If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. See general information about how to correct material in RePEc.įor technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact. When requesting a correction, please mention this item's handle: RePEc:wsi:wschap:9789813141643_0002. You can help correct errors and omissions. Suggested CitationĪll material on this site has been provided by the respective publishers and authors. Finally, we use Laplace inversion to evaluate the drawdown preceding drawup probability and the conditional density of the maximum relative drawup given a drawdown event, under a geometric Brownian motion (GBM) model. Using a classical approximation argument as in Lehoczky (1977), we derive analytical formulas for this Laplace transform under general linear diffusion models. For the general case, we randomize the time-horizon with an independent exponential random variable - a technique known as Canadization, and reduce the probability of interest to the Laplace transform of the first passage time of the drawdown when it precedes a drawup. To determine this probability, we first consider the simple case with equal-sized drawdown/drawup (i.e., a = b), and derive analytic formulas of this probability by drawing connections to the first exit problems under a simple random walk model and a Brownian motion with drift model. Thus, this probability assesses the relative strength of downside risk (drawdown) compared to upward momentum (drawup) over a finite time-horizon. is defined as Ut := Xt − Xt, ∀t ≥ 0 where Xt := infs∈ Xs denotes the running minimum of X.Formally, the drawup of a stochastic process X We begin our journey to the subject of drawdown in Chapter 2, where we determine the probability that a drawdown of a units precedes a drawup of b units in a finite time-horizon.
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