World currency options market efficiency

Transcription

1 Arful Hoque (Australa) World optons market effcency Abstract The World Currency Optons (WCO) maket began tradng n July 2007 on the Phladelpha Stock Exchange (PHLX) wth the new features. These optons are desgned for monthly maturty wth smaller contract sze than the exstng opton contract whch matures quarterly. As a result, the volume of tradng has soared, ncreasng the effcency of opton prces. The objectve of ths study s to analyze the early stage performance of WCO market. We adapt the no-arbtrage put-call party (PCP) relatonshp based econometrc approach wth accommodatng all potental tme seres problem to examne the WCO market effcency. The overall results strongly suggest that WCO market s effcent even though t s young and n the settlng curve. Keywords: world optons, put-call party, unt root, seral correlaton, ARCH. JEL Classfcaton: G13, G14. Introducton The World Currency Optons (WCO) s an entrely new class of optons launched n Phladelpha Stock Exchange (PHLX) on July 24, These optons are desgned to mature monthly rather than quarterly. Before WCO market, the optons were traded only for maturty months: March, June, September and December on the PHLX. Further, each opton contract represents 10,000 unts of the underlyng, except for Japanese yen (1,000,000), whch s smaller than the exstng opton contract, openng up the world of tradng to those wth smaller nvestment accounts. As a result, the volume of tradng has soared, ncreasng the effcency of opton prces. Ths paper provdes a systematc analyss of the effcency ssues n the WCO market for sx major currences: Australan dollar (), Brtsh pound (), Canadan dollar (), Euro (), Japanese yen () and Swss franc (). Emprcal analyss s carred out based on the wellaccepted PCP no-arbtrage condton to examne whether the WCO market s effcent. Gddy (1983) and Grabbe (1983) were among the frst to develop relatonshps for put and call optons such as the put-call party theorem for foregn, whch must be satsfed to prevent domnance or arbtrage possbltes. Several studes have performed the optons market effcency test wthout allowng for transacton costs (see, for example, Trpp, 1977; Chras and Manaster, 1978; Shastr and Tandon, 1985; Bodurtha and Courtadon, 1986). The results, n general, dd not support market effcency. Phllps and Smth (1980) provded a systematc treatment of the transacton costs facng traders n the organzed optons market. They ncluded explct costs, n the form of commssons and other fees, and mplct costs, such as bd-ask spreads for prcng of transacton servces. The explct costs of Arful Hoque, commssons and other fees are nsttutondependent. The mplct cost of the bd-ask spread s the dfference between the hghest quote to buy and the lowest offer to sell the asset n the market. Phllps and Smth (1980) also documented the transacton cost ranges for ndvdual nvestors, optons market makers and arbtrageurs when they ntate trades n ether stocks or optons. Ther studes ndcated relatvely hgh transacton costs ncurred by an ndvdual nvestor, but refuted the assumpton of several prevous researchers that market maker transacton costs are neglgble. Ther results ndcate that the larger the transacton cost, the wder the band s wthn whch prces can swng wthout creatng arbtrage opportuntes. Kem (1989) and Yadav and Pope (1990) estmated 1 percent as an average bd-ask spread n ther PCP tests. Subsequently, Puttonen (1993) used an estmate of a 2 percent bd-ask spread for the Helsnk Stock Exchange, whch s regarded as much more thnly traded than ts U.S. and Englsh counterparts, and the FOX ndex, whch conssts of the 25 most lqud stocks. Nsbet (1992) dentfed sgnfcant numbers of PCP devatons n the presence of bdask spreads that almost dsappear when commssons are taken nto account wth bd-ask spreads as transacton costs. Chateauneuf et al. (1996) ponted out that bd-ask spreads dffer from the tradtonal formalzaton of proportonal transacton costs. Brunett and Torrcell (2005) suggested that other types of costs (e.g., clearng fees, short sellng costs and so on) should be consdered n addton to bd-ask spreads and commssons to be more precse about the transacton costs. El-Mekkaou and Flood (1998) conducted PCP tests for exchange-traded (PHLX) German mark optons market effcency n the presence of transacton costs usng ntra-daly data. In ther studes, a foregn exchange transacton fee of percent was taken from Surajaras and Sweeney (1992). Note that Rhee and Chang (1992) used a transacton cost of percent for the spot 173

