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Article: A valuation model for perpetual convertible bonds with markov regime-switching models

TitleA valuation model for perpetual convertible bonds with markov regime-switching models
Authors
KeywordsEsscher transform
Incomplete market
Markov chain
Optimal stopping
Perpetual convertible bonds
Regime-switching
Issue Date2009
PublisherAcademic Publications. The Journal's web site is located at http://www.uctm.edu/~jmath/IJPAM
Citation
International Journal Of Pure And Applied Mathematics, 2009, v. 53 n. 4, p. 583-600 How to Cite?
AbstractThis paper develops a valuation model for a perpetual convertible bond when the price dynamics of the underlying share are governed by continuous-time Markovian regime-switching models. We suppose that the appreciation rate and the volatility of the underlying share are modulated by a continuous-time, finite-state, observable Markov chain. The states of this chain are interpreted as the states of an economy. Here the valuation problem of the perpetual convertible bond can be viewed as that of valuing a perpetual stock loan, or a perpetual American option with time-dependent strike price. With the presence of the regime-switching effect, the market in the model is, in general, incomplete. To provide a convenient method to determine a price kernel for valuation, we employ the regime-switching Esscher transform introduced in Elliott, Chan and Siu (2005) [4]. We then adopt the differential equation approach in Guo and Zhang (2004) [7] to solve the optimal stopping problem associated with the valuation of the perpetual convertible bond. Numerical examples are presented to illustrate the practical implementation of the proposed model. © 2009 Academic Publications.
Persistent Identifierhttp://hdl.handle.net/10722/75420
ISSN
2015 SCImago Journal Rankings: 0.299
References

 

DC FieldValueLanguage
dc.contributor.authorSong, Nen_HK
dc.contributor.authorJiao, Yen_HK
dc.contributor.authorChing, WKen_HK
dc.contributor.authorSiu, TKen_HK
dc.contributor.authorWu, ZYen_HK
dc.date.accessioned2010-09-06T07:10:56Z-
dc.date.available2010-09-06T07:10:56Z-
dc.date.issued2009en_HK
dc.identifier.citationInternational Journal Of Pure And Applied Mathematics, 2009, v. 53 n. 4, p. 583-600en_HK
dc.identifier.issn1311-8080en_HK
dc.identifier.urihttp://hdl.handle.net/10722/75420-
dc.description.abstractThis paper develops a valuation model for a perpetual convertible bond when the price dynamics of the underlying share are governed by continuous-time Markovian regime-switching models. We suppose that the appreciation rate and the volatility of the underlying share are modulated by a continuous-time, finite-state, observable Markov chain. The states of this chain are interpreted as the states of an economy. Here the valuation problem of the perpetual convertible bond can be viewed as that of valuing a perpetual stock loan, or a perpetual American option with time-dependent strike price. With the presence of the regime-switching effect, the market in the model is, in general, incomplete. To provide a convenient method to determine a price kernel for valuation, we employ the regime-switching Esscher transform introduced in Elliott, Chan and Siu (2005) [4]. We then adopt the differential equation approach in Guo and Zhang (2004) [7] to solve the optimal stopping problem associated with the valuation of the perpetual convertible bond. Numerical examples are presented to illustrate the practical implementation of the proposed model. © 2009 Academic Publications.en_HK
dc.languageengen_HK
dc.publisherAcademic Publications. The Journal's web site is located at http://www.uctm.edu/~jmath/IJPAMen_HK
dc.relation.ispartofInternational Journal of Pure and Applied Mathematicsen_HK
dc.subjectEsscher transformen_HK
dc.subjectIncomplete marketen_HK
dc.subjectMarkov chainen_HK
dc.subjectOptimal stoppingen_HK
dc.subjectPerpetual convertible bondsen_HK
dc.subjectRegime-switchingen_HK
dc.titleA valuation model for perpetual convertible bonds with markov regime-switching modelsen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=1311-8080&volume=53&spage=583&epage=600&date=2009&atitle=A+Valuation+Model+for+Perpetual+Convertible+Bonds+with+Markov+Regime-switching+Modelsen_HK
dc.identifier.emailChing, WK:wching@hku.hken_HK
dc.identifier.authorityChing, WK=rp00679en_HK
dc.description.naturelink_to_OA_fulltext-
dc.identifier.scopuseid_2-s2.0-78649771811en_HK
dc.identifier.hkuros163929en_HK
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-78649771811&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume53en_HK
dc.identifier.issue4en_HK
dc.identifier.spage583en_HK
dc.identifier.epage600en_HK
dc.publisher.placeBulgariaen_HK
dc.identifier.scopusauthoridSong, N=36466983800en_HK
dc.identifier.scopusauthoridJiao, Y=24764580800en_HK
dc.identifier.scopusauthoridChing, WK=13310265500en_HK
dc.identifier.scopusauthoridSiu, TK=8655758200en_HK
dc.identifier.scopusauthoridWu, ZY=35209289200en_HK

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