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The SABR model of Hagan is described by the following system of stochastic differential equations

$$\begin{align} & d{{f}_{t}}={{\alpha }_{t}}f_{t}^{\beta }d{{W}_{t}}^{1} \\ & d{{\alpha }_{t}}=v\,{{\alpha }_{t}}d{{W}_{t}}^{2} \\ & {{E}^{Q}}[d{{W}_{t}}^{1},d{{W}_{t}}^{2}]=\rho dt \\ \end{align}$$

In these equations, $f_t$ is the forward rate, $\alpha$ is the initial variance, $\beta$ is the exponent for the forward rate and $v$ is the volatility of variance.