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A model-free approach to multivariate option pricing

Author

Listed:
  • Carole Bernard

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

  • Oleg Bondarenko

    (University of Illinois at Chicago (UIC))

  • Steven Vanduffel

    (Vrije Universiteit Brussel (VUB))

Abstract

We propose a novel model-free approach to extract a joint multivariate distribution, which is consistent with options written on individual stocks as well as on various available indices. To do so, we first use the market prices of traded options to infer the risk-neutral marginal distributions for the stocks and the linear combinations given by the indices and then apply a new combinatorial algorithm to find a compatible joint distribution. Armed with the joint distribution, we can price general path-independent multivariate options.

Suggested Citation

  • Carole Bernard & Oleg Bondarenko & Steven Vanduffel, 2021. "A model-free approach to multivariate option pricing," Review of Derivatives Research, Springer, vol. 24(2), pages 135-155, July.
    • Handle: RePEc:kap:revdev:v:24:y:2021:i:2:d:10.1007_s11147-020-09172-2
    DOI: 10.1007/s11147-020-09172-2
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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. Benjamin Jourdain & Mohamed Sbai, 2012. "Coupling index and stocks," Quantitative Finance, Taylor & Francis Journals, vol. 12(5), pages 805-818, March.
    3. David Hobson & Peter Laurence & Tai-Ho Wang, 2005. "Static-arbitrage upper bounds for the prices of basket options," Quantitative Finance, Taylor & Francis Journals, vol. 5(4), pages 329-342.
    4. Stutzer, Michael, 1996. "A Simple Nonparametric Approach to Derivative Security Valuation," Journal of Finance, American Finance Association, vol. 51(5), pages 1633-1652, December.
    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. Bondarenko, Oleg, 2003. "Estimation of risk-neutral densities using positive convolution approximation," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 85-112.
    7. 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.
    8. Ian Martin, 2017. "What is the Expected Return on the Market?," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 132(1), pages 367-433.
    9. Carole Bernard & Ludger Rüschendorf & Steven Vanduffel, 2017. "Value-at-Risk Bounds With Variance Constraints," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 84(3), pages 923-959, September.
    10. Kris Boudt & Edgars Jakobsons & Steven Vanduffel, 2018. "Block rearranging elements within matrix columns to minimize the variability of the row sums," 4OR, Springer, vol. 16(1), pages 31-50, March.
    11. Embrechts, Paul & Puccetti, Giovanni & Rüschendorf, Ludger, 2013. "Model uncertainty and VaR aggregation," Journal of Banking & Finance, Elsevier, vol. 37(8), pages 2750-2764.
    12. Rama Cont & Romain Deguest, 2013. "Equity Correlations Implied By Index Options: Estimation And Model Uncertainty Analysis," Post-Print hal-00835272, HAL.
    13. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
    14. Laura Ballotta & Efrem Bonfiglioli, 2016. "Multivariate asset models using Lévy processes and applications," The European Journal of Finance, Taylor & Francis Journals, vol. 22(13), pages 1320-1350, October.
    15. Stephen A. Ross, 1976. "Options and Efficiency," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 90(1), pages 75-89.
    16. Justel, Ana & Peña, Daniel & Zamar, Rubén, 1997. "A multivariate Kolmogorov-Smirnov test of goodness of fit," Statistics & Probability Letters, Elsevier, vol. 35(3), pages 251-259, October.
    17. Wang, Bin & Wang, Ruodu, 2011. "The complete mixability and convex minimization problems with monotone marginal densities," Journal of Multivariate Analysis, Elsevier, vol. 102(10), pages 1344-1360, November.
    18. Carole Bernard & Don McLeish, 2016. "Algorithms for Finding Copulas Minimizing Convex Functions of Sums," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 33(05), pages 1-26, October.
    19. Ballotta, Laura & Fusai, Gianluca & Loregian, Angela & Perez, M. Fabricio, 2019. "Estimation of Multivariate Asset Models with Jumps," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 54(5), pages 2053-2083, October.
    20. Justel, Ana & Peña, Daniel & Zamar, Rubén, 1997. "A multivariate Kolmogorov-Smirnov test of goodness of fit," Statistics & Probability Letters, Elsevier, vol. 35(3), pages 251-259, October.
    21. Carole Bernard & Oleg Bondarenko & Steven Vanduffel, 2018. "Rearrangement algorithm and maximum entropy," Annals of Operations Research, Springer, vol. 261(1), pages 107-134, February.
    22. Chen, X. & Deelstra, G. & Dhaene, J. & Vanmaele, M., 2008. "Static super-replicating strategies for a class of exotic options," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 1067-1085, June.
    23. Rubinstein, Mark, 1994. "Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
    24. Stephen Figlewski, 2018. "Risk-Neutral Densities: A Review," Annual Review of Financial Economics, Annual Reviews, vol. 10(1), pages 329-359, November.
    25. 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.
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