Available online ISSN: Society for Business and Management Dynamics

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1 Applcatn f Extreme Value Cpulas t Palm Ol Prces Analyss Kantaprn Chuangchd 1, Aree Wbnpngse 2, Sngsak Srbnchtta 3 & Chukat Chabnsr 4 Abstract In ths paper we study the tal behavr f the palm l future markets usng the Extreme Value Thery and fcusng n the dependence structure between the returns n palm l future prce n three palm l futures markets, namely Malaysan futures markets (KLSE), Dalan Cmmdty Exchange (DCE) and Sngapre Exchange Dervatves Tradng Lmted (SGX-DT) by usng the Extreme Value Cpulas. The results demnstrated that the returns n palm l future prce amng KLSE and SGX-DT have dependence n extreme, whereas the returns n palm l future prce amng KLSE and DCE, SGX-DT and DCE d nt have any dependence. The results culd be benefcal fr any persn r cmpany wshng t be engaged n the cmmerce f tradng palm l. Key wrds: Extreme Value Thery, Extreme Value Cpulas, Dependence structure, Malaysan futures markets, Dalan Cmmdty Exchange, Sngapre Exchange, Palm l. Avalable nlne ISSN: INTRODUCTION Extreme Value Thery (EVT) s a cncept that s cncerned wth the analyss and mdelng f extreme hgh r lw bservatns. The EVT dstrbuted assumptn gves the results fr the dstrbutn f the nrmalzed maxmum f a hgh number f bservatns, r equvalently, the dstrbutn f exceedances f bservatns ver a hgh threshld (Rakncza and Tajvd, 2010). Under EVT assumptns n the underlyng dstrbutn f bservatns, t s ften superr t nrmal dstrbutn n many stuatns and has been wdely used n many felds such as fnancal, hydrlgcal, nsurance and envrnmental scence (Lu et al., 2008). The jnt extreme events can have sme serus mpact n a partcular feld f study; therefre t needs t be carefully mdeled. Wth a calculatn f the prbablty that there s an bservatn exceedng a certan benchmark, t requres knwledge f the jnt dstrbutn f maxmal heghts durng the frecastng perd. Ths s a typcal feld f applcatn fr EVT (Gudendrf and Segers, 2009). Cpulas methd has becme rapdly develped and has brught the attentn n varus felds as a way tvercme the lmtatns f classcal dependence measures as exemplfed by the lnear crrelatn. The cpulas apprach s a statstcal tl that s cnsdered as the mst general margn-free descrptn f the dependence structure f a multvarate dstrbutn (Segers, 2005). The fact that the thery f multvarate maxma n EVT can be expressed n terms f cpulas, ts phlsphy has been recently acknwledged as a frm fr applcatn. Cpulas s revealed t be a very strng tl n fnancal rsk mdelng that deals wth dfferent classes f exstng rsks (Cherubn et al., 2004). Schlars that have mplemented the extreme value cpulas n ther study ncludes Starca (1999) wh had nvestgated the jnt behavr f extreme returns n a fregn exchange rate market, and Lu, Tan and Zhang (2008) wh had repeatedly taken up the fregn exchange t analyze the dependence structure between the asset return. The results shwed that three cpulas are sutable t measure the jnt tal rsk and tal dependence fr markets data. In addtn, Lngn and Slnk (2001) used EVT t study the dependence structure f nternatnal equty markets characterzed. An applcatn t the Scety f Actuares medcal large clams that the data, n terms f nsurance thrugh extreme-value cpulas, s the tpc f the mngraph by Cebran, Denut and Lambert (2003) Palm l s ne f the mst mprtant energy-crp n the wrld (USDA, 2011), ts mplcatn as an energy crp s due t beng a hghly effcent and hgh yeldng surce f fd and fuel. Palm l s prduced entrely n develpng cuntres. Sutheast Asan cuntres are the largest prducng regn; palm l was prduced mlln tns n 1992, whch ncreased t mlln tns n 2011, a 286% ncrease n 19 years (USDA, 2011). Malaysa s ne f the wrld s bggest palm l prducers. The factrs nvlved n 1 Faculty f Ecnmcs, Chang Ma Unversty, Chang Ma, Thaland. E-Mal: kaekanta@htmal.cm 2 Faculty f Agrculture, Chang Ma Unversty, Chang Ma, Thaland. E-mal: areewbnpngse@gmal.cm 3 Faculty f Ecnmcs, Chang Ma Unversty, Chang Ma, Thaland. E-Mal: sngsak@ecn.cmu.ac.th 4 Faculty f Ecnmcs, Chang Ma Unversty, Chang Ma, Thaland. E-Mal: chukat1973@gmal.cm

