Pure -Jump Levy Processes and Self-decomposability in Financial Modeling | Zendy

Ömer Önalan | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Open Access

Pure -Jump Levy Processes and Self-decomposability in Financial Modeling

Author(s) -

Ömer Önalan

Publication year - 2011

Publication title -

journal of mathematics research

Language(s) - English

Resource type - Journals

eISSN - 1916-9809

pISSN - 1916-9795

DOI - 10.5539/jmr.v3n2p41

Subject(s) - mathematics , lévy process , stable process , pure mathematics , generalization , self similarity , estimator , limit (mathematics) , jump , quadratic equation , type (biology) , jump process , quadratic variation , stochastic process , mathematical analysis , brownian motion , statistics , ecology , physics , biology , geometry , quantum mechanics

In this study, we review the connections between L'{e}vy processes with jumps and self-decomposable laws. Self-decomposable laws constitute a subclass of infinitely divisible laws. L'{e}vy processes additive processes and independent increments can be related using self-similarity property. Sato (1991) defined additive processes as a generalization of L'{e}vy processes. In this way, additive processes are those processes with inhomogeneous (in general) and independent increments and L'{e}vy processes correspond with the particular case in which the increments are time homogeneous. Hence L'{e}vy processes are considerable as a particular type. Self-decomposable distributions occur as limit law an Ornstein-Uhlenbeck type process associated with a background driving L'{e}vy process. Finally as an application, asset returns are representing by a normal inverse Gaussian process. Then to test applicability of this representation, we use the nonparametric threshold estimator of the quadratic variation, proposed by Cont and Mancini (2007).

The content you want is available to Zendy users.

Already have an account? Click here to sign in.

Having issues? You can contact us here

Accelerating Research