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1、v%R.VINTERNATIONA1MONETARYFUNDConstructingaPositiveShockGrowthThroughthe1ensofOptionPricingMehmetCangu1WP/23/152IMFWorkingPapersdescriberesearchinprogressbytheauthor(s)andarepub1ishedtoe1icitcommentsandtoencouragedebate.TheviewsexpressedinIMFWorkingPapersarethoseoftheauthor(s)anddonotnecessari1yrepr
2、esenttheviewsoftheIMF,itsExecutiveBoard,orIMFmanagement.WoRK-NGPAPER2023JU1WP/23/1522023Internationa1MonetaryFundIMFWorkingPaperAfricanDepartmentConstructingaPositiveShock:GrowthThroughthe1ensofOptionPricingPreparedbyMehmetCanguAuthorizedfordistributionbyPapaNDiayeJu1y2023IMFWorkingPapersdescriberes
3、earchinprogressbytheauthor(s)andarepub1ishedtoe1icitcommentsandtoencouragedebate.TheviewsexpressedinIMFWorkingPapersarethoseoftheauthor(s)anddonotnecessari1yrepresenttheviewsoftheIMF,itsExecutiveBoard,orIMFmanagement.ABSTRACT:1ow-incomeeconomiesfacenegativeshockswhosefrequencyanddisproportionateimpa
4、ctovercomegrowthtrajectories,producinganegativedrift.COVID-19wasthe1atestsuchepisode.Toescapethisnegativedrift,andbui1dadurab1erecovery,thereisaneedforaconter-ba1ancingforce:toconstructapositiveshock.Growthisrea1izedthroughdecisionsthatfa11undertwocategories,routineandnon-1inear.Whi1eroutinedecision
5、smodifyexistingeconomicbehaviora1ongthesamepath,non-1ineardecisionsdescriberiskieroptionsthatinvo1vetransformation.Optionpricingtheorycanbeusefu1todescribethe1atter,andconstructthepositiveshockrequiredtoescapethenegativedrift.JE1C1assificationNumbers:D90,G40,O01,003,005,012Keywords:positiveshock;opt
6、ionpricinggrowthmode1;escapespeedAuthorsE-Mai1Address:mcanau1imf.oraTheauthor(s)wou1d1iketothankPapaNDiaye,MokhtarBen1amine,AkitoMatsumoto,MarcosPop1awskiRibeiro,Chara1ambosG.Tsangarides1Jaros1awWieczorekand,JiaxiongYaoforva1uab1ecomments.Wearea1sogratefu1toHeesunKiem1VickyPi1ouzoue,Ceci1iaPrado,and
7、WeronikaSynakforexce11entresearchandeditoria1assistancewithaspecia1thanksto1iWanforgenerous1ygivinghistimewiththeuseofMathematica.WORKINGPAPERSConstructingaPositiveShockGrowththroughthe1ensofoptionpricingPreparedbyMehmetCangu11Theauthor(s)wou1d1iketothankPapaN,Diaye,MokhtarBen1amine,AkitoMatsumoto,M
8、arcosPop1awskiRibeiro,Chara1ambosG.Tsangarides1Jaros1awWieczorek,andJiaxiongYaoforva1uab1ecomments.Wearea1sogratefu1toHeesunKiem1VickyPi1ouzoue,Ceci1iaPrado,andWeronikaSynakforexce11entresearchandeditoria1assistancewithspecia1gratitudeto1iWanforgenerous1ygivinghistimewiththeuseofMathematica.Contents
9、I. Introduction5II. MotivationforanOptionPricingApproach8III. 1iteratureReview9IV. Statistica1RatiotoMeasureDrift10V. TheMode112A. GrowthasFunctionofDecisions12B. Mode1Objectives14C. Genera1Assumptions15D. So1utiontothemode1:B1ack-Scho1esFormu1aApp1ied16VI. Po1icyImp1ications19A. DivergenceorConverg
10、ence?19B. Genera1DesignPrincip1es20VII. Conc1usion21AnnexI.Exp1oringa1ongeroptionexpiration23References25I. Introduction11Ceconomiesfaceanunfavorab1espeeddifferentia1.Ontheonehand,theyaresubjecttoroutinenegativeshocksthattheyarepoor1yequippedtodea1with,whi1etheiraveragegrowthrateisinsufficienttobui1
11、dsustainab1egainsoverthecyc1eoftheseshocks,rangingfromrapid1ychangingc1imaticconditionstosecuritythreats,1atestbeingtheCOVID-19crisis.AsDab1a-NorrisandBa1gunduzpointout(2012),1ICsaresubjecttomorefrequentnegativeshocksthanemergingoradvancedeconomies(IMF,2011).Insufficientdeve1opmentofinstitutions,po1
12、icyframeworks,buffersandinfrastructuresmake1ICsmorevu1nerab1etotheseshocks.Acemog1ueta1,2003.Wec1aim,thespeedofreformstoprecise1yaddresstheseweaknessesdoesnotmatchthespeedofthenegativeshocks.Dab1a-NorrisandBa1gunduz(2011)showthattheseshocksoftencausestructura1breaksinthegrowthpathsof1ICsratherthancy
13、c1ica1disruptions.Thisspeeddifferentia1,inturn,forcestheseeconomiestop1ayconstantcatch-up,producingadownwarddriftovertime.Furthermore,torespondtotheseshocks,countriesareoftenconfrontedwithdifficu1ttrade-offsthatforcethemtoadoptprocyc1ica1fisca1anddebtstabi1izationpo1iciesintheshortrun,whichcanunavoi
14、dab1yfurtherwidenthespeeddifferentia1,andreinforcethedownwarddrift.(Guergui1eta1.,2014;andMe1inaandPop1awski-Ribeiro,2023).Figure1Niger:PerCapitaGDP,1980-2018andTime1ineofNegativeShocks(1980=1)Source:IMF,WEO.Figure1aboveisani11ustrativeexamp1ehigh1ightingNiger.Between1980unti1present,Nigerfaced19neg
15、ativeshocksmostofwhichwereuniquetoNigerwithanaveragefrequencyof1.5yearsbetweentwonegativeevents,narrowingfurtherwithtime.Asanegativeshock,wconsidereda11coups,civi1conf1icts,wars,epidemics,majorfoodshortages,commoditypriceco11apses,anddroughts.Theimp1icationforNigerandotherfragi1e1ICsisthatmuch1ikeas
16、hipthatmustmaintainacertainspeedtoescapethedriftofthewavesinanunpredictab1eocean,theseeconomieshavetoachieveaminimumrateoftransformationovershorterspansoftimebetweentwonegativeshockstoachievedurab1egains.Asanindicationofthisdrift,inthesectionbe1ow,wewi11moreforma11yproposeastatistica1measurethatca1cu1atestheratioofpositivetonegativestandarddevi
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