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A local volatility correction to mean-reverting stochastic volatility model for pricing derivatives

Author

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  • Kim, Donghyun
  • Ha, Mijin
  • Kim, Jeong-Hoon
  • Yoon, Ji-Hun

Abstract

Generally, in the real market, empirical findings suggest that either local volatility (LV) or stochastic volatility (SV) models have a limit to capture the full dynamics and geometry of the implied volatilities of the given equity options. In this study, to overcome the disadvantage of such LV and SV models, we propose a special type of hybrid stochastic-local volatility (SLV∗) model in which the volatility is given by the squared logarithmic function of the underlying asset price added to a function of a fast mean-reverting process. By making use of asymptotic analysis and Mellin transform, we derive analytic pricing formulas for European derivatives with both smooth and non-smooth payoffs under the SLV∗ model. We run numerical experiments to verify the accuracy of the pricing formulas using a Monte-Carlo simulation method and to display that the proposed new model fits the geometry of the market implied volatility more closely than other models such as the Heston model, the stochastic elasticity of variance (SEV) model, the hybrid stochastic and CEV type local volatility (SVCEV) model and the multiscale stochastic volatility (MSV) model, especially for short time-to-maturity options.

Suggested Citation

  • Kim, Donghyun & Ha, Mijin & Kim, Jeong-Hoon & Yoon, Ji-Hun, 2024. "A local volatility correction to mean-reverting stochastic volatility model for pricing derivatives," The Quarterly Review of Economics and Finance, Elsevier, vol. 97(C).
  • Handle: RePEc:eee:quaeco:v:97:y:2024:i:c:s1062976924001078
    DOI: 10.1016/j.qref.2024.101901
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    References listed on IDEAS

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    More about this item

    Keywords

    Stochastic-local volatility (SLV⁎); Asymptotic analysis; Mellin transform; Implied volatility; Option data fitting;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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