File Download
  Links for fulltext
     (May Require Subscription)
Supplementary

Article: Valuing equity-linked death benefits and other contingent options: A discounted density approach

TitleValuing equity-linked death benefits and other contingent options: A discounted density approach
Authors
KeywordsDiscounted Density
Equity-Linked Death Benefits
Exponential Stopping
Minimum Guaranteed Death Benefits
Option Pricing
Variable Annuities
Issue Date2012
PublisherElsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/ime
Citation
Insurance: Mathematics And Economics, 2012, v. 51 n. 1, p. 73-92 How to Cite?
AbstractMotivated by the Guaranteed Minimum Death Benefits in various deferred annuities, we investigate the calculation of the expected discounted value of a payment at the time of death. The payment depends on the price of a stock at that time and possibly also on the history of the stock price. If the payment turns out to be the payoff of an option, we call the contract for the payment a (life) contingent option. Because each time-until-death distribution can be approximated by a combination of exponential distributions, the analysis is made for the case where the time until death is exponentially distributed, i.e., under the assumption of a constant force of mortality. The time-until-death random variable is assumed to be independent of the stock price process which is a geometric Brownian motion. Our key tool is a discounted joint density function. A substantial series of closed-form formulas is obtained, for the contingent call and put options, for lookback options, for barrier options, for dynamic fund protection, and for dynamic withdrawal benefits. In a section on several stocks, the method of Esscher transforms proves to be useful for finding among others an explicit result for valuing contingent Margrabe options or exchange options. For the case where the contracts have a finite expiry date, closed-form formulas are found for the contingent call and put options. From these, results for De Moivre's law are obtained as limits. We also discuss equity-linked death benefit reserves and investment strategies for maintaining such reserves. The elasticity of the reserve with respect to the stock price plays an important role. Whereas in the most important applications the stopping time is the time of death, it could be different in other applications, for example, the time of the next catastrophe. © 2012 Elsevier B.V.
Persistent Identifierhttp://hdl.handle.net/10722/172493
ISSN
2015 Impact Factor: 1.378
2015 SCImago Journal Rankings: 1.000
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorGerber, HUen_US
dc.contributor.authorShiu, ESWen_US
dc.contributor.authorYang, Hen_US
dc.date.accessioned2012-10-30T06:22:47Z-
dc.date.available2012-10-30T06:22:47Z-
dc.date.issued2012en_US
dc.identifier.citationInsurance: Mathematics And Economics, 2012, v. 51 n. 1, p. 73-92en_US
dc.identifier.issn0167-6687en_US
dc.identifier.urihttp://hdl.handle.net/10722/172493-
dc.description.abstractMotivated by the Guaranteed Minimum Death Benefits in various deferred annuities, we investigate the calculation of the expected discounted value of a payment at the time of death. The payment depends on the price of a stock at that time and possibly also on the history of the stock price. If the payment turns out to be the payoff of an option, we call the contract for the payment a (life) contingent option. Because each time-until-death distribution can be approximated by a combination of exponential distributions, the analysis is made for the case where the time until death is exponentially distributed, i.e., under the assumption of a constant force of mortality. The time-until-death random variable is assumed to be independent of the stock price process which is a geometric Brownian motion. Our key tool is a discounted joint density function. A substantial series of closed-form formulas is obtained, for the contingent call and put options, for lookback options, for barrier options, for dynamic fund protection, and for dynamic withdrawal benefits. In a section on several stocks, the method of Esscher transforms proves to be useful for finding among others an explicit result for valuing contingent Margrabe options or exchange options. For the case where the contracts have a finite expiry date, closed-form formulas are found for the contingent call and put options. From these, results for De Moivre's law are obtained as limits. We also discuss equity-linked death benefit reserves and investment strategies for maintaining such reserves. The elasticity of the reserve with respect to the stock price plays an important role. Whereas in the most important applications the stopping time is the time of death, it could be different in other applications, for example, the time of the next catastrophe. © 2012 Elsevier B.V.en_US
dc.languageengen_US
dc.publisherElsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/imeen_US
dc.relation.ispartofInsurance: Mathematics and Economicsen_US
dc.rightsNOTICE: this is the author’s version of a work that was accepted for publication in Insurance: Mathematics And Economics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Insurance: Mathematics And Economics, 2012, v. 51 n. 1, p. 73-92. DOI: 10.1016/j.insmatheco.2012.03.001-
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.subjectDiscounted Densityen_US
dc.subjectEquity-Linked Death Benefitsen_US
dc.subjectExponential Stoppingen_US
dc.subjectMinimum Guaranteed Death Benefitsen_US
dc.subjectOption Pricingen_US
dc.subjectVariable Annuitiesen_US
dc.titleValuing equity-linked death benefits and other contingent options: A discounted density approachen_US
dc.typeArticleen_US
dc.identifier.emailYang, H: hlyang@hku.hken_US
dc.identifier.authorityYang, H=rp00826en_US
dc.description.naturepublished_or_final_versionen_US
dc.identifier.doi10.1016/j.insmatheco.2012.03.001en_US
dc.identifier.scopuseid_2-s2.0-84859339556en_US
dc.identifier.hkuros218762-
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-84859339556&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume51en_US
dc.identifier.issue1en_US
dc.identifier.spage73en_US
dc.identifier.epage92en_US
dc.identifier.eissn1873-5959-
dc.identifier.isiWOS:000305259800008-
dc.publisher.placeNetherlandsen_US
dc.identifier.scopusauthoridGerber, HU=7202185517en_US
dc.identifier.scopusauthoridShiu, ESW=6603568601en_US
dc.identifier.scopusauthoridYang, H=7406559537en_US
dc.identifier.citeulike10487941-

Export via OAI-PMH Interface in XML Formats


OR


Export to Other Non-XML Formats