Johan Rasmusson

Two short rate models with numerical swaption pricing procedures

Abstract

The short rate model by Hull & White (1994a) and the one where the interest rate
is described by Cox, Ingersoll & Ross (1985) are introduced. Their closed form
solutions for analytical swaption pricing are presented and calibration to a 
swaption is done. The one factor models are afterwards used to numerically 
replicate a number of swaption price surfaces. The pricing formula by 
Black (1976) will be used to acquire the market prices for the swaptions from 
a volatility surface.

These market prices will be compared to the simulated prices replicated by the 
models.  Given this comparison an analysis in the replicating ability will be 
made. A comparison in between the models will also be made and suggestions for 
a continuation of this work are presented.