Zero coupon bonds assesment using a stochastic model for the discount factor

Abstract

In many empirical situations (e.g.:Libor), the rate of interest will remain fixed at a certain level (random instantaneous rate oi) for a random periodof time(ti) until a new random rate should be considered, oi+1, that will remain for ti+1, waiting time untill the next change in the rate of interest. Three models were developed using the approach cited aboye for random rate of interest and random waiting times between changes in the rate of interest. Using easy integral transforms (Laplace and Fourier) we will be able to calculate the moments of the probability function of the cliscount factor, V(t), and even its c.d.f.. The approach will also be extended to the calculation of the expected value and variance of a zero coupon bond with maturity t and we will also approximate the c.d.f.