 We derive an almost sure limit and a large deviations result for the log-asset price in the n%DIFDELCMD < \to %%% \infty limit . The rate function of the large deviations result does not depend on the discretization time step \tau. The implied volatility surface \sigma_{\rm BS for arbitrary maturity and strike in the limit \omega^2 T%DIFDELCMD < \to %%% 0 , \sigma_0^2 T%DIFDELCMD < \to %%% \infty at fixed (\omega^2 T)(\sigma_0^2 T) is represented as an extremal problem .
<clarity>  We derive an almost sure limit and a large deviations result for the log-asset price in the n%DIFDELCMD < \to %%% \infty limit . The rate function of the large deviations result does not depend on the discretization time step \tau. The implied volatility surface \sigma_{\rm BS for arbitrary maturity and strike in the limit \omega^2 T%DIFDELCMD < \to %%% 0 , \sigma_0^2 T%DIFDELCMD < \to %%% \infty at fixed (\omega^2 T)(\sigma_0^2 T) is represented as an extremal problem .
 We derive an almost sure limit and a large deviations result for the log-asset price in the n%DIFDELCMD < \to %%% limit of large number of time steps. We derive an exact representation of the implied volatility surface \sigma_{\rm BS for arbitrary maturity and strike in the limit \omega^2 T%DIFDELCMD < \to %%% 0 , \sigma_0^2 T%DIFDELCMD < \to %%% \infty at fixed (\omega^2 T)(\sigma_0^2 T) is represented as an extremal problem .