Hedging of Options in the Presence of Jump Clustering

36 Pages Posted: 3 Dec 2018

See all articles by Donatien Hainaut

Donatien Hainaut

Université Catholique de Louvain

Franck Moraux

Université de Rennes I and CREM

Date Written: November 26, 2018

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.

Keywords: self-excitation, Hawkes process, minimum variance hedging, options pricing, shot noise process

Suggested Citation

Hainaut, Donatien and Moraux, Franck, Hedging of Options in the Presence of Jump Clustering (November 26, 2018). Journal of Computational Finance, Forthcoming. Available at SSRN: https://ssrn.com/abstract=3290709

Donatien Hainaut (Contact Author)

Université Catholique de Louvain ( email )

Voie du Roman Pays 20,
Louvain La Neuve, 1348
Belgium

Franck Moraux

Université de Rennes I and CREM ( email )

IAE de Rennes
11, rue Jean Macé
Rennes, 35000
France
+33 (0)2 23 23 78 08 (Phone)
+33 (0)2 23 23 78 00 (Fax)

HOME PAGE: http://perso.univ-rennes1.fr/franck.moraux/

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