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A Measure-Valued Differentiation Approach to Sensitivity Analysis of Quantiles

Author

Listed:
  • Bernd Heidergott

    (VU University Amsterdam)

  • Warren Volk-Makarewicz

    (VU University Amsterdam)

Abstract

This discussion paper led to a publication in 'Mathematics of Operations Research' . Quantiles play an important role in modelling quality of service in the service industry and in modelling risk in the financial industry. Recently, Hong showed in his breakthrough papers that efficient simulation based estimators can be obtained for quantile sensitivities by means of sample path differentiation. This has led to an intensive search for sample-path differentiation based estimators for quantile sensitivities. In this paper we present a novel approach to quantile sensitivity estimation. Our approach elaborates on the concept of measure-valued differentiation (MVD). Thereby, we overcome the main obstacle of the sample path approach which is the requirement that the sample cost have to be Lipschitz continuous with respect to the parameter of interest. Specifically, we perform a sensitivity analysis of the quantile of the value of a multi-asset option and a portfolio. In addition, we discuss application of our sensitivity estimator to the Variance-Gamma process and to queueing networks.

Suggested Citation

  • Bernd Heidergott & Warren Volk-Makarewicz, 2013. "A Measure-Valued Differentiation Approach to Sensitivity Analysis of Quantiles," Tinbergen Institute Discussion Papers 13-082/III, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20130082
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    File URL: https://papers.tinbergen.nl/13082.pdf
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    References listed on IDEAS

    as
    1. Dilip B. Madan & Peter P. Carr & Eric C. Chang, 1998. "The Variance Gamma Process and Option Pricing," Review of Finance, European Finance Association, vol. 2(1), pages 79-105.
    2. Sen, Pranab Kumar, 1972. "On the Bahadur representation of sample quantiles for sequences of [phi]-mixing random variables," Journal of Multivariate Analysis, Elsevier, vol. 2(1), pages 77-95, March.
    3. L. Jeff Hong, 2009. "Estimating Quantile Sensitivities," Operations Research, INFORMS, vol. 57(1), pages 118-130, February.
    4. Nielsen, Lars Tyge, 1999. "Pricing and Hedging of Derivative Securities," OUP Catalogue, Oxford University Press, number 9780198776192.
    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.
    6. Michael C. Fu & L. Jeff Hong & Jian-Qiang Hu, 2009. "Conditional Monte Carlo Estimation of Quantile Sensitivities," Management Science, INFORMS, vol. 55(12), pages 2019-2027, December.
    7. L. Jeff Hong & Guangwu Liu, 2010. "Pathwise Estimation of Probability Sensitivities Through Terminating or Steady-State Simulations," Operations Research, INFORMS, vol. 58(2), pages 357-370, April.
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    Cited by:

    1. Bernd Heidergott & Warren Volk-Makarewicz, 2016. "A Measure-Valued Differentiation Approach to Sensitivities of Quantiles," Mathematics of Operations Research, INFORMS, vol. 41(1), pages 293-317, February.

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    More about this item

    Keywords

    quantile; sensitivity analysis; Monte-Carlo simulation; measure-valued differentiation; options; multi-asset option; Variance-Gamma process;
    All these keywords.

    JEL classification:

    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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