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1 Unverstà degl Stud d Modena e Reggo Emla Dpartmento d Economa Poltca Materal d dscussone \\ 472 \\ The nternal effcency of Index Opton Markets: Tests on the Italan Market by Maranna Brunett Costanza Torrcell 2 November 24 Unverstà d Modena e Reggo Emla Dpartmento d Economa Poltca Va Berengaro, 5 4 Modena, Italy e-mal: marnna.brunett@unmore.t 2 e-mal: costanza.torrcell@unmore.t Vale Jacopo Berengaro 5 4 MODENA (Italy) tel Centralno) /3 fax

2 The nternal effcency of Index Opton Markets: Tests on the Italan Market Maranna Brunett Costanza Torrcell Abstract The am of the present paper s to provde evdence on the nternal market effcency of the Italan ndex opton market. To ths end a model-free approach s taken, whereby strateges nvolvng only optons are tested by means of a hgh frequency dataset coverng the perod September 3 December 22. Ths pece of research thus completes our prevous analyss (Brunett and Torrcell(23, 26)), whch focused on the crossmarket effcency of the same market. The results obtaned further support the effcency of one of the most mportant ndex optons markets n Europe. Keywords: ndex optons, nternal market effcency, no-arbtrage, opton spreads. JEL Classfcaton: G3, G4

3 . Introducton The effcency of a fnancal market s of greatest mportance for ts functonng and ts development and can be nvestgated ether by means of model-based tests or by explorng arbtrage prcng relatonshps that must hold among fnancal assets. Gven that the former approach nvolves a jont test of the market effcency and of the opton prcng model specfcaton, most emprcal research rests on the defnton of market effcency as the absence of arbtrage opportuntes. When opton market effcency s nvestgated, two are the relevant notons of effcency: the cross markets effcency, whch s based on tests of the jont effcency of the opton and the underlyng market, and the nternal opton market effcency, that ams at assessng the exstence of arbtrage opportuntes wthn the very same opton market. The former tests of effcency are performed on the lower boundary condtons that have to hold for call and put optons and on the most famous arbtrage prcng relatonshp,.e. the put-call party. By contrast, the latter tests of effcency are performed on varous types of arbtrage strateges nvolvng optons only, such as box and butterfly spreads. Ackert and Tan(2) stress that As only optons are nvolved, an examnaton of these relatonshps may provde a superor test of party among ndex optons. Snce the semnal paper by Stoll (969), most of the lterature on the effcency of ndex optons has focused on US markets (e.g. Ackert and Tan(2), Evnne and Rudd(985), Kamara and Mller(995)), whle only a few contrbutons have nvestgated some relatvely new European ndex opton markets. As far as we know, only a few recent papers, propose effcency tests on European markets and specfcally: Capelle-Blancard and Chaudhury (2) for the French ndex (CAC4) opton market, Mttnk and Reken(2a,b) for the German ndex (DAX) opton, Cavallo and Mammola (2) and Brunett and Torrcell (23, 26) for Italan ndex (MIB3) opton market. 2 Moreover, but for the French study, the exstng analyses on European markets focus on cross- In lne wth most of the lterature cted n ths paper, ths s the noton of effcency we adopt here. However, t should be stressed that, even when the no-arbtrage restrctons hold, the market may stll be neffcent n other respects: for example, market prces mght stll devate from theoretcal (e.g. Black and Scholes) prces. 2 Earler works nclude Chesney et al.(995) on the Swss ndex opton market and Puttonen(993) on the Fnnsh ndex opton market. 2

