The dynamics of stochastic volatility: evidence from underlying and options markets.

*(English)*Zbl 1016.62122Summary: This paper proposes and estimates a more general parametric stochastic variance model of equity index returns than has been previously considered using data from both underlying and options markets. I conclude that the square root stochastic variance model of S. L. Heston [“A closed-form solution for options with stochastic volatility with applications to bond and currency options”, Rev. Financ. Stud. 6, No. 2, 327–343 (1993; doi:10.1093/rfs/6.2.327)] is incapable of generating realistic returns behavior, and that the data are better represented by a stochastic variance model in the CEV class or a model with a time-varying leverage effect. As the level of market variance increases, the volatility of market variance increases rapidly and the leverage effect becomes substantially stronger. The heightened heteroskedasticity in market variance that results causes returns to display unconditional skewness and kurtosis much closer to their sample values, while the model falls short of explaining the implied volatility smile for short-dated options and conditional higher moments in returns.

##### MSC:

62P05 | Applications of statistics to actuarial sciences and financial mathematics |

62M99 | Inference from stochastic processes |

91G20 | Derivative securities (option pricing, hedging, etc.) |

62P20 | Applications of statistics to economics |

##### Keywords:

continuous-time estimation; stochastic volatility; option pricing; Bayesian analysis; stock market crashes
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DOI

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