Markov-modulated affine processes

Kevin Kurt; Rüdiger Frey

doi:10.1016/j.spa.2022.08.009

Markov-modulated affine processes

Kevin Kurt, Rüdiger Frey

Institute for Statistics and Mathematics

Publication: Scientific journal › Journal article › peer-review

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 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 is an unbounded operator. We prove existence of MMAPs via a martingale problem approach, we derive the formula for their characteristic function and we study various mathematical properties.

Original language	English
Pages (from-to)	391-422
Journal	Stochastic Processes and their Applications
Volume	153
DOIs	https://doi.org/10.1016/j.spa.2022.08.009
Publication status	Published - Nov 2022

Austrian Classification of Fields of Science and Technology (ÖFOS)

101007 Financial mathematics
101019 Stochastics

Keywords

Markov processes
Affine processes
Martingale problem
Analytical tractability
Pricing of financial instruments
Markov processes with discontinuous coefficients

Access to Document

10.1016/j.spa.2022.08.009

Check availability

University Library Catalogue

Cite this

@article{53bf1c73ff114add8ba3efe6967fd069,

title = "Markov-modulated affine processes",

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 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 is an unbounded operator. We prove existence of MMAPs via a martingale problem approach, we derive the formula for their characteristic function and we study various mathematical properties.",

keywords = "Markov processes, Affine processes, Martingale problem, Analytical tractability, Pricing of financial instruments, Markov processes with discontinuous coefficients",

author = "Kevin Kurt and R{\"u}diger Frey",

year = "2022",

month = nov,

doi = "10.1016/j.spa.2022.08.009",

language = "English",

volume = "153",

pages = "391--422",

journal = "Stochastic Processes and their Applications",

issn = "0304-4149",

publisher = "Elsevier B.V.",

}

TY - JOUR

T1 - Markov-modulated affine processes

AU - Kurt, Kevin

AU - Frey, Rüdiger

PY - 2022/11

Y1 - 2022/11

N2 - 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 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 is an unbounded operator. We prove existence of MMAPs via a martingale problem approach, we derive the formula for their characteristic function and we study various mathematical properties.

AB - 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 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 is an unbounded operator. We prove existence of MMAPs via a martingale problem approach, we derive the formula for their characteristic function and we study various mathematical properties.

KW - Markov processes

KW - Affine processes

KW - Martingale problem

KW - Analytical tractability

KW - Pricing of financial instruments

KW - Markov processes with discontinuous coefficients

UR - https://doi.org/10.1016/j.spa.2022.08.009

U2 - 10.1016/j.spa.2022.08.009

DO - 10.1016/j.spa.2022.08.009

M3 - Journal article

SN - 0304-4149

VL - 153

SP - 391

EP - 422

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

ER -

Markov-modulated affine processes

Abstract

Austrian Classification of Fields of Science and Technology (ÖFOS)

Keywords

Access to Document

Check availability

Other files and links