Three Make a Smile – Dynamic Volatility, Skewness and Term Structure Components in Option Valutation
44 Pages Posted: 30 Mar 2011
Date Written: February 1, 2010
We propose a new modeling framework for the valuation of European options, in which dynamic short and long run volatility components drive the smile dynamics. The model state dynamics is driven by a matrix jump diffusion, provides efficient pricing formulas for plain vanilla options by means of standard transform methods, and it nests as special cases a number of affine option pricing models in the literature. In contrast to other approaches, short and long run volatility components interact dynamically with a further component linked to stochastic skewness, which we show is important in order to capture accurately the joint behavior of the implied volatility skew and the volatility term structure. We estimate our model and a number of competing benchmarks without interactions using S&P 500 index options. We find that models with dynamic interactions provide better pricing performance and a more accurate description of the joint dynamics of the implied volatility skew and term structure, both in-sample and out-of-sample. These findings support the use of option pricing models with (i) at least three dynamic volatility factors and (ii) dynamic interactions between volatility and stochastic skewness components.
Keywords: Option Pricing, Stochastic Volatility, Short and Long Term Volatility Risk, Stochastic Leverage, Wishart Diffusion
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