A Fractal Version of the Hull-White Interest Rate Model
19 Pages Posted: 3 Jun 2012
Date Written: June 1, 2012
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
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