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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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