An Analytical Formula for VIX Futures and its Applications

Journal of Futures Markets, 2009

25 Pages Posted: 15 Feb 2011

See all articles by Song-Ping Zhu

Song-Ping Zhu

University of Wollongong

Guanghua Lian

University of South Australia - School of Commerce

Date Written: August 15, 2009

Abstract

In this study we present a closed-form, exact solution for the pricing of VIX futures in a stochastic volatility model with simultaneous jumps in both the asset price and volatility processes. The newly derived formula is then used to show that the well-known convexity correction approximations can sometimes lead to large errors. Utilizing the newly derived formula, we also conduct an empirical study, the results of which demonstrate that the Heston stochastic volatility model is a good candidate for the pricing of VIX futures. While incorporating jumps into the underlying price can further improve the pricing of VIX futures, adding jumps to the volatility process appears to contribute little improvement for pricing VIX futures.

Suggested Citation

Zhu, Song-Ping and Lian, Guanghua, An Analytical Formula for VIX Futures and its Applications (August 15, 2009). Journal of Futures Markets, 2009. Available at SSRN: https://ssrn.com/abstract=1762332

Song-Ping Zhu

University of Wollongong ( email )

Northfield Ave.
Wollongong, NSW
Australia
61-2-42213807 (Phone)

Guanghua Lian (Contact Author)

University of South Australia - School of Commerce ( email )

37-44 North Terrace
Adelaide SA 5000, South Australia 5001
Australia

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