CIR process
From Wikipedia, the free encyclopedia
The CIR process (named after its creators John C. Cox, Jonathan E. Ingersoll, and Stephen A. Ross) is a
Markov process with continuous paths defined by the following stochastic differential equation:
where θ and σ are parameters. Ths process is sometimes called squared Bessel process (also see Bessel process) in the mathematical literature, and can also be defined as a sum of squared Ornstein-Uhlenbeck processes. The process value at time t, i.e. rt follows a noncentral chi-square distribution. The CIR is an ergodic process, and possesses a stationary distribution, which is a gamma.
This process is widely used in finance to model short term interest rate.
[edit] References
Cox, J.C. Ingersoll, J.E. and Ross, S.A. (1985). A Theory of the Term Structure of Interest Rates. Econometrica 53, pp 385-407.
