Stochastic jump intensity models

Issue title: Fractional Calculus and Its Applications

Guest editors: Sergio Bianchi

Article type: Research Article

Authors: Lévy dit Véhel, P.E.^{a; *} | Lévy Véhel, J.^b

Affiliations: [a] Société Générale, France. E-mail: pierem2@gmail.com | [b] INRIA & Case Law Analytics, France. E-mail: jacques.levy-vehel@inria.fr

Correspondence: [*] Corresponding author. E-mail: pierem2@gmail.com.

Abstract: Stochastic volatility models have proven relevant for various purposes, e.g. explaining the term structure of implied volatility or correlations in absolute returns. When used in conjunction with jump models, they provide powerful tools that have been applied successfully in recent years. Volatility is however but one aspect of risk: in the frame of jump processes, the (local) intensity of jumps is another one, which is equally important. It thus seems natural to supplement stochastic volatility models with “stochastic jump intensity” ones, where the local intensity of jumps evolves according to a random dynamics. The aim of this preliminary work is merely to set up such models as extensions of the celebrated CGMY process, leaving their exploration both for risk management and for option pricing to further studies.

Keywords: Tempered stable processes, CGMY model, stochastic jump intensity, risk management, VaR

DOI: 10.3233/RDA-180139

Journal: Risk and Decision Analysis, vol. 7, no. 1-2, pp. 63-75, 2018