Pairs Trading of Two Assets with Uncertainty in Co-integration’s Level of Mean Reversion

《Pairs Trading of Two Assets with Uncertainty in Co-integration’s Level of Mean Reversion》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。

1、PairsTradingofTwoAssetswithUncertaintyinCo-integration’sLevelofMeanReversionSangminLeeAndrewPapanicolaouyThispaperconsidersastochasticcontrolproblemderivedfromamodelforpairstradingunderincompleteinformation.Wedecomposeanindividualasset’sdriftintotwopa

2、rts:anindustrydriftplussomeadditionalstochasticity.Theextrastochasticitymaybeunobserved,whichmeanstheinvestorhasonlypartialinformation.WesolvethecontrolproblemunderbothfullandpartialinformationforutilityfunctionU(x)=x1=(1),andwemakecomparisons.Weshow

3、theexistenceofstablesolutiontotheassociatedmatrixRiccatiequationsinbothcasesfor >1,butfor0< <1thereremainspotentialforinfinitevaluefunctionsinfinitetime.Also,wequantifytheexpectedlossinutilityduetopartialinformation,andpresentanumericalstudytoillustratet

4、hecontributionofthispaper.Keywords:Pairstrading;Co-integration;Kalmanfilter;PartialInformation;StochasticControl.1IntroductionWestudytheproblemofoptimalpairstradingstrategywithuncertaintyinthelevelofmeanreversion.Weconsidertwoco-integratedassets:anindus

5、trybenchmarkwithdeterministicvolatilityanddrift-rate;ariskierassetrelatedtoafirmintheindustrywithdeterministicvolatilityanddriftt=+additionalstochasticity.Thisadditionalstochasticityisproportionaltothelevelofmeanreversionintheassets’co-integration.W

6、econsidertwomarketconditions:amarketwhereinvestorsobservedriftsandanotherwhereinvestorsdonotobservedrifts.Ourmotivationforconsideringunobserveddriftsisbecausereal-worldgrowthratesforindividualfirmsarenoteasytoobserve.Withoutobservationofthedriftprocesse

7、s,wesaythattheinvestorsarepartiallyinformed.Partially-informedinvestorswillfilterthedriftofindividualfirmsgiventheobservedprices,andwillthenusethefilterastheymaximizetheirexpectedutilityoveradmissibletradingstrategies.Incontrast,aworldwheredriftprocessesa

8、refullyobserved,wesaythattheinvestorsarefullyinformed.Inbothmarketconditions,thedriftoftheindustrybenchmarkhasrelativelylownoise,andtherefore,inthispaperweconsideritobserved(i.e.isknown).Forbothfullandpartially-informedinvestment,thepr