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A Damped Diffusion Framework for Financial Modeling and Closed-form Maximum Likelihood Estimation

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  • Li, Minqiang

Abstract

Asset price bubbles can arise unintentionally when one uses continuous-time diffusion processes to model financial quantities. We propose a flexible damped diffusion framework that is able to break many types of bubbles and preserve the martingale pricing approach. Damping can be done on either the diffusion or drift function. Oftentimes, certain solutions to the valuation PDE can be ruled out by requiring the solution to be a limit of martingale prices for damped diffusion models. Monte Carlo study shows that with finite time-series length, maximum likelihood estimation often fails to detect the damped diffusion function while fabricates nonlinear drift function.

Suggested Citation

  • Li, Minqiang, 2008. "A Damped Diffusion Framework for Financial Modeling and Closed-form Maximum Likelihood Estimation," MPRA Paper 11185, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:11185
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    References listed on IDEAS

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    Cited by:

    1. Choi, Seungmoon, 2013. "Closed-form likelihood expansions for multivariate time-inhomogeneous diffusions," Journal of Econometrics, Elsevier, vol. 174(2), pages 45-65.
    2. 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.
    3. Choi, Seungmoon, 2015. "Explicit form of approximate transition probability density functions of diffusion processes," Journal of Econometrics, Elsevier, vol. 187(1), pages 57-73.
    4. Li, Minqiang, 2013. "An examination of the continuous-time dynamics of international volatility indices amid the recent market turmoil," Journal of Empirical Finance, Elsevier, vol. 22(C), pages 128-139.

    More about this item

    Keywords

    Damped diffusion; asset price bubbles; martingale pricing; maximum likelihood estimation;

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General

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