A Fractal Version of the Hull-White Interest Rate Model

19 Pages Posted: 3 Jun 2012

See all articles by Donatien Hainaut

Donatien Hainaut

Université Catholique de Louvain

Date Written: June 1, 2012

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.

Keywords: Hidden Markov process, switching Brownian motion, Interest rates

JEL Classification: C5

Suggested Citation

Hainaut, Donatien, A Fractal Version of the Hull-White Interest Rate Model (June 1, 2012). Paris December 2012 Finance Meeting EUROFIDAI-AFFI Paper, Available at SSRN: https://ssrn.com/abstract=2071758 or http://dx.doi.org/10.2139/ssrn.2071758

Donatien Hainaut (Contact Author)

Université Catholique de Louvain ( email )

Voie du Roman Pays 20,
Louvain La Neuve, 1348
Belgium

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