Cointegration Pairs Trading Strategy on Derivatives

Transcription

1 Proceedings 59h II World isics Congress, 5-3 Augus 3, Hong Kong ession 73 p.54 Coinegrion Pirs rding reg on Derivives Dr. LEE Pk Kuen, Philip Join Work wih Prof. CHAN Ngi Hng nd Miss PUN Li Fun Augus 6 h 3

2 Inroducion ome finncil insrumens move more or less in line wih ech oher ecuse he re driven similr fundmenl e.g. economic fcors. For emple, ock prices of Coc Col nd Pepsi Currenc Pirs AUD/UD vs NZD/UD Proceedings 59h II World isics Congress, 5-3 Augus 3, Hong Kong ession 73 p.54 However, he do no move EXACLY he sme ecuse of heir individul echnicl fcors, which cn e ssumed o e noises on op of he common movemen. isicl Approch: Coinegrion - Assume h he underling re sochsic processes shring he sme sochsic drif. - Filer ou he co-movemen of pirs of mrke insrumens idenifing possile sionr series which is liner cominion of wo non-sionr series e.g. price of socks.

3 Overview Proceedings 59h II World isics Congress, 5-3 Augus 3, Hong Kong ession 73 p.54 ecion : Bckground ecion : Coinegrion Pir rding reg on Derivives ecion 3: Inclusion of Relized Voliliies Forecss on Model elecion Crieri ecion 4: Conclusion 3

4 Proceedings 59h II World isics Congress, 5-3 Augus 3, Hong Kong ession 73 p.543 ecion Inroducion 4

5 Coinegrion Definiion: wo non-sionr ime series { X } nd { Y } re coinegred if some liner cominion X + Y, is sionr series. h is X + Y ~ I Chn Le nd e he prices of wo socks ime. Assume h { log + log } is sionr, hen nd re pproimel coinegred. Proof: Consider Coinegrion Pir rding reg: Long nd shres of nd, which is sionr men-revering. 5 log log log log log log consn Proceedings 59h II World isics Congress, 5-3 Augus 3, Hong Kong ession 73 p.544

6 Pir rding reg on Coinegrion Proceedings 59h II World isics Congress, 5-3 Augus 3, Hong Kong ession 73 p.545 Implemenion of he reg Invesige possile coinegred series from pirs of logsock prices [or logechnge res] sed on he Johnsen es picll 5% of pirs For ech coinegrion pirs, check if he curren level of he sionr series i.e. X log log is oo low/high gins is hisoricl men e.g. Z-score =-, + Ener he rde i.e. u/sell of nd of ime nd epec he sionr series X o men-rever ck o i hisoricl verge level. E.g. 46 socks => 46 C = 575 possile cominion of sock pirs ENumer of coinegred series 5755% 9 6

7 Proceedings 59h II World isics Congress, 5-3 Augus 3, Hong Kong ession 73 p.546 Performnce of Coinegrion Pir rding reg Works well for sock prices in he sme secor, hrder o inerpre for socks from differen secors. No much juice on simple finncil insrumens, s oher sisicl echniques sed on men-reversion ssumpion e.g. PCA is le o deec similr rdes. Would like o eend he coinegrion sreg on derivives Emple: Eend from Currenc pirs of AUD/UD vs NZD/UD o Opion on AUD/UD vs opion on NZD/UD 7

8 Proceedings 59h II World isics Congress, 5-3 Augus 3, Hong Kong ession 73 p.547 ecion Coinegrion Pir rding reg on Derivives 8

9 Pir rding on Derivives rde he Implied Voliliies σ hrough -he-mone Europen rddles. Blck-choles Formul: Prices of Europen Cll nd Pu of sock price wih epir ime is given where, r nd q he risk-free re nd he dividend ield respecivel, σ is he implied vol. 9, d e d Ke P d Ke d e C q r r q q r K d / / log Proceedings 59h II World isics Congress, 5-3 Augus 3, Hong Kong ession 73 p.548

