An Interest Rate Tree Driven by a Lévy Process

We propose an interest rate model driven by a particular Lévy Process, the normal inverse Gaussian (NIG) process, in which the SDE chosen to govern the evolution of the short term rate is directly inspired from the Hull & White model. The interest rate dynamics is still mean reverting but the Brownian motion is replaced by a NIG process. The principal motivation for this approach stems from the empirical evidence that a NIG process provides a better fit of bond returns than those driven by a Brownian motion. Above all, it captures the asymmetry and the leptokurticity of short term rates distribution. We show that derivatives may be priced numerically by setting up a pentanomial tree, fitting the first four moments of the NIG process. Finally, we have compared its performance with those of the Hull-White model. The estimated parameters exhibit stability and consistency over a variety of yield curves. Furthermore, our tests reveal that one parameter, beta, plays a relatively strong role in distinguishing between the curve shapes