On the drawdown of completely asymmetric Levy processes

Details On the drawdown of completely asymmetric Levy processes On the drawdown of completely asymmetric Levy processes

2011-03-08

arxiv.org/abs/1103.1460v1

Mathematics

Probability

24 pages, 3 figures

Scientific paper

The drawdown process $Y=\bar{X} - X$ of a completely asymmetric L\'{e}vy process $X$ is given by $X$ reflected at its running supremum $\bar{X}$.In this paper we explicitly express the law of the sextuple $(\tau_a,\bar{G}_{\tau_a},\underline{X}_{\tau_a},\bar{X}_{\tau_a},Y_{\tau_a-},Y_{\tau_a}-a)$ 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 $X$. We also explicitly identify the distribution of the drawup $\hat{Y}_{\tau_a}$ at the moment $\tau_a$, where $\hat{Y} = X-\underline{X}$, and derive the probability of a large drawdown preceding a small rally. These results are applied to the Carr & Wu \cite{CarrWu} model for S&P 500.

Affiliated with

Also associated with

No associations

Rating

On the drawdown of completely asymmetric Levy processes does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On the drawdown of completely asymmetric Levy processes, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the drawdown of completely asymmetric Levy processes will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-82169