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Reducible Diffusions with Time-Varying Transformations with Application to Short-Term Interest Rates

Author

Listed:
  • Ruijun Bu
  • Jie Cheng
  • Kaddour Hadri

Abstract

Reducible diffusions (RDs) are nonlinear transformations of analytically solvable Basic Diffusions (BDs). Therefore, they are constructed to be analytically tractable and flexible diffusion processes. Existing literature on RDs has mostly focused on time-homogeneous transformations, which to a significant extent fail to explore the full potential of RDs from both theoretical and practical point of views. In this paper, we propose flexible and economically justifiable time-variations to the transformations of RDs. Concentrating on the Constant Elasticity Variance (CEV) RDs, we consider nonlinear dynamics for our time-varying transformations with both deterministic and stochastic designs. Such time-variations can greatly enhance the flexibility of RDs while maintain sufficient tractability of the resulting models. Our approach also enjoys the benefits of classical inferential techniques as much as the advocated time-varying nonlinear dynamics. Our application to UK and US short-term interest rates suggests that from an empirical point of view time-varying transformations are highly relevant and statistically significant.

Suggested Citation

  • Ruijun Bu & Jie Cheng & Kaddour Hadri, 2014. "Reducible Diffusions with Time-Varying Transformations with Application to Short-Term Interest Rates," Economics Working Papers 14-01, Queen's Management School, Queen's University Belfast.
  • Handle: RePEc:qub:wpaper:1401
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    References listed on IDEAS

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    1. Jiang, George J. & Knight, John L., 1997. "A Nonparametric Approach to the Estimation of Diffusion Processes, With an Application to a Short-Term Interest Rate Model," Econometric Theory, Cambridge University Press, vol. 13(5), pages 615-645, October.
    2. Hansen, Bruce E, 1992. "The Likelihood Ratio Test under Nonstandard Conditions: Testing the Markov Switching Model of GNP," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 7(S), pages 61-82, Suppl. De.
    3. Elerain, Ola & Chib, Siddhartha & Shephard, Neil, 2001. "Likelihood Inference for Discretely Observed Nonlinear Diffusions," Econometrica, Econometric Society, vol. 69(4), pages 959-93, July.
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    Cited by:

    1. Bu, Ruijun & Jawadi, Fredj & Li, Yuyi, 2017. "An empirical comparison of transformed diffusion models for VIX and VIX futures," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 46(C), pages 116-127.
    2. Ruijun Bu & Fredj Jawadi & Yuyi Li, 2020. "A multifactor transformed diffusion model with applications to VIX and VIX futures," Econometric Reviews, Taylor & Francis Journals, vol. 39(1), pages 27-53, January.
    3. Oscar García, 2019. "Estimating reducible stochastic differential equations by conversion to a least-squares problem," Computational Statistics, Springer, vol. 34(1), pages 23-46, March.
    4. Zhigang Tong & Allen Liu, 2018. "Analytical pricing of discrete arithmetic Asian options under generalized CIR process with time change," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 5(01), pages 1-21, March.
    5. Bu Ruijun & Cheng Jie & Hadri Kaddour, 2017. "Specification analysis in regime-switching continuous-time diffusion models for market volatility," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 21(1), pages 65-80, February.

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    More about this item

    Keywords

    Stochastic Differential Equation; Reducible Diffusion; Constant Elasticity Variance; Time-Varying Transformation; Maximum Likelihood Estimation; Short-Term Interest Rate;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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