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Pricing options with VG model using FFT

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  • Andrey Itkin

Abstract

We discuss various analytic and numerical methods that have been used to get option prices within a framework of the VG model. We show that some popular methods, for instance, Carr-Madan's FFT method could blow up for certain values of the model parameters even for an European vanilla option. Alternative methods - one originally proposed by Lewis, and Black-Scholes-wise method are considered that seem to work fine for any value of the VG parameters. Test examples are given to demonstrate efficiency of these methods. Convergency of all methods is also discussed.}

Suggested Citation

  • Andrey Itkin, 2005. "Pricing options with VG model using FFT," Papers physics/0503137, arXiv.org, revised Jan 2010.
    • Handle: RePEc:arx:papers:physics/0503137
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    References listed on IDEAS

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    1. Dilip B. Madan & Peter P. Carr & Eric C. Chang, 1998. "The Variance Gamma Process and Option Pricing," Review of Finance, European Finance Association, vol. 2(1), pages 79-105.
    2. Alan L. Lewis, 2000. "Option Valuation under Stochastic Volatility," Option Valuation under Stochastic Volatility, Finance Press, number ovsv, December.
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    Cited by:

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    3. Ricardo Crisóstomo, 2017. "Speed and biases of Fourier-based pricing choices: Analysis of the Bates and Asymmetric Variance Gamma models," CNMV Working Papers CNMV Working Papers no. 6, CNMV- Spanish Securities Markets Commission - Research and Statistics Department.
    4. Tat Lung Chan, 2017. "Singular Fourier-Pad\'e Series Expansion of European Option Prices," Papers 1706.06709, arXiv.org, revised Nov 2017.
    5. Ricardo Crisóstomo, 2021. "Estimating real‐world probabilities: A forward‐looking behavioral framework," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 41(11), pages 1797-1823, November.

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