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

CREATES Research Paper 2009-34

43 Pages Posted: 13 Aug 2009  

Peter Christoffersen

University of Toronto - Rotman School of Management; Copenhagen Business School; University of Aarhus - CREATES

Steven L. Heston

University of Maryland - Department of Finance

Kris Jacobs

University of Houston - C.T. Bauer College of Business

Multiple version iconThere are 2 versions of this paper

Date Written: June 17, 2009

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.

Keywords: stochastic correlation, stochastic volatility, equity index options, multifactor model, persistence, affine, out-of-sample

JEL Classification: G12

Suggested Citation

Christoffersen, Peter and Heston, Steven L. and Jacobs, Kris, The Shape and Term Structure of the Index Option Smirk: Why Multifactor Stochastic Volatility Models Work so Well (June 17, 2009). CREATES Research Paper 2009-34. Available at SSRN: https://ssrn.com/abstract=1447362 or http://dx.doi.org/10.2139/ssrn.1447362

Peter Christoffersen (Contact Author)

University of Toronto - Rotman School of Management ( email )

105 St. George Street
Toronto, Ontario M5S 3E6 M5P 3C4
Canada
416-946-5511 (Phone)

HOME PAGE: http://www.christoffersen.com

Copenhagen Business School

Solbjerg Plads 3
Frederiksberg C, DK - 2000
Denmark

University of Aarhus - CREATES

School of Economics and Management
Building 1322, Bartholins Alle 10
DK-8000 Aarhus C
Denmark

Steven L. Heston

University of Maryland - Department of Finance ( email )

Robert H. Smith School of Business
Van Munching Hall
College Park, MD 20742
United States

Kris Jacobs

University of Houston - C.T. Bauer College of Business ( email )

Houston, TX 77204-6021
United States

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