Jump Size Distributions of Additive Compound Poisson Processes That Are Closed Under the Esscher Transform

50 Pages Posted: 13 May 2018

Date Written: August 29, 2013

Abstract

We model logarithmic asset price dynamics under the physical probability measure as additive jump-diffusion processes, which exhibit a time-dependent jump intensity and jump size distribution. The corresponding risk-neutral probability measure is defined through an Esscher transform. We are interested in the conditions under which the jump size distributions under the two probability measures fall into the same parametric class. We show that it is necessary and sufficient for the jump size distribution to follow a natural exponential mixture family at all points in time. Immediate applications of these results in financial engineering are discussed.

Keywords: Esscher Transform, Additive Processes, Compound Poisson, Jump Size Distribution, Natural Exponential Family

JEL Classification: G13

Suggested Citation

Thul, Matthias, Jump Size Distributions of Additive Compound Poisson Processes That Are Closed Under the Esscher Transform (August 29, 2013). Available at SSRN: https://ssrn.com/abstract=3171480 or http://dx.doi.org/10.2139/ssrn.3171480

Matthias Thul (Contact Author)

IMC Financial Markets ( email )

Strawinskylaan 377, WTC D-tower
Amsterdam, 1077 XX
Netherlands

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
59
Abstract Views
476
rank
486,943
PlumX Metrics