2 Deutsche Mark (DEM). Mttnk and Reken (2000) examned the nformatonal effcency of the relatvely new German DAX-ndex optons market n the presence of transacton costs. In ther studes, a fee of DM0.40 per contract for market makers tradng DAX optons at the German optons and futures exchange (DTB) and 0.1 percent of the ndex value (half of the lowest dscount-broker fee charged to prvate nvestors for tradng German stocks) represented the tradng costs. Overall, the lterature provdes several weaknesses n the tradtonal methodology used to examne PCP holds for optons market effcency. Frst, most researchers reported the number of PCP volatons wthout settng up the mnmum arbtrage proft margn to establsh the optons market s effcency. The PCP volaton should not be sad to contrbute to the optons market s neffcency f t fals to attract the arbtrageur wth ts generated proft. Second, the PCP volatons were substantally decreased n the presence of transacton costs. Snce transacton costs vary across markets and currences, t s not easy to standardze the data n order to apply study results to all currences across markets. In most cases, therefore, the researchers used transacton costs as a proxy. Consequently, the number of PCP volatons both wth and wthout transacton costs makes the opton market effcency reported n the lterature msleadng. To conquer the weaknesses of the tradtonal method, an econometrc approach can be used where the ssues of transacton cost estmaton and PCP volaton both wth and wthout transacton costs are not ncluded n the analyss. Hoque et al. (2008) conducted econometrc analyss to test the valdty of the PCP condton for the optons wth quarterly maturty. They faled to conclude that the optons markets are effcent. The newly launched WCO markets offer optons wth monthly maturty. Ths paper provdes PCP relatonshp based econometrc framework accommodatng all potental tme seres problems to examne the WCO market effcency. We fnd that the WCO market s effcent. The paper s organzed as follows. Secton 1 gves the research methodology. Secton 2 provdes data descrptons and analyss. Secton 3 dscusses the econometrc analyss and the results. Fnally, the last secton concludes the paper. 1. Methodology In ths secton, the PCP relatonshp based statstcal analyss model s developed. Table 1 descrbes Table 1. Notatons and descrptons of the varables Varables Notatons Descrptons Call prce Ct Call prce n domestc at tme t. Put prce Pt Put prce n domestc at tme t. Spot prce Strke prce Domestc nterest rate Foregn nterest rate St Xt Rt,d Rt,f Spot prce n domestc at tme t for one unt of foregn. Opton exercse prce n domestc at tme t for one unt of foregn. Domestc rsk-free nterest rate at tme t. Foregn rsk-free nterest rate at tme t. Opton lfe T Expraton tme of the opton. the notatons and defntons of the varables used n ths study. The PCP condton states that there exsts a determnstc relatonshp between put and call prces f both optons are wrtten on the same and have the same exercse prces and expraton dates. The PCP relatonshp s based on the arbtrage prncple as stated n Eq. (1), R dt R f T C X e,, P Se, (1) where j,,,,,. Now we rearrange Eq. (1) and consder that R, f T R, dt C P Y, S e X e X to develop the regresson Eq. (2) as follows: Y 0 1 X, (2) for the statstcal analyss. If the PCP relatonshp s volated, an arbtrage opportunty arses, ndcatng the optons msprcng. Under the null hypothess that PCP s vald, the coeffcents 0 and 1 n Eq. (2) should be 0 and 1, respectvely, to conclude that the optons market s effcent. The followng steps are followed to estmate the unbased values of coeffcents 0 and 1 n Eq. (2) by conductng the unt root tests and accommodatng the potental autocorrelaton and condtonal heteroskedastcty. Frst, the unt root test s carred out for Y and X at level. We take nto account the frst dfference of Y and X n the regresson analyss f the unt root s found for any of these varables. Secondly, accommodate potental autocorrelaton and condtonal heteroskedastcty, Eq. (2) needs to be augmented as shown n Eq. (3), Y p 0 1 X Y. (3) Wthout accommodatng the seral correlaton and heteroskedastcty, the result would lead to based and nconsstent nferences for 0 and 1, as shown n the econometrc analyss secton. The choce of the lag order, p and q, wll be drven by the results of the dagnostc tests and varous nformaton crtera. In the presence of GARCH(r,s) error n Eq. (3), followng Bollerslev (1986), can be decomposed to q 174

