Modeling Mortality With Jumps: Applications to Mortality Securitization
Identifieur interne : 000B70 ( Istex/Corpus ); précédent : 000B69; suivant : 000B71Modeling Mortality With Jumps: Applications to Mortality Securitization
Auteurs : Hua Chen ; Samuel H. CoxSource :
- Journal of Risk and Insurance [ 0022-4367 ] ; 2009-09.
Abstract
In this article, we incorporate a jump process into the original Lee–Carter model, and use it to forecast mortality rates and analyze mortality securitization. We explore alternative models with transitory versus permanent jump effects and find that modeling mortality via transitory jump effects may be more appropriate in mortality securitization. We use the Swiss Re mortality bond in 2003 as an example to show how to apply our model together with the distortion measure approach to value mortality‐linked securities. Pricing the Swiss Re mortality bond is challenging because the mortality index is correlated across countries and over time. Cox, Lin, and Wang (2006) employ the normalized multivariate exponential tilting to take into account correlations across countries, but the problem of correlation over time remains unsolved. We show in this article how to account for the correlations of the mortality index over time by simulating the mortality index and changing the measure on paths.
Url:
DOI: 10.1111/j.1539-6975.2009.01313.x
Links to Exploration step
ISTEX:E94CF1715DCB967FBDB5FD888BDB3AFD32535982Le document en format XML
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(2006)</json:string><json:string>November 2004</json:string><json:string>Cox, Lin, and Wang, 2006</json:string><json:string>Diebold, Schuermann, and Stroughair, 1998</json:string><json:string>Biffis, 2005</json:string><json:string>Lee and Miller, 2001</json:string><json:string>Schrager, 2006</json:string><json:string>Wang, 2000, 2002</json:string><json:string>Olivieri and Pitacco, 2002</json:string><json:string>Renshaw and Harberman (2003)</json:string><json:string>Dahl and Møller, 2006</json:string><json:string>Renshaw, Haberman, and Hatzoupoulos, 1996</json:string><json:string>Lin and Cox (2005, 2008)</json:string><json:string>Milevsky and Promislow, 2001</json:string><json:string>Sithole, Haberman, and Verrall, 2000</json:string><json:string>Li and Chan (2005, 2007)</json:string></ref_bibl><bibl></bibl></unitex></namedEntities><ark><json:string>ark:/67375/WNG-JDVGTF24-H</json:string></ark><categories><wos><json:string>1 - social science</json:string><json:string>2 - economics</json:string><json:string>2 - business, finance</json:string></wos><scienceMetrix><json:string>1 - economic & social sciences</json:string><json:string>2 - economics & business</json:string><json:string>3 - finance</json:string></scienceMetrix><scopus><json:string>1 - Social Sciences</json:string><json:string>2 - Economics, Econometrics and Finance</json:string><json:string>3 - Economics and Econometrics</json:string><json:string>1 - Social Sciences</json:string><json:string>2 - Economics, Econometrics and Finance</json:string><json:string>3 - Finance</json:string><json:string>1 - Social Sciences</json:string><json:string>2 - Business, Management and Accounting</json:string><json:string>3 - Accounting</json:string></scopus><inist><json:string>1 - sciences appliquees, technologies et medecines</json:string><json:string>2 - sciences biologiques et medicales</json:string><json:string>3 - sciences medicales</json:string></inist></categories><publicationDate>2009</publicationDate><copyrightDate>2009</copyrightDate><doi><json:string>10.1111/j.1539-6975.2009.01313.x</json:string></doi><id>E94CF1715DCB967FBDB5FD888BDB3AFD32535982</id><score>1</score><fulltext><json:item><extension>pdf</extension><original>true</original><mimetype>application/pdf</mimetype><uri>https://api.istex.fr/ark:/67375/WNG-JDVGTF24-H/fulltext.pdf</uri></json:item><json:item><extension>zip</extension><original>false</original><mimetype>application/zip</mimetype><uri>https://api.istex.fr/ark:/67375/WNG-JDVGTF24-H/bundle.zip</uri></json:item><istex:fulltextTEI uri="https://api.istex.fr/ark:/67375/WNG-JDVGTF24-H/fulltext.tei"><teiHeader><fileDesc><titleStmt><title level="a" type="main">Modeling Mortality With Jumps: Applications to Mortality Securitization</title></titleStmt><publicationStmt><authority>ISTEX</authority><publisher>Blackwell Publishing Inc</publisher><pubPlace>Malden, USA</pubPlace><availability><licence>© The Journal of Risk and Insurance, 2009</licence></availability><date