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A Refinement to Ait-Sahalia's (2002) "Maximum Likelihood Estimation of Discretely Sampled Diffusions: A Closed-Form Approximation Approach"

Author

Listed:
  • Gurdip Bakshi

    (Smith School of Business, University of Maryland)

  • Nengjiu Ju

    (School of Business and Management, Hong Kong University of Science and Technology)

Abstract

This paper provides a closed-form density approximation when the underlying state variable is a one-dimensional diffusion. Building on Aït-Sahalia (2002), we show that our refinement is applicable under a wide class of drift and diffusion functions. In addition, it facilitates the maximum likelihood estimation of discretely sampled diffusion models of short interest-rate or stock volatility with unknown conditional densities. Our interest-rate examples demonstrate that the analytical approximation is sufficiently accurate.

Suggested Citation

  • 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.
    • Handle: RePEc:ucp:jnlbus:v:78:y:2005:i:5:p:2037-2036
    DOI: 10.1086/431451
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    Cited by:

    1. Kaffel, Bilel & Abid, Fathi, 2009. "A methodology for the choice of the best fitting continuous-time stochastic models of crude oil price," The Quarterly Review of Economics and Finance, Elsevier, vol. 49(3), pages 971-1000, August.
    2. 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.
    3. Xiu, Dacheng, 2014. "Hermite polynomial based expansion of European option prices," Journal of Econometrics, Elsevier, vol. 179(2), pages 158-177.
    4. Lee, Yoon Dong & Song, Seongjoo & Lee, Eun-Kyung, 2014. "The delta expansion for the transition density of diffusion models," Journal of Econometrics, Elsevier, vol. 178(P3), pages 694-705.
    5. Choi, Seungmoon, 2015. "Explicit form of approximate transition probability density functions of diffusion processes," Journal of Econometrics, Elsevier, vol. 187(1), pages 57-73.
    6. Salima El Kolei & Fabien Navarro, 2022. "Contrast estimation for noisy observations of diffusion processes via closed-form density expansions," Statistical Inference for Stochastic Processes, Springer, vol. 25(2), pages 303-336, July.

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