2017 3rd International Conference on E-commerce and Contemporary Economic Development (ECED 2017) ISBN:

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1 7 3rd Inernaional Conference on E-commerce and Conemporary Economic Developmen (ECED 7) ISBN: Fuures Arbirage of Differen Varieies and based on he Coinegraion Which is under he Framework of Bayesian In he Case of Soy Oil and Palm Oil Bing-ing FAN Shanghai Universiy, 99 Shang Da Road, Baoshan Disric, Shanghai Ciy, China Keywords: Coinegraion Model; Expeced Reurn Maximizaion; The Bayesian Framework; Arbirage Beween Differen Varieies. Absrac. This paper mainly sudies commodiy fuures arbirage opporuniies across he soy oil and palm oil. The radiional way is raders can carry ino he marke when he spread ou of he reasonable scope. When he price back o normal levels, unwinding operaion and complee an arbirage process. However, spreads of soy oil and palm oil does no mee he sabiliy, so we need o es coinegraion model residual error afer regression, combined wih he maximizaion of expeced reurn o deermine he arbirage opporuniy. In radiional coinegraion model, long-erm equilibrium relaionship is y = x. When he residual absolue value is greaer han 6.5, arbirageurs may ake posiions ino he marke, unil he residual back o a reasonable range. However he radiional coinegraion model wihou considering he esimaion error, and esimaed parameer has high sensiiviy. So we will use he bayesian mehod o esimae parameers, we ge he Bayesian- coinegraion is y = x. The residual under his model is sable. Therefore, we can find arbirage opporuniies hrough he model. When he residual is more han or less han riggered buying condiions, and can gain maximum expeced reurn. Inroducion Zhengzhou grain wholesale marke in 99 formal inroducion of fuures rading mechanism, Help opens he door of he fuures marke in our counry. Since 993, he sae council noice regulaes he marke and fuures marke gradually ino he sandard sage of developmen, China's fuures marke walked hrough he 3 years of wind and rain. Our counry as large agriculural producs consumers, he analysis of agriculural producs fuures arbirage opporuniies across varieies has he pracical significance, arbirage make he marke price is more reasonable, o enhance he sabiliy and liquidiy of he marke. Soybean oil and palm oil are wo imporan oil producs, hey have a srong alernaive in he daily consumpion and use. So hey are in he fuures marke showed a srong correlaion. Because he coinegraion model wihou considering possible nonlinear relaionship beween he wo commodiy fuures and i canno consider asymmeric volailiy near he error of he mean. So some scholars on he basis of radiional coinegraion model inroducing he hreshold, and combining he fundamenal analysis and echnical analysis o he agriculural produc fuures marke arbirage opporuniies o make judgmen. This paper is o refer o previous experience, combined wih bayesian framework o ge sable coinegraion model and inroducing hreshold judgmen arbirage opporuniies. Daa In order o avoid he risk, liquidiy risk and delivery o ensure he efficiency of he model, his paper use of soybean fuures and he main palm oil fuures conracs daa for empirical analysis. We will choose acive conrac selemen price of soy oil and palm oil commodiy fuures on May 4, 5 o May 9, 6. Correlaion beween commodiy fuures can make cross varieies arbirage, and in his aricle, heir correlaion coefficien is.93, so he srong correlaion beween hem. We need o judge he saionariy of soy oil and palm oil prices sequence before modeling, We can ge 3

2 he resuls hrough he uni roo es: P value of soy oil and palm oil are boh.8, boh are far greaer han.5 and boh are non-saionary sequence. Mean-revering process On he marke ha decided by he power of supply and demand, The price of any asse is unlikely o presen unilaeral rend for a long ime, The marke price of he asse eiher above or below is inrinsic value will reply o is inrinsic value wih large probabiliy, his is he heory of mean reversion, I is an imporan heoreical basis across a variey of arbirage. Coinegraion regression analysis In an economic sysem, alhough various economic variables have heir long-erm variaion rule due o differen influence facors, bu hey maybe exis sable linear relaionship, o show he non-saionary economic variables have a long-erm and sable relaionship. According o he resul of uni roo es deermine soy oil and palm oil commodiy fuures conrac daa is non-saionary, so wheher here is a linear combinaion beween he wo conracs is smooh, i is need o se up he coinegraion regression o observe. x means sequence daa of palm oil, y means sequence daa of soy oil. Coinegraion regression model can be se up as follows: y = α + β x + ε Using OLS esimaes can obained he model y = x. For coinegraion model, residual sabiliy deermines wheher here is a long-erm equilibrium relaionship beween he wo conracs. In his model, he residual error sequence hrough he saionary es, he p value is.9, is far less han.5, i shows ha spreads has srong abiliy of mean reversion. Coinegraion under he framework of bayesian The classical coinegraion model use sample esimaes of parameers as if hey were he rue parameers, bu is sensiiviy is higher. So we can use he Bayesian framework o solve his sensiiviy. The bayesian framework is a rade-off beween he sample informaion and prior disribuion, which is under he background of probabiliy knowledge. Soy oil and palm oil commodiy fuures conrac price here is a coinegraion relaionship as y = α + β x + ε. Parameer space is Θ = ( θ, θ ), ε ~ N (, ), θ = [ α, β]. Assume ha he prior disribuion of θ = [ α, β] is noninformaive prior disribuions, as π (θ) =. follows he Gamma disribuion,as π( ) e. Each parameer is independen of each oher. Join prior disribuion can be expressed in he following way: π(θ ) e. When he parameers are known, he join likelihood funcion can be wrien as : ' L( Θ, X, Y ) exp{ ( Y θ X ) ( Y θx )} () π he a poseriori probabiliy of parameers is π( Θ X,Y) e exp( ( θ ) ( ˆ θ X X θ θ)) π And he marginal poserior disribuion are given,respecively, by π π ( α β, θ,x,y) e ( β α, θ,x,y) e exp( π exp( π ( θ ) ( ˆ θ X X θ θ)) ( θ ) ( ˆ θ X X θ θ)) () (3) (4) (5) 3