4 market effcency only. Ths s true also for the two mentoned studes on the Italan market,.e. Brunett and Torrcell (23, 26) and Cavallo and Mammola (2). The am of the present paper s to provde evdence on the nternal market effcency of the Italan Index Opton (Mbo) market thus addng evdence to the exstng studes and completng our prevous analyss. To ths end and for comparablty wth other papers (manly Capelle-Blancard and Chaudhury (2) and Ackert and Tan(998, 2)), we wll test the call (put) spread, the call (put) butterfly spread and the box spreads. Ths pece of research allows for a thorough comparson wth the nternal market effcency analyses conducted on other markets, and specfcally wth the French one, whch represent one of the most mportant ndex opton markets n contnental Europe. Therefore, ths type of comparatve analyss s also mportant n the lght of the ssue of the fnancal markets ntegraton n Europe. The paper s organsed as follows. Secton 2 ntroduces the Mbo contract and motvates the present study wth respect to the Italan market features and the exstng studes. In secton 3 the arbtrage relatonshps that must hold wthn an opton market are descrbed. Secton 4 llustrates the hgh frequency dataset used n the present work. The nternal market effcency tests and the results for the Mbo market are presented and dscussed n Secton 5, whle Secton 6 presents a comparatve dscusson wth other studes. Last secton concludes. 2. The Italan Index Opton Market The Mbo contract, whch was ntroduced n the Italan Dervatves Market (IDEM) n November 995, s a European-style ndex opton contract based on one of the most representatve Italan ndexes, the Mb3. 3 Every day, sx dfferent expratons are quoted: four quarterly (March, June, September and December) and two monthly (the nearest two months). The expraton day s the thrd Frday of the expraton month, f the Exchange s open, the prevous day of open Exchange otherwse. At expraton, n the money optons are automatcally exercsed. The exercse prces have fxed ncrements of 5 ndex ponts and every day at least nne dfferent strkes for each expraton are 3 Snce 2 nd June 23 a new ndex has been quoted on the Italan Market: the S&P/Mb. Ths ndex, whose components are not fxed and that at the tme of wrtng contans 4 assets, from September 24 has 3

5 quoted: one at the money, four n and four out of the money. The cash settlement of the optons s overseen by the Italan Clearng House, Cassa d Compensazone e Garanza (CC&G), whch also calculates and manages the margns. By now, no lmts are provded for open nterests and prce changes durng the negotaton tme (9:5-7:4). From ts brth n 995 up to 2, the volume of Mbo contracts negotated has sgnfcantly ncreased and the notonal value of the Mbo exchanged every year s very mportant and even bgger than that of the Isoα,.e. Italan opton contracts on sngle stocks (see Fgures, 2 and 3). Thus, despte the IDEM s a relatvely young market, t has become the ffth dervatves market n Europe (after Lffe, DTB, Monep and Dutch Eurex). [Fgure, 2 and 3 about here] By nspecton of Fgures 2 and 3, a declne both n volumes and notonal values s observable as from 2. The latter, whch s stronger, s qute natural snce t follows the declne n the underlyng ndex Mb3. By contrast, the dynamcs of the traded contracts represented n Fgure does not follow the S shape of a logstc growth curve typcally characterzng the lfe cycle of a dervatve 4. Of course, the lfe cycle of dervatves s not necessarly unform. As Remolona(993) puts t Demand factors have shaped and stretched the varous S curves to cause some contracts to grow much faster and others much slower than mght be ndcated by a smple lfe cycle explanaton. However, n the case of the Mbo lfe cycle, we observe a concave shape and a natural queston arses: s the drop followng the year 2 justfed by the demand condtons or s t related to changes n the market effcency? An answer to ths queston was provded n Brunett and Torrcell (23, 26) based on the nvestgaton of the cross-market effcency, whch supported a hgh level of effcency of the Italan ndex opton market n the perod under analyss. However, those studes as well as Cavallo and Mammola (2) - are manly based on tests of the put-call party, whch may not ndcate market neffcency. In fact, arbtrage at low cost may be dffcult to mplement due to the specfc nature of the underlyng, whch requres ether portfolo replcaton or the use of become the new underlyng of the Italan ndex dervatves. However, contract specfcatons have remaned practcally unchanged (see 4 Specfcally, the years 999 and 2 regstered an ncrease n tradng volumes of 38% and 27% respectvely, the drop n the years 2 and 22 amounted to 4% and 5% respectvely. 4

