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

Mozumder, Sharif; Sorwar, Ghulam; Dowd, Kevin

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.

Citation

Mozumder, S., Sorwar, G., & Dowd, K. (2015). Revisiting variance gamma pricing: An application to S&P500 index options. International Journal of Financial Engineering, 02(02), Article 1550022. https://doi.org/10.1142/s242478631550022x

• Journal Article Type: Article
• Publication Date: 2015-06
• Deposit Date: Sep 13, 2024
• Journal: International Journal of Financial Engineering
• Print ISSN: 2424-7863
• Electronic ISSN: 2424-7944
• Publisher: World Scientific Publishing
• Peer Reviewed: Peer Reviewed
• Volume: 02
• Issue: 02
• Article Number: 1550022
• DOI: https://doi.org/10.1142/s242478631550022x
• Public URL: https://durham-repository.worktribe.com/output/2863406