the feedback effect of hedging in illiquid markets

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1、CHAPTER61thefeedbackeffectofhedginginilliquidmarketsInthisChapter...•howdeltahedginganoptionpositionorreplicationcaninfluenceandmovethemarketintheunderlying61.1INTRODUCTIONIhavereferredconstantlytothe‘underlying’asset.Theimplicationofthiswasthattheassetpricele

2、adsandtheoptionpricefollows;theoptionvalueiscontingentuponthevalueandprobabilisticpropertiesoftheasset,andnottheotherwayaround.Inpracticeinmanymarkets,however,thetradeintheoptionsonanassetcanhaveanominalvaluethatexceedsthetradeintheassetitself.So,canwestillth

3、inkoftheassetpriceasleadingtheoption?InthetraditionalderivationoftheBlack–Scholesoptionpricingequationitisassumedthatthereplicationtradingstrategyhasnoinfluenceonthepriceoftheunderlyingassetitself,thattheassetpricemovesinarandomway.Thisisabitlikesayingthatopti

4、onstradingisazero-sumgame;foreverywinnerthereisanequalandoppositeloser.Sometimesthejustificationforthisistheactionofnoisetradersortherandomflowofinformationconcerningtheassetortheeconomy.Nevertheless,asignificantnumberoftradesareforhedgingorreplicationpurposes.A

5、nd,crucially,thesetradesareforpredictableamounts.Whatistheirimpactonthemarket?Usuallyitisassumedthattheeffectofindividualtradingontheassetpriceistoosmalltobeofanyimportanceandisneglectedwhenthestrategyisderived.Thisseemsjustifiableifthemarketinquestionhasmanyp

6、articipantsandahighdegreeofliquidity,whichisusuallytrueformodernfinancialmarkets.Ontheotherhand,theportfolioinsurancetradingstrategiesareveryoftenimplementedonalargescale,andtheliquidityofthefinancialmarketsissometimesverylimited.InthecaseoftheOctober1987stockm

7、arketcrashsomeempiricalstudiesandeventheofficialreportoftheinvestigationscarriedoutbytheBradycommissionsuggestthatportfolioinsurancetradingcontributedtoaggravatetheeffectsofthecrash.Inthischapterwearegoingtoaddresstheproblemoftheinfluenceofthesetradingstrategie

8、sonthepriceoftheunderlyingassetandthus,inafeedbackloop,ontothemselves.990PartFiveadvancedtopics61.2THETRADINGSTRATEGYFOROPTIONREPLICATIONIntheory,anysimpleoptioncanbereplicatedbyfollowing