3 h h r 1, d 0,1 2 s 1 h, (4) wth the condtons 0, 0 and 0 to ensure ht 0. Once the presence of GARCH error s confrmed by the LM test of Bollerslev (1986), the lag order, r and s, wll be determned by further dagnostc tests and varous nformaton crtera as suggested n Bollerslev (1986). 2. Data descrptons and analyss Ths study ncludes the sx major optons, the,,,, and of the WCO market traded n the PHLX. The WCO market started tradng on July 24, 2007 (Offshore A-Letter, 2007), but data s only avalable from December 18, 2007 n the DATASTREM. In ths study, the at-the-money (ATM) put-call pars and ATM strke prce are obtaned from December 24, 2007 to December 18, 2009, whch represents the total number of 520 daly observatons for each sample. Snce the optons expre on the thrd Saturday of each month, the USD Currency Table 2. Descrptve statstcs of varables Banks and Bank Systems, Volume 5, Issue 2, 2010 sample perod begns (December 24, 2007, Monday) after the optons expry date (December 21, 2007) and the sample perod ends (December 18, 2009, Frday) before the optons expry date of December 19, The maxmum lfespan of the sample optons s one month. The data set conssts of the daly closng spot exchange rates and daly rskfree nterest rates for all currences ncludng the U.S. dollar, for the sample perod whch s also obtaned from DATASTREAM. All of these data are avalable on request. We start the emprcal analyss wth a dscusson of the tme seres propertes of the data used n ths paper. Table 2 reports the descrptve statstcs for call, put, strke, and spot prces and nterest rates for all sample. For most of the data seres, the mean and medan values are close and the skewness ndcates the non-symmetrc dstrbuton. However, Jarque-Bera () normalty test rejects the approxmately normal dstrbuton assumpton for sample currences. These results are smlar to those reported by Hoque et al. (2008). Snce the mean of strke prces s same as the mean of spot prces, the sample optons are traded ATM. Statstcal Varables measures Call prce Put prce Strke prce Spot prce Interest rate Mkewness * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * Notes: The Jarque-Bera () statstc follows a ch-square dstrbuton wth 2 degree of freedom. The crtcal value of the ch-square dstrbuton s 5.99 at the 5% level of sgnfcance. The statstcal level at 5% s denoted by *. 175

4 Next, the tme seres propertes of the data were examned. The standard Augmented Dckey-Fuller () and Phllps-Perron () tests are appled to nvestgate whether a unt root s present n the Y and X data seres. The test accommodates seral correlaton and tme trends by explctly specfyng the autocorrelaton structure. The test accommodates heteroskedastcty and autocorrelaton usng the non-parametrc method. As shown n Phllps and Perron (1988), the test has better power than under a wde range of crcumstances and hence, s more approprate to use for the tme seres data analyzed n ths paper. The and unt root tests run on levels of the regresson analyss varables Y and X. The results are gven n Table 3. The Y and X reject the null hypothess of unt root at a hgh level of sgnfcance under both and tests for all currences. Table 3. Unt root tests on the varable level Currency Test Call and put prce dfference (Y) Varables Dscounted spot and strke prce dfference (X) Notes: The crtcal values for the and tests are , and at the 1%, 5% and 10% levels of sgnfcance, respectvely. The crtcal values for the KPSS test are , and at the 1%, 5% and 10% levels of sgnfcance, respectvely. 3. Econometrc analyss In ths secton, econometrc analyss s conducted by estmatng Eq. (2), the PCP relatonshp statstcal model. The regresson results are gven n Table 4. To detect the possble presence of seral correlaton problems and ARCH effects, LM (Lagrange multpler) tests are employed. The P-value of the F- statstc under seral correlaton test s zero for all currences except. Further, the P-value of the F-statstc under ARCH test s zero for, and. The mxed LM test results ndcate that the null hypothess of seral correlaton and ARCH n the resdual s rejected for most of the currences. Table 4. Regresson tests wthout accommodaton of seral correlaton and ARCH effects Y Intercept (0) (0.0041) (0.0001) (0.0021) (0.1529) 0 1 X Slope (1) Seral correlaton F-statstc (0.3893) ARCH F-statstc (0.9450) (0.8449) (0.2039) Notes: Tests of H 0 : 0 = 0 and 1 = 1. The P-values are n parentheses below the estmated coeffcents. The null hypothess of the LM test s that there s no seral correlaton n the resdual up to the lag order p, where the number of lag p = max(r, q) for ARMA (r, q). Smlarly, the null hypothess of the ARCH LM test s that there s no ARCH up to the order gven n the resdual. The P-values reject the null hypotheses of the LM tests for seral correlaton and ARCH. To accommodate the seral correlaton and ARCH effects, Eq. (2) was re-estmated by employng Eqs. (3) and (4), respectvely. The results are summarzed n Table 5. The P-values for the F-statstc under LM tests ndcate that the data faled to reject the null hypothess of no seral correlaton and ARCH n the resdual for all currences. For all currences except and, the null hypothess, H 0 : 0 = 0, can be rejected at any reasonable sgnfcance level, ndcatng that the ntercepts are statstcally dfferent from 0 n most of the cases. However, the estmates of 1 are statstcally greater than 0 for all currences. Table 5. Regresson tests accommodatng seral correlaton and ARCH effects Y 0 1 X Intercept (0) Slope (1) Seral correlaton ARCH (0.0001) (0.003) F-statstc (0.5108) (0.0214) (0.3893) (0.1784) ARMA F-statstc (1,2) (0.1001) (0,3) (0.4981) (0,0) (0.6545) (1,0) (0.1557) GARCH (6,1) (0,0) (1,1) (0,0) 176

