EconPapers    
Economics at your fingertips  
 

Drawdowns and the Speed of Market Crash

Hongzhong Zhang () and Olympia Hadjiliadis ()
Additional contact information
Hongzhong Zhang: Columbia University
Olympia Hadjiliadis: Brooklyn College and the Graduate Center C.U.N.Y.

Methodology and Computing in Applied Probability, 2012, vol. 14, issue 3, 739-752

Abstract: 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; Primary 60G40; Secondary 91A60 (search for similar items in EconPapers)
Date: 2012
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3) Track citations by RSS feed

Downloads: (external link)
http://link.springer.com/10.1007/s11009-011-9262-7 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:metcap:v:14:y:2012:i:3:d:10.1007_s11009-011-9262-7

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/11009

DOI: 10.1007/s11009-011-9262-7

Access Statistics for this article

Methodology and Computing in Applied Probability is currently edited by Joseph Glaz

More articles in Methodology and Computing in Applied Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().

 
Page updated 2022-05-12
Handle: RePEc:spr:metcap:v:14:y:2012:i:3:d:10.1007_s11009-011-9262-7