Implied Volatility: What, Why & How! - QuantInsti's Blog

Implied Volatility (IV) is the measure of expected future volatility in the options market. Essentially, implied volatility was and is still ... ByPunitNandi “Whenalong-termtrendlosesitsmomentum,short-termvolatilitytendstorise.”-GeorgeSoros Well,thequotesoundsinterestingandcaptivating,buthowdoyouknowwhatisthemarket’sexpectationofvolatility?Moreover,isthereawaytocalculatefuturevolatilitywhichwouldhelpusintakinglongorshortpositionsintheoptionstradingspace?Soundsintriguing,right!! Well,wehavegotallyourquestionsrelatedto“ImpliedVolatilityinoptionstrading”coveredinthisarticle.Thetermusedtocharacterizeexpectedmarketvolatilityfromthedatewhentheoptionisboughttillitsexpirybymarketparticipantsisknownas“ImpliedVolatility(IV)”.Butbeforewejumpintothepeculiaranddistinctcharacteristicsofimpliedvolatility,let’stakealookintothesub-topicsbeingcoveredforthisarticle. UnderstandingImpliedVolatility MathbehindIV CalculatingIVusingpython FactorsaffectingtheIVofanoption UsesofIV InterpretingIV TradingStrategiesusingIV UnderstandingImpliedVolatility Beforewediveintothebasicsofimpliedvolatility,youshouldbeawareoftheoptionstradingbasics. Wewillfirststartwithabriefintroductionofvolatility. Volatility: Volatilityisoneofthemostimportantpillarsinfinancialmarkets.Insimplewords,volatilityreferstotheupwardanddownwardpricemovementsofafinancialasset.Themovementsareduetoseveralfactorsincludingdemandandsupply,sentiment,corporateactions,greed,andfear,etc. Nowthatweknowwhatvolatilityis,letusnowunderstandwhatimpliedvolatilityreallymeans!! WhatisImpliedVolatility? ImpliedVolatility(IV)isthemeasureofexpectedfuturevolatilityintheoptionsmarket.Essentially,impliedvolatilitywasandisstillconsideredtobeanintegralcomponentoftheBlack-Scholes-Mertonmodel(apopularoptionpricingmodel),whereitrepresentsfuturevolatilityassociatedwiththeunderlyingasset. But,didyouknowthatitisnottheonlytypeofvolatilitymeasureavailableinthemarket?Historicalandrealizedvolatilityareotherdifferenttypesofvolatilitymeasuresinthemarket.  Historicalvolatility Historicalvolatilityindicatesthedeviationorchangeinpricesoftheunderlyingassetoveragivenperiodoftimeinpast.Usually,historicalvolatilityiscalculatedoveraperiodofone-yeari.e.252tradingdays.Itisusedbytraderstocomparethecurrentvolatilitylevelofanunderlyingassetwithitshistoricalvolatility.Wheneverthereisagapbetweenthecurrentandhistoricalvolatility,traderstakepositionsbasedontheopportunity.However,theissuewithhistoricalvolatilityisthatitisabackwards-lookingindicatorwhichmeansitisbasedonthepastreturnsandisnotthemostreliableformofvolatility. RealizedVolatility Realizedvolatility,ontheotherhand,istheactualvolatilitythatwilltakeplaceinthefuture.Forthevolatility,thathastakenplaceinthepast,itisknownashistoricalvolatilityandforthevolatilitythatwilltakeplaceinthefuture,itisknownasrealizedvolatility.  