Variance and Volatility Swaps Bubbles and Fundamental Prices外文

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1、JohnsonSchoolResearchPaperSeries#30-2010VarianceandVolatilitySwaps:BubblesandFundamentalPricesRobertA.Jarrow—CornellUniversityPhilipProtter—CornellUniversityMartinLarsson—CornellUniversityYounesKchia—EcolePolytechnique,ParisJune2010Thispapercanbedownloadedwith

2、outchargeatTheSocialScienceResearchNetworkElectronicPaperCollection.VarianceandVolatilitySwaps:BubblesandFundamentalPricesRobertJarrow∗YounesKchia†MartinLarsson‡PhilipProtter§¶June22,2010AbstractThemartingaletheoryofpricebubblesdefinesanassetbubbletoexistwhenth

3、easset’spriceprocessisastrictlocalmartingale,thatis,alocalmartingalethatisnotamartingale.Usingthisdefinitionofapricebubble,forcontinuoussemimartingales,wecharacterizetheconditionsunderwhichvarianceandvolatilityswapsinherittheunderlyingasset’spricebubble.Weshowt

4、hattheexistenceofvarianceswapmarketpricesimpliesthattherearenoswappricebubbles.Furthermore,wealsoshowthatundersomemildadditionalassumptionsthediscretelysampledvarianceswap’smarketpricecanbewellapproximatedbytheexpectationoftheasset’squadraticvariationunderthel

5、ocalmartingalemeasure,providingatheoreticaljustificationofastandardmarketpractice.1IntroductionDuetothe2007creditcrisis,assetpricebubbleshaverecentlyreceivedconsiderableat-tentioninthefinancialpress,especiallywithrespecttoresidentialhousing,commercialrealestate,

6、oilandgoldprices.Concurrently,butinitiallyindependently,anewtheoryforunderstandingassetpricebubbleshasbeengrowingintheacademicliterature.Thisapproach,whichwelabelthemartingaletheoryforbubbles,definesapricebubbletoex-istwhentheasset’spriceprocessisastrictlocalma

7、rtingale,thatis,alocalmartingalethatisnotamartingale(seeCoxandHobson[7],Jarrow,ProtterandShimbo[19],[20],LoewensteinandWillard[22]).Thisnewtheoryisconsistentwithassetmarketsbeingbotharbitrage-freeinthesenseof“NoFreeLunchwithVanishingRisk(NFLVR)”andsatisfying“N

8、oDominance(ND),”1albeitunderND,assetmarketsmustbeincomplete∗JohnsonGraduateSchoolofManagement,CornellUniversity,Ithaca,NY,14853andKamakuraCor-poration†CentredeMath´ematiquesAppliqu