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Hedging of options in the presence of jump clustering

Abstract : This paper analyzes the efficiency of hedging strategies for stock options in the presence of jump clustering. In the proposed model, the asset is ruled by a jump-diffusion process, wherein the arrival of jumps is correlated to the amplitude of past shocks. This feature adds feedback effects and time heterogeneity to the initial jump diffusion. After a presentation of the main properties of the process, a numerical method for options pricing is proposed. Next, we develop four hedging policies, minimizing the variance of the final wealth. These strategies are based on first- and second-order approximations of option prices. The hedging instrument is either the underlying asset or another option. The performance of these hedges is measured by simulations for put and call options, with a model fitted to the Standard & Poor’s 500.
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https://halshs.archives-ouvertes.fr/halshs-02024279
Contributor : Naïla Louise-Rose <>
Submitted on : Tuesday, February 19, 2019 - 8:28:47 AM
Last modification on : Thursday, January 14, 2021 - 1:22:23 PM

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  • HAL Id : halshs-02024279, version 1

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Donatien Hainaut, Franck Moraux. Hedging of options in the presence of jump clustering. The Journal of Computational Finance, Incisive Media, 2018, 22 (3), pp.1-35. ⟨halshs-02024279⟩

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