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

Dennis Kristensen, Young Jun Lee, Antonio Mele

arXiv 17 Aug 2023 · Econometrics · publishedJournal of Economic Dynamics and Control (2024) · 1 citations (OpenAlex)

arXiv:2308.09009 · PDF · DOI · OpenAlex · Extracted main text

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.

Citation extraction

38
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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Hansen, L. P. and J. A. Scheinkman (1995) Back to the future: Generating moment implications for continuous-time markov processes0.9416383%
2Yang, N., N. Chen, and X. Wan (2019) A new delta expansion for multivariate diffusions via the ito-taylor expansion0.87412567%
3Wan, X. and N. Yang (2021) Hermite expansion of transition densities and european option prices for multivariate diffusions with jumps0.86022664%
4Kristensen, D. and A. Mele (2011) Adding and subtracting Black-Scholes: A new approach to approximating derivative prices in continuous-time models self0.84728561%
5Filipović, D., E. Mayerhofer, and P. Schneider (2013, oct) (2013) Density approximations for multivariate affine jump-diffusion processes0.64422100%
aitsahalia2002unmatched citation key aitsahalia20020.64422100%
aitsahalia2008unmatched citation key aitsahalia20080.64422100%
8Bakshi, G., N. Ju, and H. Ou-Yang (2006) Estimation of continuous-time models with an application to equity volatility dynamics0.64422100%
9Li, C (2013) Maximum-likelihood estimation for diffusion processes via closed-form density expansions0.64422100%
10Yu, J (2007) Closed-form likelihood approximation and estimation of jump-diffusions with an application to the realignment risk of the Chines…0.64422100%

Showing the top 10 of 86 scored citations. 2 of these could not be matched to a bibliography entry, so only the citation key is shown.