Lévy-Ito Models in Finance

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Bouzianis, G; Hughston, L P; Jaimungal, S and Sánchez-Betancourt, L. 2021. Lévy-Ito Models in Finance. Probability Surveys, 18, pp. 132-178. ISSN 1549-5787 [Article]

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Official URL: https://projecteuclid.org/journals/probability-sur...

Abstract or Description

We present an overview of the broad class of financial models in which the prices of assets are L évy-Ito processes driven by an n-dimensional Brownian motion and an independent Poisson random measure. The Poisson random measure is associated with an n-dimensional Lévy process. Each model consists of a pricing kernel, a money market account, and one or more risky assets. We show how the excess rate of return above the interest rate can be calculated for risky assets in such models, thus showing the relationship between risk and return when asset prices have jumps. The framework is applied to a variety of asset classes, allowing one to construct new models as well as interesting generalizations of familiar models.

Item Type:

Article

Identification Number (DOI):

https://doi.org/10.1214/21-PS1

Additional Information:

Rights: Creative Commons Attribution 4.0 International License.

ArXiv:1907.08499

Keywords:

Asset pricing, interest rate models, foreign exchange, risk premium, risk aversion, pricing kernels, Lévy processes, Lévy measure, Poisson random measure, Siegel’s paradox, Vasicek model.

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