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Mastering R for Quantitative Finance by Edina Berlinger, Ferenc Illés, Milán Badics, Ádám Banai, Gergely Daróczi, Barbara Dömötör, Gergely Gabler, Dániel Havran, Péter Juhász, István Margitai, Balázs Márkus, Péter Medvegyev, Julia Molnár, Balázs Árpád Szűcs, Ágnes Tuza, Tamás Vadász, Kata Váradi, Ágnes Vidovics-Dancs

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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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