Quotation Kurt, Kevin, Frey, Rüdiger. 2021. Markov-modulated Affine Processes.


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Abstract

We study Markov-modulated affine processes (abbreviated MMAPs), a class of Markov processes that are created from affine processes by allowing some of their coefficients to be a function of an exogenous Markov process. MMAPs allow for richer models in various applications. At the same time MMAPs largely preserve the tractability of standard affine processes, as their characteristic function has a computationally convenient functional form. Our setup is a substantial generalization of earlier work, since we consider the case where the generator of the exogenous process X is an unbounded operator (as is the case for diffusions or jump processes with infinite activity). We prove existence of MMAPs via a martingale problem approach, we derive the formula for their characteristic function and we study various mathematical properties of MMAPs. The paper closes with a discussion of several applications of MMAPs in finance.

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Publication's profile

Status of publication Published
Affiliation WU
Type of publication Working/discussion paper, preprint
Language English
Title Markov-modulated Affine Processes
Year 2021
URL https://arxiv.org/abs/2106.16240
JEL C02, G12

Associations

People
Kurt, Kevin (Former researcher)
Frey, Rüdiger (Details)
Organization
Institute for Statistics and Mathematics IN (Details)
Research areas (ÖSTAT Classification 'Statistik Austria')
1137 Financial mathematics (Details)
1165 Stochastics (Details)
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