Polynomial Jump-Diffusion Models

Damir Filipovi\'c and Martin Larsson

Papers from arXiv.org

Abstract: We develop a comprehensive mathematical framework for polynomial jump-diffusions in a semimartingale context, which nest affine jump-diffusions and have broad applications in finance. We show that the polynomial property is preserved under polynomial transformations and L\'evy time change. We present a generic method for option pricing based on moment expansions. As an application, we introduce a large class of novel financial asset pricing models with excess log returns that are conditional L\'evy based on polynomial jump-diffusions.

Date: 2017-11, Revised 2019-07
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