type="published" when="2009-09"></date></publicationStmt><notesStmt><note type="content-type" subtype="article" source="article" scheme="https://content-type.data.istex.fr/ark:/67375/XTP-6N5SZHKN-D">article</note><note type="publication-type" subtype="journal" scheme="https://publication-type.data.istex.fr/ark:/67375/JMC-0GLKJH51-B">journal</note></notesStmt><sourceDesc><biblStruct type="article"><analytic><title level="a" type="main">Modeling Mortality With Jumps: Applications to Mortality Securitization</title><author xml:id="author-0000"><persName><forename type="first">Hua</forename><surname>Chen</surname></persName><affiliation><orgName type="division">Hua Chen is an Assistant Professor in the Department of Risk</orgName><address><addrLine>Insurance</addrLine><addrLine>and Healthcare Management at Temple University, A625 Alter Hall, 1801 Liacouras Walk, Philadelphia, PA 19122.</addrLine></address></affiliation></author><author xml:id="author-0001"><persName><forename type="first">Samuel H.</forename><surname>Cox</surname></persName><affiliation><address><addrLine>Samuel H. 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<ref target="http://www.tei-c.org/">We use TEI</ref></desc></application></appInfo></encodingDesc><profileDesc><abstract xml:lang="en" style="main"><head><hi rend="smallCaps">Abstract</hi></head><p>In this article, we incorporate a jump process into the original Lee–Carter model, and use it to forecast mortality rates and analyze mortality securitization. We explore alternative models with transitory versus permanent jump effects and find that modeling mortality via transitory jump effects may be more appropriate in mortality securitization. We use the Swiss Re mortality bond in 2003 as an example to show how to apply our model together with the distortion measure approach to value mortality‐linked securities. Pricing the Swiss Re mortality bond is challenging because the mortality index is correlated across countries and over time. <ref type="bibr" target="#b13">Cox, Lin, and Wang (2006)</ref> employ the normalized multivariate exponential tilting to take into account correlations across countries, but the problem of correlation over time remains unsolved. We show in this article how to account for the correlations of the mortality index over time by simulating the mortality index and changing the measure on paths.</p></abstract><textClass><keywords rend="tocHeading1"><term>Feature Articles</term></keywords></textClass><langUsage><language ident="en"></language></langUsage></profileDesc><revisionDesc><change when="2019-12-20" who="#istex" xml:id="pub2tei">formatting</change></revisionDesc></teiHeader></istex:fulltextTEI><json:item><extension>txt</extension><original>false</original><mimetype>text/plain</mimetype><uri>https://api.istex.fr/ark:/67375/WNG-JDVGTF24-H/fulltext.txt</uri></json:item></fulltext><metadata><istex:metadataXml wicri:clean="Wiley, elements deleted: body"><istex:xmlDeclaration>version="1.0" encoding="UTF-8" standalone="yes"</istex:xmlDeclaration><istex:document><component version="2.0" type="serialArticle" xml:lang="en"><header><publicationMeta level="product"><publisherInfo><publisherName>Blackwell Publishing Inc</publisherName><publisherLoc>Malden, USA</publisherLoc></publisherInfo><doi origin="wiley" registered="yes">10.1111/(ISSN)1539-6975</doi><issn type="print">0022-4367</issn><issn type="electronic">1539-6975</issn><idGroup><id type="product" value="JORI"></id><id type="publisherDivision" value="ST"></id></idGroup><titleGroup><title type="main" sort="JOURNAL OF RISK AND INSURANCE">Journal of Risk and Insurance</title></titleGroup></publicationMeta><publicationMeta level="part" position="09003"><doi origin="wiley">10.1111/jori.2009.76.issue-3</doi><numberingGroup><numbering type="journalVolume" number="76">76</numbering><numbering type="journalIssue" number="3">3</numbering></numberingGroup><coverDate startDate="2009-09">September 2009</coverDate></publicationMeta><publicationMeta level="unit" type="article" position="11" status="forIssue"><doi origin="wiley">10.1111/j.1539-6975.2009.01313.x</doi><idGroup><id type="unit" value="JORI1313"></id></idGroup><countGroup><count type="pageTotal" number="25"></count></countGroup><titleGroup><title type="tocHeading1"><sc>Feature Articles</sc></title></titleGroup><copyright>© The Journal of Risk and Insurance, 2009</copyright><eventGroup><event type="firstOnline" date="2009-06-23"></event><event type="publishedOnlineFinalForm" date="2009-08-19"></event><event