDEAS

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    2. Alphonse Hakizimana & Joseph K. Scott, 2017. "Differentiability Conditions for Stochastic Hybrid Systems with Application to the Optimal Design of Microgrids," Journal of Optimization Theory and Applications, Springer, vol. 173(2), pages 658-682, May.
    3. Yijie Peng & Michael C. Fu & Jian-Qiang Hu, 2016. "Gradient-based simulated maximum likelihood estimation for stochastic volatility models using characteristic functions," Quantitative Finance, Taylor & Francis Journals, vol. 16(9), pages 1393-1411, September.
    4. Peter W. Glynn & Yijie Peng & Michael C. Fu & Jian-Qiang Hu, 2021. "Computing Sensitivities for Distortion Risk Measures," INFORMS Journal on Computing, INFORMS, vol. 33(4), pages 1520-1532, October.
    5. Secomandi, Nicola & Seppi, Duane J., 2014. "Real Options and Merchant Operations of Energy and Other Commodities," Foundations and Trends(R) in Technology, Information and Operations Management, now publishers, vol. 6(3-4), pages 161-331, July.
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    8. Shaolong Tong & Guangwu Liu, 2016. "Importance Sampling for Option Greeks with Discontinuous Payoffs," INFORMS Journal on Computing, INFORMS, vol. 28(2), pages 223-235, May.

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