Mastering R for Quantitative Finance

The Vasicek model

The Vasicek model (Vasicek, 1977) 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 time, and W_t denotes the standard Wiener process. In mathematics, this process is called the Ornstein-Uhlenbeck process.

As you may observe, the interest rate in the Vasicek model follows a mean-reverting process with a long-term average β; when r_t < β, the drift term becomes positive, so the interest rate is expected to increase and vice versa. ...