 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 .
<coherence>  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 .
 The implied volatility surface \sigma_{\rm BS for arbitrary maturity and strike in the limit \omega^2 T%DIFDELCMD < \to %%% %DIFDELCMD < \to %%% \infty at fixed (\omega^2 T)(\sigma_0^2 T) is represented as an extremal problem .