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

Sharif Mozumder (), Ghulam Sorwar () and Kevin Dowd ()
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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

International Journal of Financial Engineering (IJFE), 2015, vol. 02, issue 02, 1-24

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.

Keywords: Variance gamma process; infinitely divisible distribution; fast Fourier transform; fractional Fourier transform; C02; G13 (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (7)

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DOI: 10.1142/S242478631550022X

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