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The Skewness Implied in the Heston Model and Its Application

Jin E. Zhang · Fang Zhen · Xiaoxia Sun · Huimin Zhao

22 citations0/0 files storedJournal of Futures Markets

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Stochastic processes and financial applications Financial Markets and Investment Strategies Financial Risk and Volatility Modeling

Abstract

Abstract In this paper, we provide an exact formula for the skewness of stock returns implied in the Heston (1993) model by using a moment‐computing approach. We compute the moments of It integrals by using It 's Lemma skillfully. The model's affine property allows us to obtain analytical formulas for cumulants. The formulas for the variance and the third cumulant are written as time‐weighted sums of expected instantaneous variance, which are neater and more intuitive than those obtained with the characteristic function approach. Our skewness formula is then applied in calibrating Heston's model by using the market data of the CBOE VIX and SKEW. © 2016 Wiley Periodicals, Inc. Jrl Fut Mark 37:211–237, 2017

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References

1993A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options 1997Empirical Performance of Alternative Option Pricing Models 2002The jump-risk premia implicit in options: evidence from an integrated time-series study 2004Do Stock Prices and Volatility Jump? Reconciling Evidence from Spot and Option Prices 2002An Empirical Investigation of Continuous‐Time Equity Return Models 2012Ex Ante Skewness and Expected Stock Returns 2009The Shape and Term Structure of the Index Option Smirk: Why Multifactor Stochastic Volatility Models Work So Well 2006Maximum likelihood estimation of stochastic volatility models

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2020The complete Gaussian kernel in the multi-factor Heston model: Option pricing and implied volatility applications

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