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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 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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