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

73 citations0/0 files storedJournal of Futures Markets

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Stochastic processes and financial applications Financial Markets and Investment Strategies Financial Risk and Volatility Modeling

Abstract

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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References

1973The Pricing of Options and Corporate Liabilities 1993A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options 1985A Theory of the Term Structure of Interest Rates 1987The Pricing of Options on Assets with Stochastic Volatilities 1976The pricing of commodity contracts 2000Transform Analysis and Asset Pricing for Affine Jump-diffusions 1997Empirical Performance of Alternative Option Pricing Models 2002The jump-risk premia implicit in options: evidence from an integrated time-series study

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