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The Skewness Implied in the Heston Model and its Application

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 Ito integrals by using Ito'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.