2 settng palm l prces are qute nterestng. Accrdng t the relevance f Malaysa s palm l prce t the Chnese and Sngapre markets, t s mprtant t examne the relatnshp between the Malaysan futures markets (KLSE) and tw palm l futures markets, namely Dalan Cmmdty Exchange (DCE) and Sngapre Exchange Dervatves Tradng Lmted (SGX-DT). In ths paper, we wll deal wth the tal behavr f the palm l future markets usng the EVT and fcusng n the dependence structure between the returns n palm l future prce n three palm l futures markets, namely KLSE, DCE and SGX-DT by usng the extreme value cpulas. The remander f the paper s rganzed as fllwed: Sectn 2 presents the unvarate EVT and Generalzed Extreme Value (GEV) dstrbutn, Sectn 3 revews the cncept f cpulas and extreme value cpulas. Sectn 4 explans the data used n the emprcal analyss, Sectn 5 dscusses the emprcal results, and fnally Sectn 6 ffers a cnclusn. UNIVARIATE EVT AND GEV DISTRIBUTION The man dea f Extreme Value Thery (EVT) s the cncept f mdelng and measurng extreme events whch ccur wth a very small prbablty (Brdn and Kluppelberg, 2008). It prvdes methds fr quantfyng such events and ther cnsequences statstcally. Generally, there are tw prncpal appraches t dentfyng extremes n real data. The Blck Maxma (BM) and Peaks-Over-Threshld (POT) are central fr the statstcal analyss f maxma r mnma and f exceedances ver a hgher r lwer threshld (La and Wu, 2007). The BM studes the statstcal behavr f the largest r the smallest value n a sequence f ndependent randm varables (Le and Qa, 2010; Le et al., 2011). The POT apprach s based n the Generalzed Paret Dstrbutn (GPD) ntrduced by Pckands (1975) (cted n Le and Qa, 2010). These are mdels fr all large bservatns that exceed a hgh threshld. In ths paper, we wll adpt GEV mdel f the BM methd t study the tal behavr f the tal f palm l futures markets. let Z (=1,,n) dente maxmum bservatn n each blck. Z n s nrmalzed tbtan a nn-degenerated lmtng dstrbutn. The BM s clsely asscated wth the use f Generalzed Extreme Value (GEV) dstrbutn wth c.d.f: z H(z) = exp 1 (1) Where μ, σ > 0 and ξ are lcatn, scale and shape parameter respectvely. Nte that 1 ξ > 0 s called Frechet dstrbutn, ξ < 0 s called Fsher-Tppet r Webull dstrbutn and ξ = 0 s called Gumble r duble-expnental dstrbutn. Under the assumptn that Z 1,, Z n are ndependent varables havng the GEV dstrbutn, the lg-lkelhd fr the GEV parameters when ξ 0 s gven by: l(ξ, μ, σ) = -nlg σ- (1+1/ξ) Prvded that n lg1 1 z z - n 1 1 > 0, fr =1,.,n 1 1 z (2) The case ξ = 0 requres separate treatment usng the Gumbel lmt f the GEV dstrbutn. The lglkelhd n that case s: l(μ, σ) = -nlg σ- n 1 n - exp 1 The maxmzatn f ths equatn wth respect t the parameter vectr (μ, σ, ξ) leads t the maxmum lkelhd estmate wth respect t the entre GEV famly (see Cles 2001 fr detal) COPULAS AND EXTREME VALUE COPULAS Cpulas have becme the attentn multvarate mdelng n varus felds. A cpula s a functn that lnks tgether unvarate dstrbutn functns t frm a multvarate dstrbutn functn (Pattn, 2007). (3)