10 Proceedings 59h II World isics Congress, 5-3 Augus 3, Hong Kong ession 73 p.549 Bsics of n A-he-mone rddle Price of n -he-mone AM srddle srike K e rq cn e wrien s C P O <4% if - =.5 er nd σ < 4% I.e., is pproimel liner, oh in he underling nd implied volili σ. => rde he implied vol σ hrough longing/shoring he srddle

11 rding Porfolio of rddles Consider porfolio P consider of longing n -he-mone srddle for underling nd shoring n -he-mone srddle for underling : he profi nd Loss P/L of he porfolio cn e pproimed B A P P P P P P P P P Del P/L Gmm P/L mosl negive Depends on he relized voliliies of & he P/L Men-reversion of he rding ignl Chose o e Posiive Veg P/L Proceedings 59h II World isics Congress, 5-3 Augus 3, Hong Kong ession 73 p.55

12 Pirs rding reg on rddles Proceedings 59h II World isics Congress, 5-3 Augus 3, Hong Kong ession 73 p.55 he rding signl is oined from coinegrion, nd herefore i s men revering. Define he Z-score of he rding signl s follows: Z ˆ Define he porfolio of srddles of nd o e P w where w / which is he s order pproimion of Crieri for he rding reg: hor P if Z > +., nd long P if Z < -. Crr of he rde is posiive. h is, P

13 Emple of he rding reg Proceedings 59h II World isics Congress, 5-3 Augus 3, Hong Kong ession 73 p.55 rding ignl Implied,88.HK. 795 Implied,898.HK Z-score > +. Ener he rde horing one uni of 88.HK srddle nd longing.795 uni of 898.HK srddle Z-score < Men-reversion => Profi king 3

14 rde elecion Procedures Proceedings 59h II World isics Congress, 5-3 Augus 3, Hong Kong ession 73 p.553 D: Implied voliliies of he 3-monh -he-mone srddles of Hng eng Inde Consiuens 44 o 46 of hem, from 9Q4 o Q4 9 qurers. Coinegrion pirs were idenified ever qurer, sed on he dil implied voliliies for he ps 3 ps qurers. Afer iniiing pir rding on derivive, decision Rule cn e defined s follows: Profi king if Z-score of he rding signl men-revers ck o.. op loss if Z-score of he rding signl diverges o +3.5 or -3.5 c Lef he opions epire oherwise 4

15 Proceedings 59h II World isics Congress, 5-3 Augus 3, Hong Kong ession 73 p.554 reg Performnce: rddles on HK ocks Core Pr of he rde Men Reversion of rding ignl => posiive Veg Posiive he Crr rdes wih posiive he P/L over ime were chosen from our rde selecion crieri Negive Gmm Opposie o he in generl, funcion of relized voliliies Disriuion of Del roughl smmeric on verge for ech rde 5

16 reg Performnce: rddles on FX Res Proceedings 59h II World isics Congress, 5-3 Augus 3, Hong Kong ession 73 p.555 Wh doesn work on FX Res? More ffeced fundmenl fcors vs echnicl fcors for socks Wh ws hppened in Jul Augus? Risk Aversion => Relized vol => Implied vol => Coinegrion Opporuniies Need crierion on Implied vol sed on forecss of Relized vol 6

17 Proceedings 59h II World isics Congress, 5-3 Augus 3, Hong Kong ession 73 p.556 ecion 3 Modeling nd Forecsing Relized Voliliies 7

18 Esimion of Relized Voliliies R Proceedings 59h II World isics Congress, 5-3 Augus 3, Hong Kong ession 73 p.557. Hisoricl Esime: Log-dil-reurn Rˆ H H r i i r H r r / wih i i ln X ln X. J.P. Morgn Risk Merics: Eponenill Weighed Moving Averge of squred log-dil-reurn: Rˆ H H i i r r where. 94 i 3. Grmn-Klss Esimes: Assume he underling X follows he Geomeric Brownin Moion: dx X d X dw Rˆ.7 O C f where O, C, u nd d re he Open, Close, High nd Low of he underling of he -h d, nd f is frcion of non-rding hours in rding d. 8 r.83 u d f 4ln / H

