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, rt is the interest rate, t is time, and Wt 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 rt < β, the drift term becomes positive, so the interest rate is expected to increase and vice versa. ...
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