type="xmlConverted" agent="Converter:BPG_TO_WML3G version:2.3.4 mode:FullText source:FullText result:FullText" date="2010-03-30"></event><event type="xmlConverted" agent="Converter:WILEY_ML3G_TO_WILEY_ML3GV2 version:3.8.8" date="2014-01-31"></event><event type="xmlConverted" agent="Converter:WML3G_To_WML3G version:4.1.7 mode:FullText" date="2014-11-13"></event></eventGroup><numberingGroup><numbering type="pageFirst" number="727">727</numbering><numbering type="pageLast" number="751">751</numbering></numberingGroup><objectNameGroup><objectName elementName="appendix">Appendices</objectName></objectNameGroup><linkGroup><link type="toTypesetVersion" href="file:JORI.JORI1313.pdf"></link></linkGroup></publicationMeta><contentMeta><countGroup><count type="figureTotal" number="5"></count><count type="tableTotal" number="7"></count><count type="formulaTotal" number="293"></count><count type="referenceTotal" number="34"></count><count type="linksCrossRef" number="103"></count></countGroup><titleGroup><title type="main"><sc>Modeling Mortality With Jumps: Applications to Mortality Securitization</sc></title></titleGroup><creators><creator creatorRole="author" xml:id="cr1" affiliationRef="#a1"><personName><givenNames>Hua</givenNames><familyName>Chen</familyName></personName></creator><creator creatorRole="author" xml:id="cr2" affiliationRef="#a2"><personName><givenNames>Samuel H.</givenNames><familyName>Cox</familyName></personName></creator></creators><affiliationGroup><affiliation xml:id="a1"><unparsedAffiliation>Hua Chen is an Assistant Professor in the Department of Risk, Insurance, and Healthcare Management at Temple University, A625 Alter Hall, 1801 Liacouras Walk, Philadelphia, PA 19122.</unparsedAffiliation></affiliation><affiliation xml:id="a2" countryCode="CA"><unparsedAffiliation>Samuel H. Cox, FSA, CFA, is Dr. L. A. H. Warren Chair Professor in the Warren Centre for Actuarial Studies and Research at University of Manitoba, 181 Freedman Crescent, Winnipeg, MB R3T 5V4, Canada.</unparsedAffiliation></affiliation></affiliationGroup><abstractGroup><abstract type="main" xml:lang="en"><title type="main"><sc>Abstract</sc></title><p>In this article, we incorporate a jump process into the original Lee–Carter model, and use it to forecast mortality rates and analyze mortality securitization. We explore alternative models with transitory versus permanent jump effects and find that modeling mortality via transitory jump effects may be more appropriate in mortality securitization. We use the Swiss Re mortality bond in 2003 as an example to show how to apply our model together with the distortion measure approach to value mortality‐linked securities. Pricing the Swiss Re mortality bond is challenging because the mortality index is correlated across countries and over time. <link href="#b13">Cox, Lin, and Wang (2006)</link> employ the normalized multivariate exponential tilting to take into account correlations across countries, but the problem of correlation over time remains unsolved. We show in this article how to account for the correlations of the mortality index over time by simulating the mortality index and changing the measure on paths.</p></abstract></abstractGroup></contentMeta><noteGroup><note xml:id="n-fnt-1" numbered="no"><p>Dr. Chen can be contacted via e‐mail: <email>hchen@temple.edu</email>. We presented a former version of this article at the 42nd Actuarial Research Conference in Pittsburgh, the SCOR—<i>Journal of Risk and Insurance</i> Conference on New Forms of Risk Sharing and Risk Engineering in Paris. We appreciate the helpful comments and suggestions from participants at these meetings. We benefited a lot from the discussions with Shaun Wang, Eric Ulm, Daniel Bauer, and Richard MacMinn. We are especially grateful to anonymous referees for their very helpful comments that have much improved this article. We also thank the editors.</p></note></noteGroup></header></component></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>Modeling Mortality With Jumps: Applications to Mortality Securitization</title></titleInfo><titleInfo type="alternative" contentType="CDATA" lang="en"><title>Modeling Mortality With Jumps: Applications to Mortality Securitization</title></titleInfo><name type="personal"><namePart type="given">Hua</namePart><namePart type="family">Chen</namePart><affiliation>Hua Chen is an Assistant Professor in the Department of Risk, Insurance, and Healthcare Management at Temple University, A625 Alter Hall, 1801 Liacouras Walk, Philadelphia, PA 19122.