Before revision:  These results are applied to the Carr Wu \mbox{%DIFAUXCMD \cite{CarrWu }\hspace{0pt}%DIFAUXCMD modelfor S} P 500. and supremum }\ovl  of X at \tau_a and the undershoot a - Y_{\tau_a-} and overshoot Y_{\tau_a}-a of Y at \tau_a.
After revision:  These results are applied to the Carr }\hspace{0pt}%DIFAUXCMD modelfor S} P 500. and supremum }\ovl of X at \tau_a and the undershoot a - Y_{\tau_a-} and overshoot Y_{\tau_a}-a of Y at \tau_a.