So,whydoweuseimpliedvolatilityintheoptionsmarket? Thevalueofimpliedvolatilityhasbeenfactoredinafterconsideringmarketexpectations.Marketexpectationsmaybemajormarketevents,courtrulings,topmanagementshuffle,etc.Inessence,impliedvolatilityisabetterwayofestimatingfuturevolatilityincomparisontohistoricalvolatility,whichisbasedonlyonpastreturns. MathbehindIV WewillnowmoveforwardandunderstandthemathematicsbehindImpliedVolatilityandhowitiscalculatedforoptions. CalculatingIVisnotaneasytaskasitmightappeartobe.TocalculatetheImpliedVolatilityofacallorputoption,wefirstneedtounderstandthemathematicsbehindtheBlackScholesMerton(BSM)Model.Asforthepurposeofthisarticle,wewillnotdigdownmuchintotheconceptoftheBSMModelbutwewilldefinitelyhaveanoverviewofwhatistheBSMmodelsothatthecalculationofImpliedVolatilitylookssimilarandeasytounderstand. BlackScholesMertonModel: TheBlack-Scholes-MertonmodelisthemostpopularoptionpricingmodelusedbytraderswhenitcomestoEuropeanoptions.Ithastwoseparateformulasforcalculatingthecalloptionandtheputoption. TheParametersforcalculatingthecalloptionare: St–SpotPriceoftheunderlyingasset(CurrentPrice) K–StrikePriceoftheunderlyingasset r–Risk-freerate(continuouslycompounded) σ–Volatilityofreturnsoftheunderlyingasset T-t–Timetomaturity(inyears) N–CumulativedistributionfunctionofNormalDistribution Pricingthecalloption: Pricingtheputoption: Looksabitcomplicatedright?Don’tworry,onceyouinputthevaluesoftheparametersitisjustlikeanyothersimpleequation. Forexample:Iftheparametersareasfollows: SpotPrice(St):300StrikePrice(K):250Risk-freerate(r)=5%Timetomaturity(T-t)=0.5years(6months)CallPrice=57.38 Howdowefindtheimpliedvolatilityforthecalloptionwiththeparametersasmentionedabove?Wewillsimplyusethemethodofreiterationortrialanderror. UsingtheIVof15%fetchesusacalloptionpriceof56.45andusing25%givesusacallpriceof59. ItisclearfromtheabovetrialanderrormethodthattheIVisavaluebetweentherangeof15-25%.Whatabout20?.Itgivesusacallpriceof57.38!!Thesametechniquecanbeusedforputoptionsaccordingly.Onceyougetholdofthistechnique,it'seasyaspie! CalculatingIVusingpython Alright,nowthatweknowtheconceptofimpliedvolatility,whynotcreateacalculatorforcalculatingIVofanoption?Afterall,theknowledgeearnedshouldbeappliedpractically!! WewillcreateanimpliedvolatilitycalculatorusingpythonforeasycalculationofIVforanoption. ThePythonCode: ##LetusfirstimportalltherequiredlibrariesforIVCalculation. #Datamanipulation importnumpyasnp importpandasaspd importdatetime importmibian #Wewillnowusethemibianlibrarytocalculatetheimpliedvolatility. ##Thesyntaxforthevariablevaluesisintheformatasmentionedbelow: #BS([UnderlyingPrice,StrikePrice,InterestRate,Daystoexpiration],callPrice=x) #Pythoncode: c=mibian.BS([145.65,145,5,30],callPrice=3.89) #InputCode: c.impliedVolatility Outputfortheinputcode:  18.24951171875 Thismeansthattheimpliedvolatilityforthecalloptionis18.249%(approx) Wasn’tthatsimple?!PythoncalculatesacomplexmathematicalmodelsuchasBlack-Scholes-Mertonformulaveryquicklyandeasily.Thissamemechanismcanbeusedtocalculateputoptionimpliedvolatility. FactorsaffectingImpliedVolatilityinthemarket Let’stakealookatcertainfactorsthatinfluenceimpliedvolatilityinoptionstrading: SupplyandDemand-Withtheincreaseinthedemandforanunderlyingasset,theimpliedvolatilityincreasestooandsodoestheoptionprice!Ofcourse,thisphenomenonisexactlytheoppositewhenthedemandislow.HighIVstendtomovetowardsthemeanIVvaluewiththefallindemandandthesupplystartsstabilizingconcurrently.Thisalltakesplaceoncethemarketexpectationstartsfallingandleadstoareductionintheoptionprice.  