Mastering R for Quantitative Finance

The Cox-Ingersoll-Ross model

Like the Vasicek model, the Cox-Ingersoll-Ross model (Cox at al., 1985), which is often cited as the CIR model, is a continuous, affine, one-factor stochastic interest rate model. In this model, the instantaneous interest rate dynamics are given by the following stochastic differential equation:

Here, α, β, and σ are positive constants, r_t is the interest rate, t is the time, and W_t denotes the standard Wiener process. It is easy to see that the drift component is the same as in the Vasicek model; hence, the interest rate follows a mean-reverting process again, β is the long-run average, and α is the rate of adjustment. ...