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Implied value-at-risk and model-free simulation

Author

Listed:
  • Carole Bernard

    (Grenoble Ecole de Management (GEM)
    Vrije Universiteit Brussel (VUB))

  • Andrea Perchiazzo

    (Vrije Universiteit Brussel (VUB))

  • Steven Vanduffel

    (Vrije Universiteit Brussel (VUB))

Abstract

We propose a novel model-free approach for extracting the risk-neutral quantile function of an asset using options written on this asset. We develop two applications. First, we show how for a given stochastic asset model our approach makes it possible to simulate the underlying terminal asset value under the risk-neutral probability measure directly from option prices. Specifically, our approach outperforms existing approaches for simulating asset values for stochastic volatility models such as the Heston, the SVI, and the SABR models. Second, we estimate the option implied value-at-risk (VaR) and the option implied tail value-at-risk (TVaR) of a financial asset in a direct manner. We also provide an empirical illustration in which we use S &P 500 Index options to construct an implied VaR Index and we compare it with the VIX Index.

Suggested Citation

  • Carole Bernard & Andrea Perchiazzo & Steven Vanduffel, 2024. "Implied value-at-risk and model-free simulation," Annals of Operations Research, Springer, vol. 336(1), pages 925-943, May.
  • Handle: RePEc:spr:annopr:v:336:y:2024:i:1:d:10.1007_s10479-022-05048-w
    DOI: 10.1007/s10479-022-05048-w
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    References listed on IDEAS

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    1. Ait-Sahalia, Yacine & Lo, Andrew W., 2000. "Nonparametric risk management and implied risk aversion," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 9-51.
    2. Roger Lord & Remmert Koekkoek & Dick Van Dijk, 2010. "A comparison of biased simulation schemes for stochastic volatility models," Quantitative Finance, Taylor & Francis Journals, vol. 10(2), pages 177-194.
    3. Cui, Zhenyu & Kirkby, J. Lars & Nguyen, Duy, 2021. "Efficient simulation of generalized SABR and stochastic local volatility models based on Markov chain approximations," European Journal of Operational Research, Elsevier, vol. 290(3), pages 1046-1062.
    4. Jim Gatheral & Antoine Jacquier, 2014. "Arbitrage-free SVI volatility surfaces," Quantitative Finance, Taylor & Francis Journals, vol. 14(1), pages 59-71, January.
    5. Jackwerth, Jens Carsten & Rubinstein, Mark, 1996. "Recovering Probability Distributions from Option Prices," Journal of Finance, American Finance Association, vol. 51(5), pages 1611-1632, December.
    6. Giovanni Barone‐Adesi & Marinela Adriana Finta & Chiara Legnazzi & Carlo Sala, 2019. "WTI crude oil option implied VaR and CVaR: An empirical application," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 38(6), pages 552-563, September.
    7. Bondarenko, Oleg, 2003. "Estimation of risk-neutral densities using positive convolution approximation," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 85-112.
    8. Breeden, Douglas T & Litzenberger, Robert H, 1978. "Prices of State-contingent Claims Implicit in Option Prices," The Journal of Business, University of Chicago Press, vol. 51(4), pages 621-651, October.
    9. Ning Cai & Yingda Song & Nan Chen, 2017. "Exact Simulation of the SABR Model," Operations Research, INFORMS, vol. 65(4), pages 931-951, August.
    10. Stephen A. Ross, 1976. "Options and Efficiency," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 90(1), pages 75-89.
    11. Christian Kahl & Peter Jackel, 2006. "Fast strong approximation Monte Carlo schemes for stochastic volatility models," Quantitative Finance, Taylor & Francis Journals, vol. 6(6), pages 513-536.
    12. Anthonie W. Van Der Stoep & Lech A. Grzelak & Cornelis W. Oosterlee, 2014. "The Heston Stochastic-Local Volatility Model: Efficient Monte Carlo Simulation," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 17(07), pages 1-30.
    13. Mark Broadie & Özgür Kaya, 2006. "Exact Simulation of Stochastic Volatility and Other Affine Jump Diffusion Processes," Operations Research, INFORMS, vol. 54(2), pages 217-231, April.
    14. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    15. Sovan Mitra, 2015. "The relationship between conditional value at risk and option prices with a closed-form solution," The European Journal of Finance, Taylor & Francis Journals, vol. 21(5), pages 400-425, March.
    16. Bellini, Fabio & Klar, Bernhard & Müller, Alfred & Rosazza Gianin, Emanuela, 2014. "Generalized quantiles as risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 54(C), pages 41-48.
    17. Alexander J. McNeil & Rüdiger Frey & Paul Embrechts, 2015. "Quantitative Risk Management: Concepts, Techniques and Tools Revised edition," Economics Books, Princeton University Press, edition 2, number 10496.
    18. Giovanni Barone‐Adesi & Chiara Legnazzi & Carlo Sala, 2019. "Option‐implied risk measures: An empirical examination on the S&P 500 index," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 24(4), pages 1409-1428, October.
    19. Banz, Rolf W & Miller, Merton H, 1978. "Prices for State-contingent Claims: Some Estimates and Applications," The Journal of Business, University of Chicago Press, vol. 51(4), pages 653-672, October.
    20. Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
    21. Newey, Whitney K & Powell, James L, 1987. "Asymmetric Least Squares Estimation and Testing," Econometrica, Econometric Society, vol. 55(4), pages 819-847, July.
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