Closed-form approximations of moments and densities of continuous-time Markov models

Dennis Kristensen, Young Jun Lee and Antonio Mele

Papers from arXiv.org

Abstract: This paper develops power series expansions of a general class of moment functions, including transition densities and option prices, of continuous-time Markov processes, including jump--diffusions. The proposed expansions extend the ones in Kristensen and Mele (2011) to cover general Markov processes. We demonstrate that the class of expansions nests the transition density and option price expansions developed in Yang, Chen, and Wan (2019) and Wan and Yang (2021) as special cases, thereby connecting seemingly different ideas in a unified framework. We show how the general expansion can be implemented for fully general jump--diffusion models. We provide a new theory for the validity of the expansions which shows that series expansions are not guaranteed to converge as more terms are added in general. Thus, these methods should be used with caution. At the same time, the numerical studies in this paper demonstrate good performance of the proposed implementation in practice when a small number of terms are included.

Date: 2023-08
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://arxiv.org/pdf/2308.09009 Latest version (application/pdf)

Related works:
Journal Article: Closed-form approximations of moments and densities of continuous–time Markov models (2024)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2308.09009

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().