Analytic Short Rate Model with Smile and Skew

Abstract

We consider an extension of the Hull-White short rate model which incorporates smile and skew, effectively through a quadratic dependence of the diffusion on the short rate. We derive an asymptotic representation of the pricing kernel for this new model in semi-analytic form, using this to obtain accurate, easily computed, asymptotic formulae for zero coupon bonds and LIBOR options. Unlike comparable models such as SABR, ours appears to be usable even for pricing options with long times to maturity. Further, the same calibrated model can be used for all possible maturities and LIBOR tenors.

Keywords: short rate model, skew, smile, analytic solution, perturbations methods, asymptotic, caplet, swaption

JEL Classification: G13