3 The relevance f cpulas stems frm a famus result by Sklar (1959) (cted n Segers, 2005). Fr smplcty, we cnfned t t the bvarate case. Let X and Y be the stchastc behavr f tw randm varables wth respectve margnal cdf s F(x) and G(y) s apprprately descrbed wth jnt dstrbutn functn H(x,y) = P(X x, Y y) (4) And margnal dstrbutn functns F(x) = P(X x), G(y) = P(Y y) (5) Snce F(x) and G(y) are unfrmly dstrbuted between 0 and 1, then the jnt dstrbutn functn C n [0,1] 2 fr all (x,y) є R 2 such that: H(x,y) = C(F(x), G(y)) (6) Where C s called the cpula asscated wth X and Y whch cuples the jnt dstrbutn H wth t margns. Equatn (6) s equvalent t H(F -1 (u),g -1 (v)) = C(u,v) as a cnsequence f the Sklar s Therem, where u = F(x), v= G(y) are margnal dstrbutns f X,Y. The mplcatn f the Sklar s Therem s that, after standardzng the effects f margns, the dependence between X and Y s fully descrbed by the cpula (Lu, et al, 2008). A cmprehensve vervew f the cpulas prpertes can be referred t the wrk by Nelsen (1999). In ths paper, we cmbne the cpula cnstructn wth the extreme value thery. The extreme value cpula famly s used t represent the Multvarate Extreme Value Dstrbutn (MEVD) by the unfrmly dstrbuted margns. Cnsder a bvarate sample (X,Y ), =1,.,n. Dente cmpnent-wse maxma by M n = max(x 1,,X n) and N n = max(y 1,,Y n). The bject f nterest s the vectr f cmpnent-wse blck maxma: M c = (M n, N n). The bvarate extreme dstrbutn H can be cnnected by an extreme value cpula (EV cpula) C : (Segers, 2005) H x, y) C ( F( x;,, ), G( y;,, )) (7) Where ( , are GEV parameters and F(x) and G(y) are GEV margn. By Sklar s Therem, the unque cpula C f H s gven by t t t C ( u, v ) C ( u, v), t 0 (8) The EV cpula has mre famly. In ths paper, the tw famly appled are Gumbel and HuslerRess. (Cted n Lu et al., 2008) Gumbel cpula: r r r C( u, v) exp( [( ln u) ( ln v) ] ) (9) The ndependence cpula s btaned n the lmt as r = 1, and cmplete dependence s btaned n the lmt as r =. HuslerRess cpula: 1 1 u 1 1 v ( u, v) exp u ( r ln( )) v( r ln( )) r 2 v r 2 u C (10) Where u ln u, v ln v and Φ s the standardzed nrmal dstrbutn. The ndependence cpula s btaned n the lmt as r = 0, and cmplete dependence s btaned n the lmt as r =. Fr the estmatn f cpulas parameters, we used Exact Maxmum Lkelhd methd (EML): the parameters fr margns and cpula are estmated smultaneusly (see Yan 2007 fr detals). DATA Ths paper used the tmes seres data frm DataStream. We wrk wth daly future prces f palm l data n three markets, namely the Malaysan future markets (KLSE), Dalan Cmmdty Exchange (DCE) and Sngapre Exchange Dervatves Tradng Lmted (SGX-DT). We tk the daly market prces and cnverted t a return seres. Daly prces are cmputed as return f market at tme t relatves: R, t ln( p, t / p, t1) 100, where p, t and p, t1 are the daly prce f futures fr days t and t-1, 1

4 respectvely. The study perd was frm December 2007 tll June We have 1196 bservatns fr each market. EMPIRICAL RESULTS The parameter estmatn f the GEV mdel In the GEV mdel, we fcused n the statstcal behavr f blck maxmum data. Therefre, the surce data s set f 55 recrds f mnthly maxmum n each market. Table1 presents the estmatn f three parameters f GEV mdel based n the maxmum lkelhd methd. The results shw that the standard errr estmates are relatvely lw. It mples that the blck sze f data s apprprate fr the parameter estmatn. Fgure 1, 2, 3 presents the scattered plt f the mnthly maxmum return n KLSE, SGX-DT and DCE, respectvely. Insert table 1 & fgure (1-3) here The parameter estmatn f the extreme value cpulas Insert table 2 here Table 2 presents the parameter ( r ) estmatn n the Gumbel and HuslerRess cpula analyss. In the Gumbel cpula methd, the parameter ( r ) estmatn between KLSE and SGX-DT markets s equal t 3.034, whch mples that KLSE and SGX-DT markets have dependence n extreme. Whereas the parameter ( r ) estmatn amng KLSE and DCE markets, SGX-DT and DCE markets are equal 0.973, 1.065, respectvely, thus ndcatng that KLSE and DCE markets, SGX-DT and DCE markets have nether dependence r even ndependence n extremes. In the case f HuslerRess cpula, the parameter ( r ) estmatn between KLSE and SGX-DT markets s equal t Ths means that KLSE and SGX-DT markets have dependence n extreme, whle the parameter ( r ) estmatn amng KLSE and DCE markets, SGX-DT and DCE markets are equal t 0.220, 0.597, respectvely. Thus, there s an ndcatn that KLSE and DCE markets, SGX-DT and DCE markets have nether dependence nr even ndependence n extremes. CONCLUSION In ths paper, we managed wth the tal behavr f return n three palm l futures prces markets, namely KLSE, DCE and SGX-DT usng the unvarate EVT and GEV dstrbutn. The study fcused n the extreme dependence structure between the returns n palm l futures prces n three markets usng the extreme value cpulas. Tbtan ur results, the paper appled the Gumbel and HuslerRess cpula apprach t examne the extreme dependence between KLSE, DCE and SGX-DT markets. The results demnstrated that bth methds have a smlar utcme. The returns n palm l future prce amng KLSE and SGX-DT have dependence n extreme, whereas the returns n palm l future prce amng KLSE and DCE, SGX-DT and DCE d nt have any dependence. The results culd be benefcal fr any persn r cmpany wshng t be engaged n the cmmerce f tradng palm l. REFERENCES Brdn, E. and Kluppelberg, C. (2008). Extreme Value Thery n Fnance. Encyclpeda f Quanttatve Rsk Analyss and Assessment. Cebran, A., Denut, M., Lambert, P. (2003). Analyss f bvarate tal dependence usng extreme value cpulas: An applcatn t the SOA medcal large clams database. Belgan Actuaral Jurnal, 3(1), Cherubn, U., Lucan, E.,and Vecchat, W. (2004). Cpula Methds n Fnance. Wley. Cles, S. (2001). An ntrductn t statstcal mdelng f extreme values. Sprnger-Verlag Lndn Lmted. Gudendrf, G., & Segers, J. (2009). Extreme-Value Cpulas. Wrkshp n Cpula Thery and ts Applcatns., Lecture Ntes n Statstcs--Prceedng, Sprnger., La, L. and Wu, P. (2007). An Extreme Value Analyss f Tawan s Agrculture Natural Dsaster lss data. In Prceedngs f Internatnal Cnference n Busness and Infrmatn (BAI). July Tky, Japan. Le, X. and Qa, Z. (2010). Mdelng Agrcultural Catastrphc Rsk. Agrculture and Agrcultural Scence Prceda. 1,

