# Interest Rate Models, Large Deviations and the Doob Transform

by Robert Smits (New Mexico State University, USA)

In their fundamental work on the term structure, Cox, Ingersoll and Ross introduced a stochastic model to describe the short term dynamics of interest rates now known as the CIR model. Justifications for the model included its positivity, a steady-state distribution and an increase in the variance of the interest rate as the interest rate itself increases. Much later, Going-Jaeschke and Yor showed how the dynamics of the CIR model can be understood via a transformation of a generalized Bessel process and studied the large time behavior of the model. In this talk I discuss a family of stochastic processes, driven by Brownian motion together with a power law drift. In addition to the justifications for the CIR model, these models have a time to equilibrium with finite moments and variational arguments will yield the explicit, subexponential large deviation behavior.