Modeling Short-term Implied Volatilities in the Heston Stochastic Volatility Model

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Stochastic volatility models, unlike constant volatility models, which assume a fixed level of volatility, allow volatility to change. These models, such as the Heston model, introduce an additional stochastic process to account for the variability in volatility, providing a more nuanced dynamics of the market. By incorporating factors like mean reversion and volatility of volatility, stochastic volatility models offer a robust framework for pricing derivatives, managing risks, and improving investment strategies.

Despite their advantages, stochastic volatility models have difficulty in accurately characterizing both the flatness of long-term implied volatility (IV) curves and the steep curvature of short-term ones. Reference [1] addresses this issue by introducing a term-structure-based correction to the volatility of volatility (vol-vol) term in the classical Heston stochastic volatility model. The authors pointed out,

In this paper, we propose a novel and simple approach to precisely capture the shapes of implied volatility of real options with all maturities simultaneously, by introducing a term-structure-based correction to the volatility of volatility term of the classical Heston stochastic volatility model. Numerical experiments and empirical results show that the introduction of the term-structure-based correction term surely overcomes the deficiency of the classical Heston model in capturing the short-term option IVs, thus improving notably the quoting performance of the Heston model for the whole options.

Although the classical Heston stochastic volatility model is used as the plant model in this paper, this work can be easily extended to other kinds of stochastic volatility models. In addition, for future research, one can consider embedding the strike of option into the correction function to reinforce the model’s ability to characterize the whole surface of the implied volatility of option accurately.

In brief, both short- and long-term IVs are accurately modeled in the new Heston variant.

This paper improves the existing Heston model. Thus, it helps portfolio managers and risk managers to better manage the risks of investment portfolios.

Let us know what you think in the comments below or in the discussion forum.

References

[1] Youfa Sun, Yishan Gong, Xinyuan Wang & Caiyan Liu, A novel term-structure-based Heston model for implied volatility surface, International Journal of Computer Mathematics, 1–24.

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