</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Samuel H.</namePart><namePart type="family">Cox</namePart><affiliation>Samuel H. Cox, FSA, CFA, is Dr. L. A. H. Warren Chair Professor in the Warren Centre for Actuarial Studies and Research at University of Manitoba, 181 Freedman Crescent, Winnipeg, MB R3T 5V4, Canada.</affiliation><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre type="article" displayLabel="article" authority="ISTEX" authorityURI="https://content-type.data.istex.fr" valueURI="https://content-type.data.istex.fr/ark:/67375/XTP-6N5SZHKN-D">article</genre><originInfo><publisher>Blackwell Publishing Inc</publisher><place><placeTerm type="text">Malden, USA</placeTerm></place><dateIssued encoding="w3cdtf">2009-09</dateIssued><copyrightDate encoding="w3cdtf">2009</copyrightDate></originInfo><language><languageTerm type="code" authority="rfc3066">en</languageTerm><languageTerm type="code" authority="iso639-2b">eng</languageTerm></language><physicalDescription><extent unit="figures">5</extent><extent unit="tables">7</extent><extent unit="formulas">293</extent><extent unit="references">34</extent><extent unit="linksCrossRef">103</extent></physicalDescription><abstract lang="en">In this article, we incorporate a jump process into the original Lee–Carter model, and use it to forecast mortality rates and analyze mortality securitization. We explore alternative models with transitory versus permanent jump effects and find that modeling mortality via transitory jump effects may be more appropriate in mortality securitization. We use the Swiss Re mortality bond in 2003 as an example to show how to apply our model together with the distortion measure approach to value mortality‐linked securities. Pricing the Swiss Re mortality bond is challenging because the mortality index is correlated across countries and over time. Cox, Lin, and Wang (2006) employ the normalized multivariate exponential tilting to take into account correlations across countries, but the problem of correlation over time remains unsolved. We show in this article how to account for the correlations of the mortality index over time by simulating the mortality index and changing the measure on paths.</abstract><relatedItem type="host"><titleInfo><title>Journal of Risk and Insurance</title></titleInfo><genre type="journal" authority="ISTEX" authorityURI="https://publication-type.data.istex.fr" valueURI="https://publication-type.data.istex.fr/ark:/67375/JMC-0GLKJH51-B">journal</genre><identifier type="ISSN">0022-4367</identifier><identifier type="eISSN">1539-6975</identifier><identifier type="DOI">10.1111/(ISSN)1539-6975</identifier><identifier type="PublisherID">JORI</identifier><part><date>2009</date><detail type="volume"><caption>vol.</caption><number>76</number></detail><detail type="issue"><caption>no.</caption><number>3</number></detail><extent unit="pages"><start>727</start><end>751</end><total>25</total></extent></part></relatedItem><relatedItem type="references" displayLabel="cit1"><titleInfo><title>Affine Processes for Dynamic Mortality and Actuarial Valuations</title></titleInfo><name type="personal"><namePart type="given">E.</namePart><namePart type="family">Biffis</namePart><role><roleTerm type="text">author</roleTerm></role></name><genre>journal-article</genre><note type="citation/reference">Biffis, E., 2005, Affine Processes for Dynamic Mortality and Actuarial Valuations, Insurance: Mathematics and Economics, 37(3): 443‐468.</note><part><date>2005</date><detail type="volume"><caption>vol.</caption><number>37</number></detail><detail type="issue"><caption>no.</caption><number>3</number></detail><extent unit="pages"><start>443</start><end>468</end></extent></part><relatedItem type="host"><titleInfo><title>Insurance: Mathematics and Economics</title></titleInfo><part><date>2005</date><detail type="volume"><caption>vol.</caption><number>37</number></detail><detail type="issue"><caption>no.</caption><number>3</number></detail><extent unit="pages"><start>443</start><end>468</end></extent></part></relatedItem></relatedItem><relatedItem type="references" displayLabel="cit2"><titleInfo><title>Living with Mortality: Longevity Bonds and Other Mortality‐Linked Securities</title></titleInfo><name type="personal"><namePart type="given">D.</namePart><namePart type="family">Blake</namePart><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">A. 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