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
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.
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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.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Hansen, L. P. and J. A. Scheinkman (1995) Back to the future: Generating moment implications for continuous-time markov processes | 0.941 | 6 | 3 | 83% |
| 2 | Yang, N., N. Chen, and X. Wan (2019) A new delta expansion for multivariate diffusions via the ito-taylor expansion | 0.874 | 12 | 5 | 67% |
| 3 | Wan, X. and N. Yang (2021) Hermite expansion of transition densities and european option prices for multivariate diffusions with jumps | 0.860 | 22 | 6 | 64% |
| 4 | Kristensen, D. and A. Mele (2011) Adding and subtracting Black-Scholes: A new approach to approximating derivative prices in continuous-time models self | 0.847 | 28 | 5 | 61% |
| 5 | Filipović, D., E. Mayerhofer, and P. Schneider (2013, oct) (2013) Density approximations for multivariate affine jump-diffusion processes | 0.644 | 2 | 2 | 100% |
| aitsahalia2002 | unmatched citation key aitsahalia2002 | 0.644 | 2 | 2 | 100% |
| aitsahalia2008 | unmatched citation key aitsahalia2008 | 0.644 | 2 | 2 | 100% |
| 8 | Bakshi, G., N. Ju, and H. Ou-Yang (2006) Estimation of continuous-time models with an application to equity volatility dynamics | 0.644 | 2 | 2 | 100% |
| 9 | Li, C (2013) Maximum-likelihood estimation for diffusion processes via closed-form density expansions | 0.644 | 2 | 2 | 100% |
| 10 | Yu, J (2007) Closed-form likelihood approximation and estimation of jump-diffusions with an application to the realignment risk of the Chines… | 0.644 | 2 | 2 | 100% |
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.