Option Valuation with Long-run and Short-run Volatility Components

By Peter F. Christoffersen, Kris Jacobs, C. Ornthanalai, Yintian Wang. 2008

327 citations recorded by the source corpus.

This paper presents a new model for the valuation of European options, in which the volatility of returns consists of two components. One of these components is a long-run component, and it can be modeled as fully persistent. The other component is short-run and has a zero mean. Our model can be viewed as an affine version of Engle and Lee (1999), allowing for easy valuation of European options. The model substantially outperforms a benchmark single-component volatility model that is well-established in the literature, and it fits options better than a model that combines conditional heteroskedasticity and Poissonnormal jumps. The component model’s superior performance is partly due to its improved ability to model the smirk and the path of spot volatility, but its most distinctive feature is its ability to model the volatility term structure. This feature enables the component model to jointly model long-maturity and short-maturity options.

View Paper: https://www.semanticscholar.org/paper/c57e36b933dde6e15861f8c225b18cfdc1caefe5

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Citations in the corpus

• Stochastic Volatility of Volatility and Variance Risk Premia (2013, unknown): “They form a very natural generalisation of the classical one factor SV models and are very successful in the context ofoption pricing, see e.g. Christoffersen et al. (2009, 2008).”
• The Shape and Term Structure of the Index Option Smirk: Why Multifactor Stochastic Volatility Models Work So Well (2009, unknown): “Note from (15) that the correlation between stock returns and variance is not restricted to lie in between the correlations between the stock return and the respective variance factors.”
• A tale of two option markets: Pricing kernels and volatility risk ☆ (2014, unknown): “Furthermore, several recent studies document the importance of multiple volatility factors in capturing dynamics of option prices or the term structure of variance swaps, see e.g. Christoffersen et al. (2008), Egloff et al. (2010), Mencia and Sentana (2012), and Bates (2012).”
• Pricing the CBOE VIX Futures with the Heston–Nandi GARCH Model (2017, background): “The literature mainly focuses on equity option pricing, such as Duan (1995), Duan (1999), Heston and Nandi (2000), Duan et al. (2005), Christoffersen et al. (2008), Christoffersen et al. (2014), etc.2 To our best knowledge, little (if any) literature exists on the pricing of VIX derivatives under…”