VIX option pricing

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


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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    • "Carr and Lee's (2007) results resemble those from Whaley's model in terms of their patterns of errors, although the Carr and Lee results are inferior across almost all moneyness and time to expiration categories in terms of both percentage and dollar errors. Comparison of our results of these three models to the Lin and Chang (2009) results show that the models tested here clearly possess smaller errors than the Lin and Chang models. "
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    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.
    Full-text · Article · Mar 2011 · Journal of Futures Markets
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    ABSTRACT: We conduct an extensive empirical analysis of VIX derivative valuation models over the 2004-2007 bull market and the subsequent financial crisis. We show that existing models yield large distortions during the crisis because of their restrictive volatility mean reverting assumptions. We propose generalisations with a time varying central tendency, jumps and stochastic volatility, analyse their pricing performance, and their implications for the term structures of VIX futures and options, and the option volatility "skews". We find that a model combining central tendency and stochastic volatility is required to reliably price VIX futures and options, respectively, across bull and bear markets.
    Preview · Article · Jan 2009 · Journal of Financial Economics
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    ABSTRACT: This study analyses the new market for trading volatility; VIX futures. We first use market data to establish the relationship between VIX futures prices and the index itself. We observe that VIX futures and VIX are highly correlated; the term structure of average VIX futures prices is upward sloping, whereas the term structure of VIX futures volatility is downward sloping. To establish a theoretical relationship between VIX futures and VIX, we model the instantaneous variance using a simple square root mean-reverting process with a stochastic long-term mean level. Using daily calibrated long-term mean and VIX, the model gives good predictions of VIX futures prices under normal market situation. These parameter estimates could be used to price VIX options. © 2010 Wiley Periodicals, Inc. Jrl Fut Mark 30:809–833, 2010
    Full-text · Article · Sep 2010 · Journal of Futures Markets
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