Telegraph Processes with Random Jumps and Complete Market Models

We propose a new generalisation of jump-telegraph process with variable velocities and jumps. Amplitude of the jumps and velocity values are random, and they depend on the time spent by the process in the previous state of the underlying Markov process. This construction is applied to markets modell...

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Tipo de recurso:
Fecha de publicación:
2015
Institución:
Universidad del Rosario
Repositorio:
Repositorio EdocUR - U. Rosario
Idioma:
eng
OAI Identifier:
oai:repository.urosario.edu.co:10336/22586
Acceso en línea:
https://doi.org/10.1007/s11009-013-9388-x
https://repository.urosario.edu.co/handle/10336/22586
Palabra clave:
Compound poisson process
Dependence on the past
Historical volatility
Inhomogeneous Jump-telegraph process
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spelling 3203526002020-05-25T23:57:02Z2020-05-25T23:57:02Z2015We propose a new generalisation of jump-telegraph process with variable velocities and jumps. Amplitude of the jumps and velocity values are random, and they depend on the time spent by the process in the previous state of the underlying Markov process. This construction is applied to markets modelling. The distribution densities and the moments satisfy some integral equations of the Volterra type. We use them for characterisation of the equivalent risk-neutral measure and for the expression of historical volatility in various settings. The fundamental equation is derived by similar arguments. Historical volatilities are computed numerically. © 2013, Springer Science+Business Media New York.application/pdfhttps://doi.org/10.1007/s11009-013-9388-x13875841https://repository.urosario.edu.co/handle/10336/22586engKluwer Academic Publishers695No. 3677Methodology and Computing in Applied ProbabilityVol. 17Methodology and Computing in Applied Probability, ISSN:13875841, Vol.17, No.3 (2015); pp. 677-695https://www.scopus.com/inward/record.uri?eid=2-s2.0-84938977688&doi=10.1007%2fs11009-013-9388-x&partnerID=40&md5=fdd70a523c2dd0ed77161a97c0701231Abierto (Texto Completo)http://purl.org/coar/access_right/c_abf2instname:Universidad del Rosarioreponame:Repositorio Institucional EdocURCompound poisson processDependence on the pastHistorical volatilityInhomogeneous Jump-telegraph processTelegraph Processes with Random Jumps and Complete Market ModelsarticleArtículohttp://purl.org/coar/version/c_970fb48d4fbd8a85http://purl.org/coar/resource_type/c_6501Ratanov, NikitaORIGINAL2015_Article.pdfapplication/pdf649217https://repository.urosario.edu.co/bitstreams/a3112b9e-d343-4785-ac56-3c71ab96184e/download6f04ea530f275be3a6481358b7511541MD51TEXT2015_Article.pdf.txt2015_Article.pdf.txtExtracted texttext/plain36545https://repository.urosario.edu.co/bitstreams/c5645cdc-7173-4be1-a084-50893bd0464c/download62a383853a4940df517c59b01873b40cMD52THUMBNAIL2015_Article.pdf.jpg2015_Article.pdf.jpgGenerated Thumbnailimage/jpeg3727https://repository.urosario.edu.co/bitstreams/61024ceb-ec27-4de4-bd89-a58329616d54/downloadc3866a99e4b3420795ce7f733405c794MD5310336/22586oai:repository.urosario.edu.co:10336/225862021-06-10 23:02:50.6https://repository.urosario.edu.coRepositorio institucional EdocURedocur@urosario.edu.co
dc.title.spa.fl_str_mv Telegraph Processes with Random Jumps and Complete Market Models
title Telegraph Processes with Random Jumps and Complete Market Models
spellingShingle Telegraph Processes with Random Jumps and Complete Market Models
Compound poisson process
Dependence on the past
Historical volatility
Inhomogeneous Jump-telegraph process
title_short Telegraph Processes with Random Jumps and Complete Market Models
title_full Telegraph Processes with Random Jumps and Complete Market Models
title_fullStr Telegraph Processes with Random Jumps and Complete Market Models
title_full_unstemmed Telegraph Processes with Random Jumps and Complete Market Models
title_sort Telegraph Processes with Random Jumps and Complete Market Models
dc.subject.keyword.spa.fl_str_mv Compound poisson process
Dependence on the past
Historical volatility
Inhomogeneous Jump-telegraph process
topic Compound poisson process
Dependence on the past
Historical volatility
Inhomogeneous Jump-telegraph process
description We propose a new generalisation of jump-telegraph process with variable velocities and jumps. Amplitude of the jumps and velocity values are random, and they depend on the time spent by the process in the previous state of the underlying Markov process. This construction is applied to markets modelling. The distribution densities and the moments satisfy some integral equations of the Volterra type. We use them for characterisation of the equivalent risk-neutral measure and for the expression of historical volatility in various settings. The fundamental equation is derived by similar arguments. Historical volatilities are computed numerically. © 2013, Springer Science+Business Media New York.
publishDate 2015
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dc.type.eng.fl_str_mv article
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dc.identifier.issn.none.fl_str_mv 13875841
dc.identifier.uri.none.fl_str_mv https://repository.urosario.edu.co/handle/10336/22586
url https://doi.org/10.1007/s11009-013-9388-x
https://repository.urosario.edu.co/handle/10336/22586
identifier_str_mv 13875841
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dc.relation.citationIssue.none.fl_str_mv No. 3
dc.relation.citationStartPage.none.fl_str_mv 677
dc.relation.citationTitle.none.fl_str_mv Methodology and Computing in Applied Probability
dc.relation.citationVolume.none.fl_str_mv Vol. 17
dc.relation.ispartof.spa.fl_str_mv Methodology and Computing in Applied Probability, ISSN:13875841, Vol.17, No.3 (2015); pp. 677-695
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