The Shape and Term Structure of the Index Option Smirk: Why Multifactor Stochastic Volatility Models Work so Well
University of Toronto - Rotman School of Management; Copenhagen Business School; University of Aarhus - CREATES
Steven L. Heston
University of Maryland - Department of Finance
University of Houston - C.T. Bauer College of Business
June 17, 2009
CREATES Research Paper 2009-34
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.
Number of Pages in PDF File: 43
Keywords: stochastic correlation, stochastic volatility, equity index options, multifactor model, persistence, affine, out-of-sample
JEL Classification: G12
Date posted: August 13, 2009
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