Processes of class sigma, last passage times, and drawdowns

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dc.contributor.author Cheridito, P
dc.contributor.author Nikeghbali, A
dc.contributor.author Platen, E
dc.date.accessioned 2012-10-12T03:32:50Z
dc.date.issued 2012
dc.identifier.citation SIAM Journal on Financial Mathematics, 2012, 3 (1), pp. 280 - 303
dc.identifier.other C1 en_US
dc.identifier.uri http://hdl.handle.net/10453/17960
dc.description.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. Copyright © 2012 by SIAM.
dc.language eng
dc.relation.isbasedon 10.1137/09077878X
dc.title Processes of class sigma, last passage times, and drawdowns
dc.type Journal Article
dc.description.version Published
dc.parent SIAM Journal on Financial Mathematics
dc.journal.volume 1
dc.journal.volume 3
dc.journal.number en_US
dc.publocation US en_US
dc.identifier.startpage 280 en_US
dc.identifier.endpage 303 en_US
dc.cauo.name SCI.Mathematical Sciences en_US
dc.conference Verified OK en_US
dc.for 0102 Applied Mathematics
dc.personcode 970685
dc.percentage 100 en_US
dc.classification.name Applied Mathematics en_US
dc.classification.type FOR-08 en_US
dc.edition en_US
dc.custom en_US
dc.date.activity en_US
dc.location.activity en_US
dc.description.keywords Drawdowns
dc.description.keywords Last passage times
dc.description.keywords Maximum drawdowns
dc.description.keywords Options on running maxima
dc.description.keywords Processes of class Sigma
dc.description.keywords Relative drawdowns
pubs.embargo.period Not known
pubs.organisational-group /University of Technology Sydney
pubs.organisational-group /University of Technology Sydney/Faculty of Science
pubs.organisational-group /University of Technology Sydney/Strength - Quantitative Finance
utslib.copyright.status Open Access
utslib.copyright.date 2015-04-15 12:23:47.074767+10
pubs.consider-herdc true
utslib.collection.history School of Mathematical Sciences (ID: 340)
utslib.collection.history General (ID: 2)


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