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

• 成果类型: Article
• 署名作者: Christoffersen, Peter; Heston, Steven; Jacobs, Kris
• 署名单位: McGill University; Copenhagen Business School; CREATES; Aarhus University; University System of Maryland; University of Maryland College Park; University of Houston System; University of Houston
• 刊物名称: MANAGEMENT SCIENCE
• ISSN/ISSBN: 0025-1909
• DOI: 10.1287/mnsc.1090.1065
• 发表日期: 2009
• 页码: 1914-1932
• 关键词: stochastic correlation; stochastic volatility; Equity index options; multifactor model; persistence; Affine; Out-of-sample

摘要

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. Although 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 stochastic volatility 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.