Probability Density of the CIR Model
8 Pages Posted: 13 Oct 2014
Date Written: October 11, 2014
We present an alternative derivation of the transition density in the Cox-Ingersoll-Ross (CIR) model. Applying methods developed in elementary quantum mechanics we show that the transition density can be determined from the eigenvalue problem of a second order differential operator with continuous spectrum. The operator turns out to be the stochastic analogue of the time-dependent quantum mechanical position operator in one dimension. Finally, to demonstrate the applicability of this technique to other one-dimensional diffusion problems, we re-derive the familiar transition densities of the Vasicek and Black-Scholes models and write down the equations of motion for the relevant operators in the Courtadon interest rate model.
Keywords: Transition density, CIR model, Kolmogorov equation, Quantum Mechanics
JEL Classification: C63, C69
Suggested Citation: Suggested Citation