EconPapers    
Economics at your fingertips  
 

Processes of Class Sigma, Last Passage Times, and Drawdowns

Patrick Cheridito, Ashkan Nikeghbali and Eckhard Platen (eckhard.platen@uts.edu.au)

Published Paper Series from Finance Discipline Group, UTS Business School, University of Technology, Sydney

Abstract: We propose a general framework for studying last passage times, suprema, and drawdowns of a large class of continuous-time stochastic processes. Our approach is based on processes of class Sigma and the more general concept of two processes, one of which moves only when the other is at the origin. After investigating certain transformations of such processes and their convergence properties, we provide three general representation results. The first allows the recovery of a process of class Sigma from its final value and the last time it visited the origin. In many situations this gives access to the distribution of the last time a stochastic process attains a certain level or is equal to its running maximum. It also leads to recently discovered formulas expressing option prices in terms of last passage times. Our second representation result is a stochastic integral representation that will allow us to price and hedge options on the running maximum of an underlying that are triggered when the underlying drops to a given level or, alternatively, when the drawdown or relative drawdown of the underlying attains a given height. The third representation gives conditional expectations of certain functionals of processes of class Sigma. It can be used to deduce the distributions of a variety of interesting random variables such as running maxima, drawdowns, and maximum drawdowns of suitably stopped processes.

Keywords: processes of class Sigma; last passage times; drawdowns; relative drawdowns; maximum drawdowns; options on running maxima (search for similar items in EconPapers)
Pages: 24 pages
Date: 2012-01-01
References: Add references at CitEc
Citations: View citations in EconPapers (10)

Published in: Cheridito, P., Nikeghbali, A. and Platen, E., 2012, "Processes of class Sigma, last passage times, and drawdowns", SIAM Journal on Financial Mathematics, 3, 280-303.

Downloads: (external link)
https://epubs.siam.org/doi/abs/10.1137/09077878X (application/pdf)

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:uts:ppaper:2012-4

Access Statistics for this paper

More papers in Published Paper Series from Finance Discipline Group, UTS Business School, University of Technology, Sydney PO Box 123, Broadway, NSW 2007, Australia. Contact information at EDIRC.
Bibliographic data for series maintained by Duncan Ford (duncan.ford@uts.edu.au).

 
Page updated 2025-02-13
Handle: RePEc:uts:ppaper:2012-4