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R: Data Analysis and Visualization by Ágnes Vidovics-Dancs, Kata Váradi, Tamás Vadász, Ágnes Tuza, Balázs Árpád Szucs, Julia Molnár, Péter Medvegyev, Balázs Márkus, István Margitai, Péter Juhász, Dániel Havran, Gergely Gabler, Barbara Dömötör, Gergely Daróczi, Ádám Banai, Milán Badics, Ferenc Illés, Edina Berlinger, Bater Makhabel, Hrishi V. Mittal, Jaynal Abedin, Brett Lantz, Tony Fischetti

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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:

The Vasicek model

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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