A Generalized Weighted Monte Carlo Calibration Method for Derivative Pricing

Hilmar Gudmundsson and David Vyncke
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Hilmar Gudmundsson: Department of Applied Mathematics, Computer Science and Statistics, Ghent University, Krijgslaan 281-S9, B-9000 Ghent, Belgium
David Vyncke: Department of Applied Mathematics, Computer Science and Statistics, Ghent University, Krijgslaan 281-S9, B-9000 Ghent, Belgium

Mathematics, 2021, vol. 9, issue 7, 1-22

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.

Keywords: option pricing; model calibration; weighted Monte Carlo (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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