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.
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- 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, 2010.
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- 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. Full references (including those not matched with items on IDEAS)
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