Vasicek model

In finance, the Vasicek model is a mathematical model describing the evolution of interest rates. It is a type of one-factor short rate model as it describes interest rate movements as driven by only one source of market risk. The model can be used in the valuation of interest rate derivatives, and has also been adapted for credit markets. It was introduced in 1977 by Oldřich Vašíček and can be also seen as a .

The model specifies that the instantaneous interest rate follows the :

where W_t is a Wiener process under the risk neutral framework modelling the random market risk factor, in that it models the continuous inflow of randomness into the system. The standard deviation parameter, ${\displaystyle \sigma }$, determines the volatility of the interest rate and in a way characterizes the amplitude of the instantaneous randomness inflow. The typical parameters ${\displaystyle b,a}$ and ${\displaystyle \sigma }$, together with the initial condition ${\displaystyle r_{0}}$, completely characterize the dynamics, and can be quickly characterized as follows, assuming ${\displaystyle a}$ to be non-negative:

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