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

Mozumder, S; Sorwar, G

Abstract

We reformulate the Lévy-Kintchine formula to make it suitable for modelling the stochastic time-changing effects of Lévy processes. Using 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.

Citation

Mozumder, S., & Sorwar, G. (2015). Revisiting variance gamma pricing : an application to S&P500 index options. International journal of financial engineering (Print), 2(2), #1550022. https://doi.org/10.1142/s242478631550022x

• Journal Article Type: Article
• Acceptance Date: May 12, 2015
• Publication Date: Jun 19, 2015
• Deposit Date: Jun 10, 2015
• Publicly Available Date: Oct 15, 2018
• Journal: International Journal of Financial Engineering
• Print ISSN: 2424-7863
• Publisher: World Scientific Publishing
• Peer Reviewed: Peer Reviewed
• Volume: 2
• Issue: 2
• Pages: #1550022
• DOI: https://doi.org/10.1142/s242478631550022x
• Publisher URL: http://dx.doi.org/10.1142/s242478631550022x
• Related Public URLs: http://www.worldscientific.com/worldscinet/ijfe