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.
We first outline the mechanics underlying the general CIR production economy. To allow the audience to focus on the interaction between the state variables, the production processes and the consumption decision without getting lost in the generality and the matrix notation of the original paper, we then introduce a one-factor reduced form version the economy. This is the basis for the derivation of the optimal consumption decision, the risk-free interest rate and the valuation of contingent claims.
- Presentation Slides: CoxIngersollRossEconomy.pdf
Cox, John C., Jonathan E. Ingersoll and Stephen A. Ross (1985) “An Intertemporal General Equilibrium Model of Asset Prices,” Econometrica, Vol. 53, No. 2, pp. 363-384
Cox, John C., Jonathan E. Ingersoll and Stephen A. Ross (1985) “A Theory of the Term Structure of Interest Rates,” Econometrica, Vol. 53, No. 2, pp. 385-407