TimetoExpiration-Timetoexpiration,betterknownastheta,whichmeasurestheamountoftimeleftfortheoptiontoexpire,affectstheIVofanoptiondirectly.Forexample,ifthetimetoexpiryislittle,theIVusuallywouldbeonthelowerside.However,ifthetimefortheexpirationofanoptionisrelativelylongerthanusual,IVwouldbehigh.Logically,itmakessensetoo!How?Sincethetimetoexpirationishigh,thereisalotmorechancethattheunderlyingasset’spricemightmovetowardsthestrikepriceandthatistooriskyfortheoptionseller.Tocompensatefortherisktakenbytheseller,theoptionpriceisrelativelyhigherthanusualandsoistheIV. Marketcondition-Mostunderlyingassetsaredirectlyimpactedbythemarketsentimentoreventsthataretotakeplaceinthefutureforalistedorganisation.Earningsannouncement,courtruling,topmanagementshuffle,etcaresomeofthemarketeventsthatleadtohighIVwithanoptionasthemarketisunsureofthedirectionthattheunderlyingassetmightmove. UsesofIV ImpliedVolatilityiscertainlyusedfrequentlyintheoptionsmarketbytradersforvariedreasons.ListedbelowarethevarioususesofIV: Toforecastvolatility-ImpliedVolatilityisusedbytraderstounderstandtherangeofexpectedvolatilityforanunderlyingasset.Forexample,letusconsideracalloptionwithanunderlyingassetcurrentlytradingat$100,thestrikepriceat$103andthepremiumat$5.IftheImpliedvolatilityis20%forsuchacalloption,theexpectedrangefortheunderlyingassetis20%abovethecurrenttradepriceand20%belowthecurrenttradeprice.Thistellsusthatthelowerboundwouldbeat100-20%of100=100-20=80.Theupperboundat100+20%of100=100+20=120.Therangeoftheimpliedvolatilityinsuchacasewouldbefrom80-120. Tohedgecashposition-Atraderfrequentlyneedstohedgeapositiontoreducetheriskassociatedwiththeinitialorprimaryposition.IfthecurrentIVofanoptioniscomparativelylowerthantheannualizedIVortheIVfortheentireyear,atradercanbuyoptionsatalowpremiumandwaituntiltheIVincreases.WiththeincreaseinIV,thevalueoftheoptionpremiumrisestooandtherebythetotalvalueoftheoptioncontractjumpsup! Towriteoptions-Contrarytohedging,optionwriters(optionsellers)selloptionswhentheIVishighandtherebypockethighpremiumsfortherisktheyareundertaking.Thecatchhereisthatfortheinsurance(option)theyareselling,timetoexpirationkeepsdecreasing.Afteraconsiderabletimeperiodhaselapsed,thetrademovesintothefavouroftheoptionseller. Event-basedtrading-Wheneverthereisnewsrelatingtoearningsorcourtrulingpendingforalistedorganization,theIVisusuallyhigh.Thishappenswhenthefutureislikelytobeuncertain.Insuchascenario,informedorexperiencedtradersdocreateoptionstrategiesrevolvingaroundimpliedvolatility.Forexample,tradersuse calendarspreadstrategy,bullorbearspreadstrategytobenefitfromhighIV. UsageinBlack-Scholes-Merton(BSM)Model:ImpliedVolatilityisakeyparameterwhenitcomestoBSMModel.Astheimpliedvolatilityorthemarketexpectationaboutthevolatilityincreases,theoptionpriceincreases.Thiscreatesadirectrelationshipbetweenimpliedvolatilityandtheoptionprice.IV,therefore,formsanintrinsicpropertyoftheBlackScholesMertonModel. InterpretingIV Thereismorethanonewaytovisualizeandinterpretimpliedvolatilityandwewilllookateachoneofthemspecifically.  