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Threshold estimation of Markov models with jumps and interest rate modeling

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  • Mancini, Cecilia
  • Renò, Roberto

Abstract

We reconstruct the level-dependent diffusion coefficient of a univariate semimartingale with jumps which is observed discretely. The consistency and asymptotic normality of our estimator are provided in the presence of both finite and infinite activity (finite variation) jumps. Our results rely on kernel estimation, using the properties of the local time of the data generating process, and the fact that it is possible to disentangle the discontinuous part of the state variable through those squared increments between observations not exceeding a suitable threshold function. We also reconstruct the drift and the jump intensity coefficients when they are level-dependent and jumps have finite activity, through consistent and asymptotically normal estimators. Simulated experiments show that the newly proposed estimators perform better in finite samples than alternative estimators, and this allows us to reexamine the estimation of a univariate model for the short term interest rate, for which we find fewer jumps and more variance due to the diffusion part than previous studies.

Suggested Citation

  • Mancini, Cecilia & Renò, Roberto, 2011. "Threshold estimation of Markov models with jumps and interest rate modeling," Journal of Econometrics, Elsevier, vol. 160(1), pages 77-92, January.
    • Handle: RePEc:eee:econom:v:160:y:2011:i:1:p:77-92
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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. Ernst Eberlein & Sebastian Raible, 1999. "Term Structure Models Driven by General Lévy Processes," Mathematical Finance, Wiley Blackwell, vol. 9(1), pages 31-53, January.
    3. Das, Sanjiv R., 2002. "The surprise element: jumps in interest rates," Journal of Econometrics, Elsevier, vol. 106(1), pages 27-65, January.
    4. Bandi, Federico M., 2002. "Short-term interest rate dynamics: a spatial approach," Journal of Financial Economics, Elsevier, vol. 65(1), pages 73-110, July.
    5. Pan, Jun, 2002. "The jump-risk premia implicit in options: evidence from an integrated time-series study," Journal of Financial Economics, Elsevier, vol. 63(1), pages 3-50, January.
    6. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold, 2007. "Roughing It Up: Including Jump Components in the Measurement, Modeling, and Forecasting of Return Volatility," The Review of Economics and Statistics, MIT Press, vol. 89(4), pages 701-720, November.
    7. Bakshi, Gurdip & Cao, Charles & Chen, Zhiwu, 1997. "Empirical Performance of Alternative Option Pricing Models," Journal of Finance, American Finance Association, vol. 52(5), pages 2003-2049, December.
    8. Yongmiao Hong, 2005. "Nonparametric Specification Testing for Continuous-Time Models with Applications to Term Structure of Interest Rates," The Review of Financial Studies, Society for Financial Studies, vol. 18(1), pages 37-84.
    9. David A. Chapman & Neil D. Pearson, 2000. "Is the Short Rate Drift Actually Nonlinear?," Journal of Finance, American Finance Association, vol. 55(1), pages 355-388, February.
    10. Renò, Roberto, 2008. "Nonparametric Estimation Of The Diffusion Coefficient Of Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 24(5), pages 1174-1206, October.
    11. Federico M. Bandi & Peter C. B. Phillips, 2003. "Fully Nonparametric Estimation of Scalar Diffusion Models," Econometrica, Econometric Society, vol. 71(1), pages 241-283, January.
    12. David A. Chapman & Neil D. Pearson, 1998. "Is the Short Rate Drift Actually Nonlinear?," Finance 9808005, University Library of Munich, Germany.
    13. Hamilton, James D, 1996. "The Daily Market for Federal Funds," Journal of Political Economy, University of Chicago Press, vol. 104(1), pages 26-56, February.
    14. Ait-Sahalia, Yacine, 1996. "Nonparametric Pricing of Interest Rate Derivative Securities," Econometrica, Econometric Society, vol. 64(3), pages 527-560, May.
    15. Barndorff-Nielsen, Ole E. & Shephard, Neil & Winkel, Matthias, 2006. "Limit theorems for multipower variation in the presence of jumps," Stochastic Processes and their Applications, Elsevier, vol. 116(5), pages 796-806, May.
    16. Chapman, David A & Long, John B, Jr & Pearson, Neil D, 1999. "Using Proxies for the Short Rate: When Are Three Months Like an Instant?," The Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 763-806.
    17. Monika Piazzesi, 2005. "Bond Yields and the Federal Reserve," Journal of Political Economy, University of Chicago Press, vol. 113(2), pages 311-344, April.
    18. Ole E. Barndorff-Nielsen, 2004. "Power and Bipower Variation with Stochastic Volatility and Jumps," Journal of Financial Econometrics, Oxford University Press, vol. 2(1), pages 1-37.
    19. Christopher S. Jones, 2003. "Nonlinear Mean Reversion in the Short-Term Interest Rate," The Review of Financial Studies, Society for Financial Studies, vol. 16(3), pages 793-843, July.
    20. Jacod, Jean, 2008. "Asymptotic properties of realized power variations and related functionals of semimartingales," Stochastic Processes and their Applications, Elsevier, vol. 118(4), pages 517-559, April.
    21. Jiang, George J., 1998. "Nonparametric Modeling of U.S. Interest Rate Term Structure Dynamics and Implications on the Prices of Derivative Securities," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 33(4), pages 465-497, December.
    22. Bjørn Eraker & Michael Johannes & Nicholas Polson, 2003. "The Impact of Jumps in Volatility and Returns," Journal of Finance, American Finance Association, vol. 58(3), pages 1269-1300, June.
    23. Cecilia Mancini, 2009. "Non‐parametric Threshold Estimation for Models with Stochastic Diffusion Coefficient and Jumps," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(2), pages 270-296, June.
    24. repec:bla:jfinan:v:59:y:2004:i:1:p:227-260 is not listed on IDEAS
    25. Andersen, Torben G. & Lund, Jesper, 1997. "Estimating continuous-time stochastic volatility models of the short-term interest rate," Journal of Econometrics, Elsevier, vol. 77(2), pages 343-377, April.
    26. Pritsker, Matt, 1998. "Nonparametric Density Estimation and Tests of Continuous Time Interest Rate Models," The Review of Financial Studies, Society for Financial Studies, vol. 11(3), pages 449-487.
    27. 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.
    28. Bandi, Federico M. & Nguyen, Thong H., 2003. "On the functional estimation of jump-diffusion models," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 293-328.
    29. Peter Carr & Helyette Geman, 2002. "The Fine Structure of Asset Returns: An Empirical Investigation," The Journal of Business, University of Chicago Press, vol. 75(2), pages 305-332, April.
    30. Bates, David S., 2000. "Post-'87 crash fears in the S&P 500 futures option market," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 181-238.
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    Cited by:

