The drawdown process Y= - X {\em   of a completely asymmetric L\'{e}vy process X is given by X reflected at its running supremum X   . In this paper we explicitly express the law of the sextuple (\tau_a, _{\tau_a,}X _{\tau_a,}%DIFDELCMD < \bar{X}%%% _{\tau_a,Y_{\tau_a-},Y_{\tau_a}-a) } in terms of the scale function and the L\'evy measure of X , where \tau_a denotes the first-passage time of Y over the level a>0,  \bar{G}_{\tau_a} is the time of the last supremum of X prior to \tau_a and\underline{X is the running infimum of\unl X . We also explicitly identify the distribution of the drawup%DIFDELCMD < \hat{Y}%%% _{\tau_aat the moment \tau_a, where }%DIFDELCMD < \hat{Y} %%% = X-\underline{X , and derive the probability of a large drawdown preceding a small rally. These results are applied to the Carr%DIFDELCMD < & %%% Wu \mbox{%DIFAUXCMD \cite{CarrWu }\hspace{0pt}%DIFAUXCMD modelfor S}%DIFDELCMD < &%%% 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. As application we obtain explicit expressions for the laws of a number of functionals of drawdowns and rallies in a completely asymmetric exponential L\'{e}vy model.}
The {\em drawdown process Y of a completely asymmetric L\'{e}vy process X is equal to X reflected at its running supremum X : Y = - X . In this paper we explicitly express ,} ,}%DIFDELCMD < \bar{X}%%% ,Y_{\tau_a-},Y_{\tau_a}-a) } in terms of the scale function and the L\'{e measure of X the law of the sextuple of the first-passage time of Y over the level a>0, the time \bar{G}_{\tau_a} of the last supremum of X prior to \tau_a \underline{ , the infimum\unl X %DIFDELCMD < \hat{Y}%%% at the moment \tau_a, where }%DIFDELCMD < \hat{Y} %%% \underline{ %DIFDELCMD < & %%% }\hspace{0pt}%DIFAUXCMD modelfor S}%DIFDELCMD < &%%% _{\tau_a and supremum }\ovl X_{\tau_a of X at \tau_a and the undershoot a - Y_{\tau_a-} and overshoot Y_{\tau_a}-a of Y at \tau_a. As application we obtain explicit expressions for the laws of a number of functionals of drawdowns and rallies in a completely asymmetric exponential L\'{e}vy model.}
D
drawdown process Y=
D
- X
A
drawdown
A
process Y
R
given by
equal to
A
: Y =
A
- X
D
the law of the sextuple (\tau_a,
D
_{\tau_a
D
X
D
_{\tau_a
D
_{\tau_a
R
L\'evy
L\'{e
R
, where \tau_a denotes the
the law of the sextuple of the
A
the time
D
is the time
D
and
D
X
R
is the running infimum of
, the infimum
D
. We also explicitly identify the distribution of the drawup
D
_{\tau_a
D
= X-
D
X
D
, and derive the probability of a large drawdown preceding a small rally. These results are applied to the Carr
D
Wu \mbox{%DIFAUXCMD \cite{CarrWu
R
P 500.
_{\tau_a
A
X_{\tau_a