peculiarities of volatilities by ernest chan at quantcon 2016
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Peculiari)esofVola)li)es
ErnestChan,Ph.D.QTSCapitalManagement,LLC.
• Ph.D.intheore)calphysics.• Previously,researcheratIBMT.J.WatsonLabinmachine
learning,researcher/traderforMorganStanley,CreditSuisse,andvarioushedgefunds.
• ManagingMemberofQTSCapitalManagement,acommoditypooloperatorandtradingadvisor.
• Author:– Quan%ta%veTrading:HowtoBuildYourOwnAlgorithmicTradingBusiness(Wiley2009).
– AlgorithmicTrading:WinningStrategiesandTheirRa%onale(Wiley2013).
• Blogger:epchan.blogspot.com
AboutMe
2
Vola)lityPredic)on
• Predic)ngvola)lity:That’sEasy!• Successinpredic)ngrealizedvola)litydoesnotimplysuccessinpredic)ngimpliedvola)lity.
• Canarbitragebetweenpredictedrealizedvola)lityandimpliedvola)lity.
Vola)lityPredic)on
• “Therearemanythousandsofpapersonforecas)ngvola)lityusingahostofincreasinglysophis)cated,evenNobel-Prize-winning,sta)s)caltechniques.”–Ahmad&Wilmo\,2005.
• Oneofthelatest,incrediblycomplicatedbutbrilliantpaper*:Gatheral,etal,2014,basedon“frac)onalBrownianMo)on”.
GARCH• Mercifully,goodoldGARCHcanworkpre\ywellforus
prac)caltraders.• GARCH(p,q):ifr(t)islogreturnfromt-1tot,𝑟↓𝑡 = 𝑚↓𝑡 + 𝜎↓𝑡 𝜖↓𝑡, 𝜎↓𝑡↑2 =𝜔+∑𝑖=1↑𝑝▒𝛼↓𝑖 𝜎↓𝑡−𝑖↑2 +∑𝑖=1↑𝑞▒𝛽↓𝑖 𝑟↓𝑡−𝑖↑2 where𝑚↓𝑡 is expected return, and 𝜖↓𝑡 isaGaussianrandomvariablewithzeromeanandunitvariance.• 𝜎↓𝑡↑2 isthecondi)onalvarianceof𝑟↓𝑡 .• Simplyput:“predictedvarianceisalinearfunc)onofpast
predictedvariancesandpastrealizedsquaredreturns.”
GARCH
• Weneedtoes)mate𝑝,𝑞,𝜔, 𝛼↓𝑖 , 𝛽↓𝑖 usingmaximumlikelihoodes)ma)on(withpenaltyonmodelcomplexity)onsometrainingdata.
• Nottoworry:MATLAB,R,Pythonallhaveready-madetoolboxes/packagesgaloreforthis.
• TrythisonSPY(stockindex),USO(oilfutures),GLD(gold),AAPL(singlestock),andEURUSD(currency).
GARCH:predic)veaccuracy
• Out-of-sample(2010/11/30-2016/03/11)accuracyinpredic)ngsignof1-dayvola)litychange:– SPY:66%– USO:67%– GLD:59%– AAPL:60%– EURUSD:62%– Ifwehavethataccuracyinpredic)ngsignof1-daypricechange,wewouldberich!
Tradingvola)lity?
• Butwait…couldn’twetradevola)lityviaVXX,VXV,VXZ,XIV,XVZ,VXfuture,...?– NotemyomissionofVIXinabovelist.
• Intui)vestrategy:GARCHpredictsincreaseinrealizedvola)lity→BuyVXX.Viceversa.
• Result?
Implied≠RealizedVola)lity
• VIXindexandrealizedvola)litymoveinsamedirec)ononly51%ofdays.– Almostzerocorrela)onbetweensignsofimpliedandrealizedvola)litychange!
• Infact,on56%ofdayswithposi)vereturns,VIXandrealizedvola)litymoveinoppositedirec)on.– Lessdemandtobuyporoolioinsurancewhenmarketgoesup?
TradingVola)lity
• Predictedchangeinrealizedvola)litywon’thelpuspredictchangeinimpliedvola)lity.
• ButRV(t+1)-IV(t)(asopposedtoRV(t+1)-RV(t))can!– RV(t+1)istheGARCH-predictedrealizedvola)lityfornextperiod.
– IV(t)≡VIX(t)isthecurrentimpliedvola)lity• Strategy:RV(t+1)-VIX(t)>0→BuyVXX.Viceversa.– i.e.ExpectRV(t+1)tobebe\erpredictorofVIX(t+1)thanVIX(t)!
TradingVola)lity
• Result:CAGR=26%,butSharpera)o=0.7only.– (2010/11/30-2016/03/11).
• Similarly,Ahmad&Wilmo\,2005suggested– RV(t+1)-IV(t)>0→Buyop)onanddelta-hedge)llexpiry→Profit!(Noviceversahere.)
– Supposedtoworkforanyop)ons,notjustindexop)ons,thatcanbemodeledbyBlack-Scholesequa)on.
VIXvsVXX(orVX)
• WesuggestedtradingtheETNVXX(whichreflectsreturnsofVXfutures).
• Wecannottradetheunderlyingvola)lityindexVIXitself.
• TradingSPY≈tradingstockindexSPX but
TradingVXX ≉tradingvola)lityindexVIX!
VIXvsVXX(orVX)
• VIXistheweightedaveragepriceofaporoolioofOTMSPXop)onswithtenorof23-37days.
• Buttheporooliocomposi)oncanchangeminute-to-minute!– Seewww.cboe.com/micro/vix/vixwhite.pdf
• E.g.ifVIX(t)=$20,andVIX(t+1)=$21,⇏poroolioweheldatthasappreciated$1byt+1.
Timedecayofop)onspremium
• Evenifimpliedvola)lityremainsconstantin)me,marketvalueofVIXporooliowills)lldecline.– Timedecayofop)onspremium.– Nega)ve“theta”.
• Nega)vethetaofSPXop)ons⇒nega4ve“rollreturn”ofVXXorVXfutures(whenmarketcondi)onremainsconstant).
RollreturnsofVX
• Sign(RollreturnofVX)=Sign(VXfuture–VIXindex)isatradingsignal.
• RollreturnofVX>0→BuyVX.Viceversa.• Result:CAGR=60%,Sharpera)o=1.– (2004/03/26-2015/08/28).
VXrollreturnstrategy
• Notewherethereturnsstartedtofalter:2013.– Justaxerthepaper(Simon&Campasano,2012)describingthisstrategywaspublished!
• TradingofVXhavechangedpricesofSPXop)onsthemselves?
• IsVIXs)llagoodpredictoroffuturerealizedvola)lityduetothisarbitrageac)vity?– Ifnot,whatisitusefulfor?
Thankyouforyour)me!
www.epchan.comTwi\er:@chanep
Blog:epchan.blogspot.com
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