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A fractal version of the Hull–White interest rate model

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  • Hainaut, Donatien

Abstract

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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  • Hainaut, Donatien, 2013. "A fractal version of the Hull–White interest rate model," Economic Modelling, Elsevier, vol. 31(C), pages 323-334.
    • Handle: RePEc:eee:ecmode:v:31:y:2013:i:c:p:323-334
    DOI: 10.1016/j.econmod.2012.11.041
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    References listed on IDEAS

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    Cited by:

    1. Hainaut, Donatien, 2021. "Lévy interest rate models with a long memory," LIDAM Discussion Papers ISBA 2021020, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. Donatien Hainaut, 2016. "A bivariate Hawkes process based model, for interest rates," Post-Print hal-01458162, HAL.
    3. Hainaut, Donatien, 2016. "A bivariate Hawkes process for interest rate modeling," Economic Modelling, Elsevier, vol. 57(C), pages 180-196.

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