    1. Yuping Song & Chen Li & Hemin Wang & Jiayi Meng & Liang Hao, 2023. "Nonparametric Threshold Estimation for Drift Function in Jump–Diffusion Model of Interest Rate Using Asymmetric Kernel," Mathematics, MDPI, vol. 11(10), pages 1-16, May.
    2. Renò, Roberto, 2008. "Nonparametric Estimation Of The Diffusion Coefficient Of Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 24(5), pages 1174-1206, October.
    3. Cecilia Mancini & Vanessa Mattiussi & Roberto Renò, 2015. "Spot volatility estimation using delta sequences," Finance and Stochastics, Springer, vol. 19(2), pages 261-293, April.
    4. Kim, Jihyun & Park, Joon & Wang, Bin, 2020. "Estimation of Volatility Functions in Jump Diffusions Using Truncated Bipower Increments," TSE Working Papers 20-1096, Toulouse School of Economics (TSE).
    5. Corradi, Valentina & Silvapulle, Mervyn J. & Swanson, Norman R., 2018. "Testing for jumps and jump intensity path dependence," Journal of Econometrics, Elsevier, vol. 204(2), pages 248-267.
    6. Rama Cont & Cecilia Mancini, 2010. "Nonparametric tests for pathwise properties of semimartingales," Working Papers - Mathematical Economics 2010-02, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa.
    7. Ye, Xu-Guo & Lin, Jin-Guan & Zhao, Yan-Yong & Hao, Hong-Xia, 2015. "Two-step estimation of the volatility functions in diffusion models with empirical applications," Journal of Empirical Finance, Elsevier, vol. 33(C), pages 135-159.
    8. Junjie Hu & Wolfgang Karl Hardle & Weiyu Kuo, 2019. "Risk of Bitcoin Market: Volatility, Jumps, and Forecasts," Papers 1912.05228, arXiv.org, revised Dec 2021.
    9. Liu, Qiang & Liu, Yiqi & Liu, Zhi, 2018. "Estimating spot volatility in the presence of infinite variation jumps," Stochastic Processes and their Applications, Elsevier, vol. 128(6), pages 1958-1987.
    10. Park, Joon Y. & Wang, Bin, 2021. "Nonparametric estimation of jump diffusion models," Journal of Econometrics, Elsevier, vol. 222(1), pages 688-715.
    11. Jakobsen, Nina Munkholt & Sørensen, Michael, 2019. "Estimating functions for jump–diffusions," Stochastic Processes and their Applications, Elsevier, vol. 129(9), pages 3282-3318.
    12. Schmisser, Émeline, 2014. "Non-parametric adaptive estimation of the drift for a jump diffusion process," Stochastic Processes and their Applications, Elsevier, vol. 124(1), pages 883-914.
    13. Schmisser, Émeline, 2019. "Non parametric estimation of the diffusion coefficients of a diffusion with jumps," Stochastic Processes and their Applications, Elsevier, vol. 129(12), pages 5364-5405.
    14. repec:hal:journl:peer-00741630 is not listed on IDEAS
    15. Torben B. Rasmussen, 2009. "Jump Testing and the Speed of Market Adjustment," CREATES Research Papers 2009-08, Department of Economics and Business Economics, Aarhus University.
    16. Jos'e E. Figueroa-L'opez & Cecilia Mancini, 2017. "Optimum thresholding using mean and conditional mean square error," Papers 1708.04339, arXiv.org.
    17. Qiang Liu & Zhi Liu & Chuanhai Zhang, 2020. "Heteroscedasticity test of high-frequency data with jumps and microstructure noise," Papers 2010.07659, arXiv.org.

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