In this post, we consider stochastic clocks whose instantaneous rate of activity follows a square root process. We present all intermediate steps in the derivation of the characteristic function of the corresponding time change. The corresponding steps closely resemble those in the derivation of the zero-coupon bond price in the Cox et al. (1985) model for the short-term interest rate.
This is a presentation on the Cox-Ingersoll-Ross (CIR) model economy, the equilibrium interest rate process and the pricing of derivative securities. I had to hold this presentation in the PhD class FINS5591 – “Continuous Time Finance” at UNSW in the first semester of 2010.