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A Generalized Weighted Monte Carlo Calibration Method for Derivative Pricing

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  • Hilmar Gudmundsson

    (Department of Applied Mathematics, Computer Science and Statistics, Ghent University, Krijgslaan 281-S9, B-9000 Ghent, Belgium
    Verna, Ármúli 13, 108 Reykjavík, Iceland)

  • David Vyncke

    (Department of Applied Mathematics, Computer Science and Statistics, Ghent University, Krijgslaan 281-S9, B-9000 Ghent, Belgium)

Abstract

The weighted Monte Carlo method is an elegant technique to calibrate asset pricing models to market prices. Unfortunately, the accuracy can drop quite quickly for out-of-sample options as one moves away from the strike range and maturity range of the benchmark options. To improve the accuracy, we propose a generalized version of the weighted Monte Carlo calibration method with two distinguishing features. First, we use a probability distortion scheme to produce a non-uniform prior distribution for the simulated paths. Second, we assign multiple weights per path to fit with the different maturities present in the set of benchmark options. Our tests on S&P500 options data show that the new calibration method proposed here produces a significantly better out-of-sample fit than the original method for two commonly used asset pricing models.

Suggested Citation

  • Hilmar Gudmundsson & David Vyncke, 2021. "A Generalized Weighted Monte Carlo Calibration Method for Derivative Pricing," Mathematics, MDPI, vol. 9(7), pages 1-22, March.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:7:p:739-:d:526062
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    References listed on IDEAS

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    1. Jürgen Vandenbroucke, 2015. "A Cumulative Prospect View on Portfolios that Hold Structured Products," Journal of Behavioral Finance, Taylor & Francis Journals, vol. 16(4), pages 297-310, October.
    2. Polkovnichenko, Valery & Zhao, Feng, 2013. "Probability weighting functions implied in options prices," Journal of Financial Economics, Elsevier, vol. 107(3), pages 580-609.
    3. Tversky, Amos & Kahneman, Daniel, 1992. "Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
    4. Leif Andersen & Jesper Andreasen, 2000. "Jump-Diffusion Processes: Volatility Smile Fitting and Numerical Methods for Option Pricing," Review of Derivatives Research, Springer, vol. 4(3), pages 231-262, October.
    5. Fox, Craig R & Rogers, Brett A & Tversky, Amos, 1996. "Options Traders Exhibit Subadditive Decision Weights," Journal of Risk and Uncertainty, Springer, vol. 13(1), pages 5-17, July.
    6. Ludvigson, Sydney C., 2013. "Advances in Consumption-Based Asset Pricing: Empirical Tests," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, volume 2, chapter 0, pages 799-906, Elsevier.
    7. 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.
    8. Manfred Gilli & Enrico Schumann, 2010. "Calibrating Option Pricing Models with Heuristics," Working Papers 030, COMISEF.
    9. Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," The Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 69-107.
    10. Bjørn Eraker & Michael Johannes & Nicholas Polson, 2003. "The Impact of Jumps in Volatility and Returns," Journal of Finance, American Finance Association, vol. 58(3), pages 1269-1300, June.
    11. Marco Avellaneda & Robert Buff & Craig Friedman & Nicolas Grandechamp & Lukasz Kruk & Joshua Newman, 2001. "Weighted Monte Carlo: A New Technique For Calibrating Asset-Pricing Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 4(01), pages 91-119.
    12. Drazen Prelec, 1998. "The Probability Weighting Function," Econometrica, Econometric Society, vol. 66(3), pages 497-528, May.
    13. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    14. Rubinstein, Mark, 1994. "Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
    15. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
    16. Nicholas Barberis, 2013. "The Psychology of Tail Events: Progress and Challenges," American Economic Review, American Economic Association, vol. 103(3), pages 611-616, May.
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