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A fractal version of the Hull–White interest rate model

  • Hainaut, Donatien
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    This paper develops a new version of the Hull–White's model of interest rates, in which the volatility of the short term rate is driven by a Markov switching multifractal model. The interest rate dynamics is still mean reverting but the constant volatility of the Brownian motion is replaced by a multifractal process so as to capture persistent volatility shocks. In this setting, we infer properties of the short term rate distribution, a semi-closed form expression for bond prices and their dynamics under a forward measure. Finally, our work is illustrated by a numerical application in which we assess the exposure of a bonds portfolio to the interest risk.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0264999312003975
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    Article provided by Elsevier in its journal Economic Modelling.

    Volume (Year): 31 (2013)
    Issue (Month): C ()
    Pages: 323-334

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    Handle: RePEc:eee:ecmode:v:31:y:2013:i:c:p:323-334
    Contact details of provider: Web page: http://www.elsevier.com/locate/inca/30411

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    1. Laurent-Emmanuel Calvet & Adlai J. Fisher, 2004. "How to Forecast Long-Run Volatility: Regime Switching and the Estimation of Multifractal Processes," Post-Print hal-00478472, HAL.
    2. Smith, Daniel R, 2002. "Markov-Switching and Stochastic Volatility Diffusion Models of Short-Term Interest Rates," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(2), pages 183-97, April.
    3. Mills, Terence C. & Wang, Ping, 2006. "Modelling regime shift behaviour in Asian real interest rates," Economic Modelling, Elsevier, vol. 23(6), pages 952-966, December.
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    7. Camilla LandÊn, 2000. "Bond pricing in a hidden Markov model of the short rate," Finance and Stochastics, Springer, vol. 4(4), pages 371-389.
    8. Kalimipalli, Madhu & Susmel, Raul, 2004. "Regime-switching stochastic volatility and short-term interest rates," Journal of Empirical Finance, Elsevier, vol. 11(3), pages 309-329, June.
    9. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    10. Robert J. Elliott & Tak Kuen Siu & Alex Badescu, 2011. "Bond valuation under a discrete-time regime-switching term-structure model and its continuous-time extension," Managerial Finance, Emerald Group Publishing, vol. 37(11), pages 1025-1047, October.
    11. Laurent Calvet, 2000. "Forecasting Multifractal Volatility," Harvard Institute of Economic Research Working Papers 1902, Harvard - Institute of Economic Research.
    12. Asbjørn T. Hansen & Rolf Poulsen, 2000. "A simple regime switching term structure model," Finance and Stochastics, Springer, vol. 4(4), pages 409-429.
    13. Laurent-Emmanuel Calvet & Adlai J. Fisher, 2002. "Multifractality in Asset Returns: Theory and Evidence," Post-Print hal-00478175, HAL.
    14. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(04), pages 627-627, November.
    15. Robert Elliott & Tak Kuen Siu, 2009. "On Markov-modulated Exponential-affine Bond Price Formulae," Applied Mathematical Finance, Taylor & Francis Journals, vol. 16(1), pages 1-15.
    16. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-84, March.
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