DataTable-Well,themostbasicwaytovisualizeIVnumberswouldbethroughadatatableformat.Now,intheoptionsmarket,itisknownasanoptionchain.BelowisanOptionChainfortheUSStock:Apple(ticker:AAPL) Source:Investing.com(Note:Optionsdataisupdatedeachday,soyouwillbeabletoseethecurrent’sdayoptionpricesonthegivenlink)  Fromtheaboveimage,itisveryclearthattheImpliedVolatilityforthesamestrikepriceisdifferentforcallandputoptions.Also,fordifferentstrikeprices,theImpliedVolatilityfluctuateswiththeshiftinmarketexpectations.Note:ImpliedVolatilityisnotadirectionbasedparameterandthereforeitonlyindicatestherangeofpricesanunderlyingassetmightmoveinthefuture.Thischangeinimpliedvolatilityinboththeputandcalloptionatdifferentstrikepricesischaracterizedby"VolatilitySmile"andVolatilitySkew.VolatilitySmiletakesplacewhentheimpliedvolatility(IV)isthehighestatOTMandITMcallorputoptionswiththelowestat,ATMoption.InthecaseofVolatilitySkew,differentstrikepriceshavedifferentimpliedvolatilityforthesameunderlyingasset. Bothinterpretationsareusedintheoptionsmarketforbettervisualizationpurposes.Below,wehavementionedtheVolatilitySkewexamplefromthecalloptionstrikepricesandimpliedvolatilityrelatively. Chart-Alright,nowthatwehaveunderstoodandinterpretedimpliedvolatilityfromanoptionschaindatatable,wewillvisualizeimpliedvolatilitythroughachartandinterpretIVlevelsfromthesame. Source:IVolatility.com Inthechart,wehavetheimpliedaswellas30-Dayhistoricalvolatilitydataforthepastoneyear.  Marketparticipants,usehistoricalimpliedvolatilitylevelstogaugeanunderstandingofwheretheIV,say,forexample,wasat3monthsagoandatwhatlevelitistodayfortradingbasedontheopportunity. TradersalsousepasttrendsofbothhistoricalandimpliedvolatilitytounderstandiftheHVandIVtogetherarehigherorlowerthanpreviousperiods.Ifyoustarttradingoptionstoday,thisisyourgo-totoolforgaugingimpliedvolatilitylevels.Asstatedearlier,thereareanumberoffactorswhytheimpliedvolatilitylevelishighorlowatacertainpointintime. ImpliedVolatility(IV)Rank-IVRankisanotherpopularwayofcalculatingtheimpliedvolatilityoverthelastoneyearor52weeks.ItiscalculatedforfiguringouthowhighorlowthecurrentIVleveliswhencomparedwiththeannualizedlevels.ThereisaparticularformulatocalculateIVRankwhichismentionedbelow: (CurrentIV-52weekslowIV/52weekhighIV-52weekslowIV)*100 ForExample:Let’sconsidertheexampleofApple(ticker:AAPL)whichwasmentionedinthechartsectionofIV.ThecurrentIVisat32.5%,52weeklowIVis18%.52weekhighIVis34%.Solet’sdothemath: 32.5%-18%/34%-18%=14.5%/16%=90.625%. InterpretingtheIVRankiseasytoo.IntuitivelyIVrankreferstothedifferencebetweentheCurrentIVand52weeklowIVi.Inthiscase,itis90.625%.ThismeansthattheIViscurrentlyhigherthanusualandatraderwouldbeinterestedinsellingtheoptionsduetohighIV.HighIVmeanshighoptionpriceandthuswouldbenefittheoptionsellersheavily.OptionbuyerswhobuyoptionswithhighIVfacelossesduetothedecreaseinIVatalaterpointintime. ImpliedVolatility(IV)Percentile-IVPercentileisanotherinterestingwaytolookatIVortointerpretit.IVPercentilesimplyreferstothenumberofdaysthecurrentIVisunderthecurrentIVpercentagevalueascomparedtothetotalnumberoftradingdays.i.e.252tradingdays IVPercentile=NumberoftradingdaysundercurrentIV/Numberoftradingdaysinayear. Forexample:IfthenumberofdaysunderthecurrentIV(30%)is100.Thenumberoftradingdaysis252.IVPercentile=100/252=39.68percentile(approx).  