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The Shape and Term Structure of the Index Option Smirk: Why Multifactor Stochastic Volatility Models Work so Well

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Author Info
Peter Christoffersen () (McGill University and CREATES)
Steven Heston (R.H. Smith School of Business, University of Maryland)
Kris Jacobs (McGill University and Tilburg University)
Abstract

State-of-the-art stochastic volatility models generate a "volatility smirk" that explains why out-of-the-money index puts have high prices relative to the Black-Scholes benchmark. These models also adequately explain how the volatility smirk moves up and down in response to changes in risk. However, the data indicate that the slope and the level of the smirk fluctuate largely independently. While single-factor stochastic volatility models can capture the slope of the smirk, they cannot explain such largely independent fluctuations in its level and slope over time. We propose to model these movements using a two-factor stochastic volatility model. Because the factors have distinct correlations with market returns, and because the weights of the factors vary over time, the model generates stochastic correlation between volatility and stock returns. Besides providing more flexible modeling of the time variation in the smirk, the model also provides more flexible modeling of the volatility term structure. Our empirical results indicate that the model improves on the benchmark Heston model by 24% in-sample and 23% out-of-sample. The better fit results from improvements in the modeling of the term structure dimension as well as the moneyness dimension.

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Paper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2009-34.

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Length: 41
Date of creation: 17 Jun 2009
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Handle: RePEc:aah:create:2009-34

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Related research
Keywords: Stochastic correlation; stochastic volatility; equity index options; multifactor model; persistence; affine; out-of-sample;

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Find related papers by JEL classification:
G12 - Financial Economics - - General Financial Markets - - - Asset Pricing

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  2. Melino, Angelo & Turnbull, Stuart M., 1990. "Pricing foreign currency options with stochastic volatility," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 239-265. [Downloadable!] (restricted)
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  7. Chernov, Mikhail & Ronald Gallant, A. & Ghysels, Eric & Tauchen, George, 2003. "Alternative models for stock price dynamics," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 225-257. [Downloadable!] (restricted)
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  18. Bakshi, Gurdip & Cao, Charles & Chen, Zhiwu, 1997. " Empirical Performance of Alternative Option Pricing Models," Journal of Finance, American Finance Association, vol. 52(5), pages 2003-49, December. [Downloadable!] (restricted)
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  22. Jones, Christopher S., 2003. "The dynamics of stochastic volatility: evidence from underlying and options markets," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 181-224. [Downloadable!] (restricted)
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