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Online Kernel estimation of stationary stochastic diffusion models

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  • Xin Wang

Abstract

Nonparametric regression has recently become important in quantitative finance due to its distribution-free property. However, this advantage does not come without any cost. As large sample sizes are always required to adequately estimate local structures, nonparametric regression is computationally intensive in real applications. This paper proposes an online method to decrease the computational cost of nonparametric regression for estimating stationary stochastic diffusion models. We establish asymptotic behaviours of the proposed estimators under appropriate conditions. Numerical examples and an empirical study of US 3-month treasury bill rates are illustrated. The application to financial risk management is also taken into consideration.

Suggested Citation

  • Xin Wang, 2017. "Online Kernel estimation of stationary stochastic diffusion models," Quantitative Finance, Taylor & Francis Journals, vol. 17(7), pages 1089-1103, July.
    • Handle: RePEc:taf:quantf:v:17:y:2017:i:7:p:1089-1103
    DOI: 10.1080/14697688.2016.1262054
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    References listed on IDEAS

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    1. Fan J. & Zhang C., 2003. "A Reexamination of Diffusion Estimators With Applications to Financial Model Validation," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 118-134, January.
    2. Ait-Sahalia, Yacine, 1996. "Nonparametric Pricing of Interest Rate Derivative Securities," Econometrica, Econometric Society, vol. 64(3), pages 527-560, May.
    3. Christoffersen, Peter F, 1998. "Evaluating Interval Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 841-862, November.
    4. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    5. Manuel Arapis & Jiti Gao, 2006. "Empirical Comparisons in Short-Term Interest Rate Models Using Nonparametric Methods," Journal of Financial Econometrics, Oxford University Press, vol. 4(2), pages 310-345.
    6. Stanton, Richard, 1997. "A Nonparametric Model of Term Structure Dynamics and the Market Price of Interest Rate Risk," Journal of Finance, American Finance Association, vol. 52(5), pages 1973-2002, December.
    7. 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.
    8. Paul H. Kupiec, 1995. "Techniques for verifying the accuracy of risk measurement models," Finance and Economics Discussion Series 95-24, Board of Governors of the Federal Reserve System (U.S.).
    9. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "An Intertemporal General Equilibrium Model of Asset Prices," Econometrica, Econometric Society, vol. 53(2), pages 363-384, March.
    10. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 627-627, November.
    11. Masry, Elias, 1987. "Almost sure convergence of recursive density estimators for stationary mixing processes," Statistics & Probability Letters, Elsevier, vol. 5(4), pages 249-254, June.
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