A fractal version of the Hull-White interest rate model

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.

► This paper studies an extension of the Hull and White model for interest rates. ► The volatility is modeled by a Markov Switching multifractal process. ► The calibration tends to prove that this model outperforms Garch model. ► Prices and dynamics of zero coupon bonds have semi-closed form expressions. ► The pricing of interest rate derivatives under a forward measure is developed.