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Revisiting variance gamma pricing: An application to S&P500 index options

Author

Listed:
  • Sharif Mozumder

    (Department of Mathematics, University of Dhaka, Dhaka, Bangladesh)

  • Ghulam Sorwar

    (Salford Business School, Lady Hale Building, Salford M5 4WT, United Kingdom)

  • Kevin Dowd

    (Durham Business School, Mill Hill Lane, Durham DH1 3LB, United Kingdom)

Abstract

This paper reformulates the Lévy–Kintchine formula to make it suitable for modeling the stochastic time-changing effects of Lévy processes. Using the variance gamma (VG) process as an example, it illustrates the dynamic properties of a Lévy process and revisits the earlier work of Geman (2002). It also shows how the model can be calibrated to price options under a Lévy VG process, and calibrates the model on recent S&P500 index options data. It then compares the pricing performance of fast Fourier transform (FFT) and fractional Fourier transform (FRFT) approaches to model calibration and investigates the trade-off between calibration performance and required calculation time.

Suggested Citation

  • Sharif Mozumder & Ghulam Sorwar & Kevin Dowd, 2015. "Revisiting variance gamma pricing: An application to S&P500 index options," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 2(02), pages 1-24.
    • Handle: RePEc:wsi:ijfexx:v:02:y:2015:i:02:n:s242478631550022x
    DOI: 10.1142/S242478631550022X
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    Citations

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    Cited by:

    1. Roman V. Ivanov, 2018. "A Credit-Risk Valuation under the Variance-Gamma Asset Return," Risks, MDPI, vol. 6(2), pages 1-25, May.
    2. A. H. Nzokem, 2022. "Pricing European Options under Stochastic Volatility Models: Case of five-Parameter Variance-Gamma Process," Papers 2201.03378, arXiv.org, revised Jan 2023.
    3. Sharif Mozumder & Bakhtear Talukdar & M. Humayun Kabir & Bingxin Li, 2024. "Non-linear volatility with normal inverse Gaussian innovations: ad-hoc analytic option pricing," Review of Quantitative Finance and Accounting, Springer, vol. 62(1), pages 97-133, January.
    4. Roman V. Ivanov, 2023. "On the Stochastic Volatility in the Generalized Black-Scholes-Merton Model," Risks, MDPI, vol. 11(6), pages 1-23, June.
    5. A. H. Nzokem, 2023. "European Option Pricing Under Generalized Tempered Stable Process: Empirical Analysis," Papers 2304.06060, arXiv.org, revised Aug 2023.
    6. Roman V. Ivanov, 2018. "Option Pricing In The Variance-Gamma Model Under The Drift Jump," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(04), pages 1-19, June.
    7. Aubain Hilaire Nzokem, 2023. "Pricing European Options under Stochastic Volatility Models: Case of Five-Parameter Variance-Gamma Process," JRFM, MDPI, vol. 16(1), pages 1-28, January.

    More about this item

    Keywords

    Variance gamma process; infinitely divisible distribution; fast Fourier transform; fractional Fourier transform; C02; G13;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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