5 Le, X., Qa, Z. and X, Z. (2011). Evaluatn f Agrcultural Catastrphc Rsk. Chna Agrculture Ecnmc Revew. 3(4), Lngn, F., Slnk, B. (2001). Extreme crrelatn f nternatnal equty markets. The Jurnal f Fnance, 56(2), Lu, J., Tan, W.-j., & Zhang, P. (2008). The Extreme Value Cpulas Analyss f the Rsk Dependence fr the Fregn Exchange Data. Wreless Cmmuncatns, Netwrkng and Mble Cmputng., 1-6. Nelsen, B., R. (1999). An ntrductn t cpulas. Sprnger, New Yrk. Pattn, A. (2007). Cpula-Based Mdels fr Fnancal Tme Seres. UK: Department f Ecnmcs and Oxfrd-Man Insttute f Quanttatve Fnance. Pckands, J., (1975). Statstcal Inference Usng Extreme Order Statstcs. The Annals f Statstcs. 3, Rakncza, P., & Tajvd, N. (2010). On Predctn f Bvarate Extreme.Internatnal Jurnal f Intellgent Technlges and Appled Statstcs, 3(2), Segers, J. (2005). Extreme-Value Cpulas. Medum Ecnmetrsche Tepassngen., 13(1),9-11. Sklar, A. (1959). Fnctns de réparttn á n dmensns et leurs marges. Publ. Inst. Statst. Unv.Pars, 8, Starca, C., (1999). Multvarate extremes fr mdels wth cnstant cndtnal crrelatns. Jurnal f Emprcal Fnance, 6(5), Unted States Department f Agrculture, Fregn Agrcultural Servce (USDA). (2011). Olseeds: Wrld Markets and Trade, Crcular Seres FOP 05-11, May. Yan, J. (2007). Enjy the Jy f Cpulas: Wth a Package cpula. Jurnal f Statstcal Sftware, 21 (4). Table1. The parameter estmatn results usng the ML methd based n GEV mdel Market Parameter estmatn ML Methd KLSE μ 2.491(0.162) σ 1.060(0.135) ξ 0.281(0.115) SGX-DT μ 2.736(0.186) σ 1.249(0.158) ξ 0.319(0.099) DCE μ 2.827(0.333) σ 2.186(0.245) ξ 0.035(0.104) Nte: Terms n parentheses are standard errrs f parameter estmates. Table2. Estmatn f cpula parameter Market Gumbel cpula HuslerRess cpula KLSE-SGX-DT 3.034(0.473) 2.287(0.414) KLSE-DCE 0.973(0.084) 0.220(2.721) SGX-DT-DCE 1.065(0.079) 0.597(0.156) Nte: Terms n parentheses are standard errrs f parameter estmates.

6 Rs Rm Fgure1. The scatter plt f mnthly maxmum return n KLSE Fgure2. The scatter plt f mnthly maxmum return n SGX-DT

7 Rc Fgure3. The scatter plt f mnthly maxmum return n DCE