3 π( θ ) ( ˆ θ,x,y) e θ θ X X θ θ)) π (6) where θˆ T - T = ( X X) X Y. Due o he complexiy of disribuion form, we use Gibbs sampling for parameer esimaion, he ieraion seps as follow: Sep.() Se he iniial sae Θ = ( α, β, ) Sep. () Sampling from he poserior condiional disribuion π( α β,,x,y) e θ ) ( ˆ θ X X θ θ)) and ge π Sep. (3) Sampling from he poserior condiional disribuion π( β α,,x,y) e θ ) ( ˆ θ X X θ θ)) and ge π Sep. (4) Sampling from he poserior condiional disribuion π( β, α,x,y) e θ ) ( ˆ θ X X θ θ)) and ge π Sep () - (4) compleed he firs round of he ieraion, repea sep () - (4), unil he markov chain presen saionary, figure is Gibbs sampling principle diagram, Model can be expressed as y = x β α ; The Deerminaion of Arbirage Opporuniies Figure. Gibbs sampling principle diagram. How o deermine he arbirage inerval, we need o analysis residual. When he spread value deviaes from he value of he long-erm equilibrium modesly, in a smaller range, no arbirage space, a his poin should be kep shor posiions. When he price deviaing from he equilibrium value reaches a cerain degree, he exisence of arbirage opporuniies, can build arbirage porfolio. We need o build opimizaion model o deermine he arbirage inerval, o deermine he hreshold value of enry and exi he marke. Opimal hreshold of radiional coinegraion model An arbirage will make a profi Rij = θ ( Px, - Px, ) + θ βij ( Py, n - Py, ) = θ ( ε o -ε n ) n where, P x, means he price of soy oil a ime o, θ means amoun of soy fuures, βij means he coordinaion coefficien. In order o ensure a posiive earnings, can be se R ij s k δij,where δ ij is he sandard deviaion of he residual. The selecion of he k deermines he profiabiliy, If k is larger, migh miss oher profi opporuniies; If small k value, arbirage opporuniies maybe more, bu he 33

4 ransacion cos will increase. We assume ha he arbirage expeced revenue funcion is E( kσ ) = θ R( kσ ) ϕ ( kσ ), by maximizing he expeced revenue, he appropriae k value can be obained Figure. Profi probabiliy under differen k value Figure 3. Profi under differen k value Figure 4. Expeced revenue rend. Wihou considering he ransacion coss, k =.75 can maximize he expeced revenue, namely when he residual is more han 6.5 or less han- 6.5, can ge he bigges arbirage profis. Opimal hreshold of Coinegraion which under he framework of bayesian Coinegraion which under he framework of Bayesian consider he esimaion error, so his model is superior o he radiional coinegraion model Figure 5. Profi probabiliy under differen k value Figure 6. Profi under differen k value. Figure 7. Expeced revenue rend. 34

5 Wihou considering he ransacion coss, k =.65 can maximize he expeced revenue, namely when he residual is more han 4.48 or less han- 6.48, can ge he bigges arbirage profis. Summary Due o srong correlaion which creae arbirage opporuniies beween soy oil and palm oil, However, he spreads beween he wo conracs is no saionary, so need o using coinegraion model o esablish he long-erm equilibrium relaionship beween he wo conracs, and ge a seady residual which can be seen as a kind of rading fuures conracs. Tradiional coinegraion model parameers are sensiive, so we considering parameers esimaion in bayesian framework, coinegraion under he bayesian framework on he basis of he original sample combined wih he prior disribuion of he parameers, o improve he accuracy of parameer esimaion and sensiiviy. Furhermore, he aricle hrough he maximum expeced revenue obained hreshold of long posiions and shor posiions. arbirage hrough he model ha coinegraion which under he framework of bayesian can gain higher reurns and lower risks. References [] Dengzong Han, The research ha risk and speculaive comparison beween DCE and CBOT soybean fuures, Business research, 5, pp [] Guangping Zhang, correlaion analysis beween China's copper fuures and inernaional copper fuures, The Shanghai fuures exchange sudy,3. [3] Xiuling Ding, Renhai Hua, A dalian Commodiy Exchange beween soybean and soybean meal fuures arbirage, Saisical sudy, 7. [4] Zou Jiao, Fuures arbirage across species rebar and he glass, Insiue of economic and rade, 5. [5] Liu Da, Agriculural producs fuures across arbirage sraegy analysis--rape oil fuures and soybean oil fuures arbirage, Guangxi Universiy, 4. [6] Sufang Li, Huiming Zhu, Based on Gibbs sampling of high-frequency financial daa coinegraion relaionship research Bayesian, Saisics and informaion BBS,, pp