BelowisadatatableofIndianStocksdatedforthe26thofNovember,2019withtheirIVRankandIVPercentileforvisualizingIVRandIVP! Symbol IVRank IVPercentile ImpliedVolatility TATACOMM 86.99 98.47 48.2 SUZLON 93.17 98.54 184.13 NATIONALUM 73.74 96.65 61.18 CGPOWER 81.12 96.4 106.29 BOSCHLTD 78.16 87.94 36.65 RAYMOND 71.63 95.43 47.33 IDEA 73.04 96.27 167.51 NBCC 72.05 98.74 90.43 IRB 71.43 93.53 87.38 TV18BRDCST 97.1 97.84 80.15 JETAIRWAYS 100 100 483.73 Let’susdeducetheconceptofIVPwithrelationtoImpliedVolatilitywithanexampleoftwoequitystocksi.e.TataCommunicationsLimited(TATACOMM)andSuzlonEnergyLtd(SUZLON).TATACOMMhasanImpliedVolatility(IV)of48.2%whereasSUZLONhasanImpliedVolatilityof184.13%.GiventhatthereisahugegapbetweentheIVsofboththeequitystockoptions,tothelogicalmind,itlooksliketheIVPshouldhaveahugedifferencetoo.However,inreality,theIVPofTATACOMMis98.47andforSUZLON,itis98.54,whichmakesadifferenceofonly0.07percentile! ThismeansthateveniftheIVofTATACOMMwasat48.2%,itwasstilltradingatoneofitshighestlevelssimilartoSUZLON.Therefore,beforetradingoptionsusingIV,oneshouldbeawareastowhathasbeenthehistoricalIVvaluesforanoptionandwhereitstandscurrently.ThisisexactlywheretheapplicationofImpliedVolatilityPercentilebecomescrucial,whereithelpsusinidentifyingcurrentIVvaluesincomparisontowheretheIVhasbeenoverthepastoneyear(252tradingdays). HistoricalIVvsRealizedVolatility-Historically,IVhasatrendofmostlybeingmorethantherealizedvolatility.Marketexpectationskeepfluctuatingwhichmeansthattheyarealwayseithermoreorlessthantherealizedvolatilityvalueoftheunderlyingasset.Inthebelowexample,weshowtheDowJonesIndex’scomparisonbetweenImpliedVolatilityandrealizedvolatility(volatilitythatactuallytookplace)tovisualizethesameconcept.TheBluelinerepresentsrealizedvolatilityandtheyellowlinerepresentsimpliedvolatility.ImpliedVolatilityismostlyabovetherealizedvolatilityduetofluctuationinmarketexpectations. TradingStrategiesusingIV Giventhatthereisapositiverelationshipbetweenimpliedvolatilityandpriceofanoption,tradersuseimpliedvolatilityasakeyparameterfortheirstrategies.Thismayincludebasicoptionsstrategieslikebullspread,bearspreadandcoveredcallstrategy.Usageofimpliedvolatilitycanalsobeseenintradingstrategiesusingforwardvolatilityorwhilepricingoptions.Also,advancedoptionsstrategiesliketheironcondorandmodifiedbutterflystrategiesinvolvetheuseofimpliedvolatility. Conclusion Finally,wehavecometotheendofthisarticle.WelearnedabouttheconceptofImpliedVolatility,whyitisusedandhowitisusedinoptionstrading.WeunderstoodtheBlack-Scholes-MertonmodelandlearnedhowtocalculateIVbyreiteratingtheformula.WealsolearnedhowtocalculateIVusingpython.Allinall,nowthatyouknowaboutimpliedvolatility,youareawareoftheimportancethatIVasaparameterinoptionstradingcarries.However,sinceoptionstradingrequiresriskmanagementandperfectstrategyexecutionmindset,knowledgelearnedfromthisarticlecanbeutilizedasacomplementarytoolwhiletradingoptions! Disclaimer:Allinvestmentsandtradinginthestockmarketinvolverisk.Anydecisionstoplacetradesinthefinancialmarkets,includingtradinginstockoroptionsorotherfinancialinstrumentsisapersonaldecisionthatshouldonlybemadeafterthoroughresearch,includingapersonalriskandfinancialassessmentandtheengagementofprofessionalassistancetotheextentyoubelievenecessary.Thetradingstrategiesorrelatedinformationmentionedinthisarticleisforinformationalpurposesonly. 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