A Note on Esscher Transformed Martingale Measures for Geometric Lévy Processes
نویسنده
چکیده
The Esscher transform is one of the very useful methods to obtain the reasonable equivalent martingale measures, and it is defined with relation to the corresponding risk process. In this article we consider two kinds of risk processes (compound return process and simple return process). Then we obtain two kinds of Esscher transformed martingale measures. The first one is the one which was introduced by Gerber and Shiu, and the second one is identified with the MEMM (minimal entropy martingale measure). We set up the economical characterization of these two kinds of Esscher transforms, and then we study the properties of the above two kinds of Esscher transformed martingale measures, comparing each others.
منابع مشابه
Martingale measures for the geometric Lévy process models
The equivalent martingale measures for the geometric Lévy processes are investigated. They are separated to two groups. One is the group of martingale measures which are obtained by Esscher transform. The other one is such group that are obtained as the minimal distance martingale measures. We try to obtain the explicit forms of the martingale measures, and we compare the properties of the mart...
متن کاملExponential Stock Models Driven by Tempered Stable Processes
We investigate exponential stock models driven by tempered stable processes, which constitute a rich family of purely discontinuous Lévy processes. With a view of option pricing, we provide a systematic analysis of the existence of equivalent martingale measures, under which the model remains analytically tractable. This includes the existence of Esscher martingale measures and martingale measu...
متن کاملOption Pricing in Bilateral Gamma Stock Models
In the framework of bilateral Gamma stock models we seek for adequate option pricing measures, which have an economic interpretation and allow numerical calculations of option prices. Our investigations encompass Esscher transforms, minimal entropy martingale measures, p-optimal martingale measures, bilateral Esscher transforms and the minimal martingale measure. We illustrate our theory by a n...
متن کاملMinimal q-entropy martingale measures for exponential time-changed Lévy processes
In this paper, we consider structure preserving measure transforms for time-changed Lévy processes. Within this class of transforms preserving the time-changed Lévy structure, we derive equivalent martingale measures minimizing relative q-entropy. Structure preservation is found to be an inherent property of minimal q-entropy martingale measures under continuous time changes, whereas it imposes...
متن کاملCost-efficiency in multivariate Lévy models
In this paper we determine lowest cost strategies for given payoff distributions called cost-efficient strategies in multivariate exponential Lévy models where the pricing is based on the multivariate Esscher martingale measure. This extended framework allows to deal with dependent price processes as arising in typical applications. Dependence of the components of the Lévy Process implies an in...
متن کامل