Article

VIX option pricing

Journal of Futures Markets (Impact Factor: 0.46). 06/2009; 29(6):523 - 543. DOI: 10.1002/fut.20387

ABSTRACT Substantial progress has been made in developing more realistic option pricing models for S&P 500 index (SPX) options. Empirically, however, it is not known whether and by how much each generalization of SPX price dynamics improves VIX option pricing. This article fills this gap by first deriving a VIX option model that reconciles the most general price processes of the SPX in the literature. The relative empirical performance of several models of distinct interest is examined. Our results show that state-dependent price jumps and volatility jumps are important for pricing VIX options. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 29:523–543, 2009

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    ABSTRACT: Y.-N. Lin and C.-H. Chang [“VIX option pricing”, J. Futures Markets 29, No. 6, 523–543; J. Econ. Dyn. Control 34, No. 11, 2302–2319 (2010; Zbl 1201.91202)] establish a VIX futures and option pricing theory when modeling S&P 500 index by using a stochastic volatility process with asset return and volatility jumps. In this note, we prove that Lin and Chang’s formula is not an exact solution of their pricing equation. More generally, we show that the characteristic function of their pricing equation cannot be exponentially affine, as proposed by them. Furthermore, their formula cannot serve as a reasonable approximation. Using the S. L. Heston model [“A closed-form solution for options with stochastic volatility with applications to bond and currency options”, Rev. Financ. Stud. 6, No. 2, 327–343 (1993; doi:10.1093/rfs/6.2.327)] as a special case, we demonstrate that the Lin and Chang formula misprices VIX futures and options in general and the error can become substantially large.
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    ABSTRACT: This study presents an analytical exact solution for the price of VIX options under stochastic volatility model with simultaneous jumps in the asset price and volatility processes. We shall demonstrate that our new pricing formula can be used to efficiently compute the numerical values of a VIX option. While we also show that the numerical results obtained from our formula consistently match those obtained from Monte Carlo simulation perfectly as a verification of the correctness of our formula, numerical evidence is offered to illustrate that the correctness of the formula proposed in Lin & Chang (2009) is in serious doubt. Moreover, some important and distinct properties of VIX options (e.g., put-call parity, hedging ratios) are also examined and discussed.
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