19 Esimion of Relized Voliliies R Proceedings 59h II World isics Congress, 5-3 Augus 3, Hong Kong ession 73 p High Frequenc Esime: Le {, }, n,, N,, e he log-reurn of n underling sse he n h minue of he h d. Assume h r n, re i.i.d wih men zero nd consn vrince σ /N. he High Frequenc Esime is N Rˆ rn, for,, n Advnges of High Frequenc Esime: r n, he esime depends on od s informion ONLY => No lgging issue s in Hisoricl Esime nd JP Morgn Risk Merics Unised esimor for σ. In conrs, Grmn-Klss underesimes σ, s he high nd low oserved in discree ime under- nd over-esime he high nd low in GBM. 9

20 Forecsing Relized Voliliies R Andersen, Bollerslev, Dieold nd Ls 3 proposed he use of ARFIMA,, model on he log of relized voliliies of high-frequenc esimes Proceedings 59h II World isics Congress, 5-3 Augus 3, Hong Kong ession 73 p.559 L he model is le o L, ~ N, cpure he smmeric proper of he uncondiionl disriuion of Rˆ ; cpure he long-memor proper of ; ln Rˆ d provide he es - nd -d hed relized voliliies forecss mong + models. iid Rˆ

21 rde elecion Crieri Curren Crierion hor P if Z > +., or long P if Z < -. Posiive he Addiion Crieri Implied/Relized Rio: Define he rio hor P if K.7, or Long P if K.3 Limiing loss due o Gmm P/L vs gin in Veg P/L: Iniie he rde if P / / R R K Implied Vol Relized Vol n i i i o o o o R R n d R R E ˆ ˆ Gmm P/L o o E Veg P/L. Gmm P/L Veg P/L L E E Proceedings 59h II World isics Congress, 5-3 Augus 3, Hong Kong ession 73 p.56

22 rde elecion Crieri Addiion Crieri o Limi he loss due o Gmm Limiing he loss wihin EGmm P/L: Define he rio K Crieri: hor P if K.7, or Long P if K.3 Limiing loss due o Gmm P/L vs gin in Veg P/L: Iniie he rde if n i i n i i R R K ˆ / ˆ / Forecss of Relized Vol n i i i o o o o R R n d R R E ˆ ˆ Gmm P/L o o Veg P/L rgeed. Gmm P/L Veg P/L rged L E Proceedings 59h II World isics Congress, 5-3 Augus 3, Hong Kong ession 73 p.56

23 Performnce of he Originl reg Proceedings 59h II World isics Congress, 5-3 Augus 3, Hong Kong ession 73 p.56 Period wih High Relized Voliliies Jul Augus 3

24 Performnce of rding reg Proceedings 59h II World isics Congress, 5-3 Augus 3, Hong Kong ession 73 p.563 Mos of he rdes in Jul-Augus were filered ou 4

25 Performnce of rding reg 3 Proceedings 59h II World isics Congress, 5-3 Augus 3, Hong Kong ession 73 p.564 5

26 ummr of rding regies Proceedings 59h II World isics Congress, 5-3 Augus 3, Hong Kong ession 73 p.565 6

27 Conclusion Proceedings 59h II World isics Congress, 5-3 Augus 3, Hong Kong ession 73 p.566 Coinegrion Pir rding reg works well on -hemone srddles. ARFIMA,, model on High Frequenc Esime of Relized Voliliies is le o provide useful forecss on he epeced Gmm P/L of n -he-mone srddle. he inclusion of relized voliliies forecss ino rde selecion crieri is le o provide eer P/L of he pir rding sregies on derivives. 7