Before revision: We propose a novel time discretization for the log-normal SABR model dS_t = \sigma_t S_t dW_t, d\sigma_t = \omega \sigma_t dZ_t, with \mbox{corr(W_t,Z_t)=\varrho, } which is a  variant of the Euler-Maruyama scheme , and study its asymptotic properties in the limit of a large number of time steps n \infty at fixed \beta = \omega^2 n^2\tau, \rho = \sigma_0\sqrt{\tau .
After revision: We propose a novel time discretization for the log-normal SABR model dS_t = \sigma_t S_t dW_t, d\sigma_t = \omega \sigma_t dZ_t, with \mbox{corr(W_t,Z_t)=\varrho, } which is a variant of the Euler-Maruyama scheme , and study its asymptotic properties in the limit of a large number of time steps  \infty at fixed \beta = \omega^2 n^2\tau, \rho = \sigma_0\sqrt{\tau .