The delta expansion for the transition density of diffusion models
This paper is on the issue of finding a closed-form likelihood approximation of diffusion processes and rearranging the Hermite expansion in the order of the power of the observational time interval. We propose an algorithm that calculates the coefficients of the rearranged expansion that Aït-Sahalia (2002) suggested. That is, a general expression of the coefficients is provided explicitly, which as far as we know has not been given in the existing literature. We also introduce a reduced form of the rearranged expansion and call it as the delta expansion in the paper. Moreover, we are able to obtain an explicit expansion of the moments in the order of the power of the observational time interval.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Seungmoon Choi, 2011. "Closed-Form Likelihood Expansions for Multivariate Time-Inhomogeneous Diffusions," School of Economics Working Papers 2011-26, University of Adelaide, School of Economics.
- Chang, Jinyuan & Chen, Songxi, 2011. "On the Approximate Maximum Likelihood Estimation for Diffusion Processes," MPRA Paper 46279, University Library of Munich, Germany.
- Li, Minqiang, 2008.
"A Damped Diffusion Framework for Financial Modeling and Closed-form Maximum Likelihood Estimation,"
11185, University Library of Munich, Germany.
- Li, Minqiang, 2010. "A damped diffusion framework for financial modeling and closed-form maximum likelihood estimation," Journal of Economic Dynamics and Control, Elsevier, vol. 34(2), pages 132-157, February.
- Osnat Stramer & Matthew Bognar & Paul Schneider, 2010. "Bayesian Inference for Discretely Sampled Markov Processes with Closed-Form Likelihood Expansions," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 8(4), pages 450-480, Fall.
- Ai[dieresis]t-Sahalia, Yacine & Yu, Jialin, 2006. "Saddlepoint approximations for continuous-time Markov processes," Journal of Econometrics, Elsevier, vol. 134(2), pages 507-551, October.
- Egorov, Alexei V. & Li, Haitao & Xu, Yuewu, 2003. "Maximum likelihood estimation of time-inhomogeneous diffusions," Journal of Econometrics, Elsevier, vol. 114(1), pages 107-139, May.
- Chan, K C, et al, 1992.
" An Empirical Comparison of Alternative Models of the Short-Term Interest Rate,"
Journal of Finance,
American Finance Association, vol. 47(3), pages 1209-1227, July.
- Tom Doan, "undated". "RATS programs to replicate CKLS(1992) estimation of interest rate models," Statistical Software Components RTZ00035, Boston College Department of Economics.
- Alexandros Beskos & Omiros Papaspiliopoulos & Gareth O. Roberts & Paul Fearnhead, 2006. "Exact and computationally efficient likelihood-based estimation for discretely observed diffusion processes (with discussion)," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(3), pages 333-382.
- Yu, Jialin, 2007. "Closed-form likelihood approximation and estimation of jump-diffusions with an application to the realignment risk of the Chinese Yuan," Journal of Econometrics, Elsevier, vol. 141(2), pages 1245-1280, December.
- Bakshi, Gurdip & Ju, Nengjiu & Ou-Yang, Hui, 2006. "Estimation of continuous-time models with an application to equity volatility dynamics," Journal of Financial Economics, Elsevier, vol. 82(1), pages 227-249, October.
- Gurdip Bakshi & Nengjiu Ju, 2005. "A Refinement to Ait-Sahalia's (2002) "Maximum Likelihood Estimation of Discretely Sampled Diffusions: A Closed-Form Approximation Approach"," The Journal of Business, University of Chicago Press, vol. 78(5), pages 2037-2052, September.
- Yacine Ait-Sahalia, 2002. "Maximum Likelihood Estimation of Discretely Sampled Diffusions: A Closed-form Approximation Approach," Econometrica, Econometric Society, vol. 70(1), pages 223-262, January.
When requesting a correction, please mention this item's handle: RePEc:eee:econom:v:178:y:2014:i:p3:p:694-705. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.