Methodology and Computing in Applied Probability

, Volume 14, Issue 3, pp 739–752 | Cite as

Drawdowns and the Speed of Market Crash

Article

Abstract

In this paper we examine the probabilistic behavior of two quantities closely related to market crashes. The first is the drawdown of an asset and the second is the duration of time between the last reset of the maximum before the drawdown and the time of the drawdown. The former is the first time the current drop of an investor’s wealth from its historical maximum reaches a pre-specified level and has been used extensively as a path-dependent measure of a market crash in the financial risk management literature. The latter is the speed at which the drawdown occurs and thus provides a measure of how fast a market crash takes place. We call this the speed of market crash. In this work we derive the joint Laplace transform of the last visit time of the maximum of a process preceding the drawdown, the speed of market crash, and the maximum of the process under general diffusion dynamics. We discuss applications of these results in the pricing of insurance claims related to the drawdown and its speed. Our applications are developed under the drifted Brownian motion model and the constant elasticity of variance (CEV) model.

Keywords

Drawdown Speed of market crash Diffusions Drawdown insurance 

AMS 2000 Subject Classifications

Primary 60G40; Secondary 91A60 

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of StatisticsColumbia UniversityNew YorkUSA
  2. 2.Department of MathematicsBrooklyn College and the Graduate Center C.U.N.Y.BrooklynUSA

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