Term structure of interest rates, Bessel processes, Girsanov theorem, Time transformation, Bonds and option pricing
Abstract
This paper presents a simple construction of the extended Cox, Ingersoll & Ross model (ECIR) far term structure of interest rate, and a simple way of pricing general interest rate derivatives with this model. To price zero-cupon bonds , we calculate the Laplace transform of functionals of an "elementary process", which is taken as a squared Bessel process. This approach takes advantage of martingales and the Girsanov's theorem providing a presentation of results in a "user friendly" form. Furthermore, we propose and apply a method for the calibration of the one factor ECIR model using data of bonds prices.
