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The performance of VIX option pricing models: Empirical evidence beyond simulation

Authors


  • An earlier version of this study was presented at the 2008 Financial Management Meetings in Dallas. We thank the editor (Bob Webb) for extensive suggestions on how to best improve this study. We also thank the two referees and Robert Kozarski for their comments that helped clarify the presentation of this study.

Abstract

We examine the pricing performance of VIX option models. Such models possess a wide-range of underlying characteristics regarding the behavior of both the S&P500 index and the underlying VIX. Our tests employ three representative models for VIX options: Whaley (1993), Grunbichler and Longstaff (1996), Carr and Lee (2007), Lin and Chang (2009), who test four stochastic volatility models, as well as to previous simulation results of VIX option models. We find that no model has small pricing errors over the entire range of strike prices and times to expiration. In particular, out-of-the-money VIX options are difficult to price, with Grunbichler and Longstaff's mean-reverting model producing the smallest dollar errors in this category. Whaley's Black-like option model produces the best results for in-the-money VIX options. However, the Whaley model does under/overprice out-of-the-money call/put VIX options, which is opposite the behavior of stock index option pricing models. VIX options exhibit a volatility skew opposite the skew of index options. © 2010 Wiley Periodicals, Inc. Jrl Fut Mark31:251–281, 2011

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