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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 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:

The Cox-Ingersoll-Ross model

Here, α, β, and σ are positive constants, rt is the interest rate, t is the time, and Wt 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. ...

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