5 Table 5 (cont). Regresson tests accommodatng seral correlaton and ARCH effects Y 0 1 X Intercept (0) Slope (1) Seral correlaton ARCH (0.0969) (0.2624) F-statstc (0.9950) (0.1917) ARMA (1,2) (0.3528) (1,1) (0.7141) Intercept (0) (7,2) (8,5) Notes: Tests of H 0 : 0 = 0 and 1 = 1. The P-values are n parentheses below the estmated coeffcents. The null hypothess of the LM test s that there s no seral correlaton n the resdual up to the lag order p, where the number of lag p = max(r, q) for ARMA (r, q). Smlarly, the null hypothess of the ARCH LM test s that there s no ARCH up to the order gven n the resdual. The P-values reject the null hypotheses of the LM tests for seral correlaton and ARCH. The null hypothess, H 0 : 1 = 1, test results are reported n Table 6. The regresson results for slopes 1 from Table 5 are reproduced n Table 6 wth the standard errors under T-tests. The standard errors are gven n parentheses below the estmated coeffcents. A T-test reveals that the null hypothess, H 0 : 1 = 1, cannot be rejected at any reasonable sgnfcance level. To obtan a precse level of sgnfcance, a Wald test was conducted, and the results are also presented n Table 6. Under the Wald test, the P-value below the F-statstc n parentheses ndcates that the null hypothess, H 0 : 1 = 1, cannot be rejected at the 1 percent level of sgnfcance for all currences. As a whole, the results ndcate that the slopes 1 are not statstcally dfferent from 1 at the hgher level of sgnfcance. The evdence of the econometrc analyss strongly suggests that PCP holds for all currences whch confrms the WCO market effcency. Table 6. Analyss of equalty of slope coeffcents to 1 T-tests coeffcent (std. error) (0.1488) (0.0904) (0.0479) (0.0805) (0.0726) (0.1070) Slope (1= 1) Wald tests F-statstc (0.1374) (0.1345) (0.2394) (0.3316) (0.2841) (0.0982) Notes: Tests of H 0 : 1 = 1. The regresson results of slopes from Table 5 are reproduced n Table 6 wth ther standard errors. The standard errors are n parentheses below the estmated coeffcents. For the Wald test, the P-values are n parentheses below the estmated coeffcents. Concluson The World Currency Optons (WCO) market began tradng n July 2007 on the Phladelpha Stock Exchange (PHLX). The WCO market started wth sx major currences: the Australan dollar, Brtsh pound, Canadan dollar, Euro, Japanese yen and Swss franc. These optons are desgned to mature monthly rather than quarterly. Before WCO market, the optons were traded only for the maturty months: March, June, September and December n the PHLX. The WCO market has also attracted nvestors wth smaller nvestment accounts. Consequently, the volume of tradng has soared, makng opton prces more effcent. The objectve of ths study s to examne the performance of newly launched WCO market. In ths study, the econometrc approach s adapted where the thorny ssues of transacton cost estmaton and PCP volaton both wth and wthout transacton costs are not encountered. Ths paper contrbutes to the lterature a robust PCP relatonshp econometrc framework accommodatng all potental tme seres problems that can be used to analyze the PCP condton to determne optons market effcency. Under the econometrc analyss, the results ndcate that the PCP holds at hgh level of sgnfcance for all sample optons markets. The overall PCP test results mply that the WCO market s effcent although the market stll s young and n the settlng curve. The robustness of the WCO market effcency wll attract market partcpants, even ncludng novce nvestors, to trade optons for dfferent purposes, ncludng nvestment and fnancal rsk management. Further, the WCO market effcency represents equlbrum market prce whch can be used as market s best forecast regardng future optons prce (see Hoque et al., 2009). In ths study, the monthly maturty optons market effcency test results are nconsstent wth the fndngs of Hoque et al. (2008) where they used optons wth quarterly maturty. Interestngly, ths nconsstency ndcates the optons market effcency could be senstve to the choce of optons maturty. We left t for future research. 177

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