6 futures contracts. For example Ackert and Tan(998) analyse the Canadan ndex and opton market and conlcude that whle the opton market effcency ncreased n the perod under nvestgaton the connecton between opton and underlyng market dd not. Based on these arguments, the present paper ams to complement prevous studes on the effcency of the Mbo market, whch are based on arbtrage prcng relatonshps nvolvng both the opton and underlyng market. The arbtrage relatonshps used n the present paper are dscussed n the next secton. 3. Tests of the nternal market effcency Only small body of papers n the lterature offers an analyss of the nternal opton market effcency besde the cross-market one (e.g. Bllngsley and Chance (985), Chance (986), Ronn and Ronn (989), Capelle-Blancard and Chaudhury (2) and Ackert and Tan (998, 2)). Moreover, most of them focus on the US market, the only exceptons beng Capelle-Blancard and Chaudhury (2) and Ackert and Tan (998) who analyse the French and the Canadan Market respectvley. As for the methodology, ths lterature s based on a model-free approach, whch mples effcency tests performed on arbtrage strateges nvolvng optons only. Many are the advantages of such an approach: t does not requre specfcaton of any prcng model and hence does not rest on the valdty of the model underlyng assumptons, t takes market frctons nto account and t consders only feasble transactons. Moreover, n contrast to cross-market effcency tests, strateges nvolvng optons only are not affected by dfferent closng tmes n the stock and opton markets and do not nvolve the problems connected wth the replcaton of the underlyng. 5 On the other hand, these tests requre hgh data synchroncty, whch s attanable when a hgh frequency dataset s avalable. More specfcally, the most common strateges nvolvng optons only are: call and put spreads, call and put butterfly spreads and box spreads. The call (put) spread can be created by buyng a call (put) opton wth a certan strke prce and sellng a call (put) opton on the same underlyng wth a dfferent strke prce. Dependng on whether ths latter prce s hgher or lower than the strke of the opton purchased the spread s referred to as a bull or a bear spread. 5

7 The call (put) butterfly spread nvolve postons n optons wth three dfferent strke prces. It can be created by buyng a call (put) opton wth a relatvely low strke prce, buyng a call opton wth a relatvely hgh strke prce and sellng two call (put) optons wth a strke prce halfway between the prevous two. The box spread can be created by combnng a bull call spread and a bear put spread. Ackert and Tan (2) stress that the box spread s smlar to the put-call party except that two pars of matched call and put optons are used and the ndex tself s removed from the relatonshp. In an effcent market all the optons strateges just descrbed produce a postve payoff n any state of the world. In order to formally represent the payoffs of these strateges, let: a C /P a = -th call/put ask prce, =,2,3; b C /P b = -th call/put bd prce, =,2,3; K = strke of the -th opton, =,2,3; r = rsk-free rate; τ = tme to maturty; TC, c p = call/put transacton costs; and defne: K = 3 K w 2. K 3 K The payoffs of call and put spreads are represented by the followng relatonshps respectvely: a b ( C ) + ( K K ) exp( r ) + 2TC C τ () 2 2 c a b ( P ) + ( K K ) exp( r ) + 2TC P τ (2) 2 2 p 5 As Ackert And Tan (2) put t As only optons are nvolved, an examnaton of these relatonshps may provde a superor test of party among ndex opton. 6

8 The payoffs of call and put butterfly spreads are represented by the followng relatonshps respectvely: a b ( w) C C + 3TC wc (3) a c a b ( w) P P + 3TC wp (4) a p The payoffs of box spreads are represented by the followng relatonshps: a b b a ( C ) ( P P ) + ( K K ) exp( r ) + 2TC + 2TC C τ (5) c p a b b a ( C ) ( P P ) + ( K K ) exp( r ) + 2TC + 2TC C τ (6) c p 4. The Dataset The dataset used n the present analyss covers the perod st of September 3 st December 2 and was kndly provded by Borsa Italana Spa. More precsely, the Mbo dataset ncludes, for each opton transacton: the negotaton hour, the clearng hour 6, the type, the maturty, the opton prce (expressed n ndex ponts, each worth 2.5 ) and the quantty of optons traded. The no arbtrage relatonshps () (6) hold for couples (or, as for the call/put butterfly spreads, trples) of optons wth dentcal maturty and nstant of tradng but wth dfferent strkes. Thus, some flters have to be appled to the orgnal data set. More precsely, as for the opton prces synchroncty, the ntra-day hgh frequency data set allows to mpose a very hgh level of prce synchroncty. Specfcally, followng Capelle-Blancard and Chaudhury (2), we retan only those put/call optons pars traded consequently and wthn 6 seconds, n order to mpose all prces n a gven arbtrage condton to be wthn the same mnute. Ths level of synchronzaton s much 6 In the followng, we wll consder only the negotaton hour as an ndcator of the tme of the exchange, gven that the gap between the negotaton and the clearng hour s less than one second n the 99,% of the cases. 7

9 hgher than that mposed by Ackert and Tan (998, 2) who, n both papers, use daly data. As for maturty matchng, we frst remove all couples of optons charactersed by dfferent expraton date. Then, n order to mplement the strateges () (6), we make sure that the exercse prces are not equal. 7 To perform the emprcal analyss, the rsk-free rate has to be chosen and the transacton costs have to be determned. As a proxy for the rsk-free rate, we use the Eurbor, 3, 6 and 2 months, consstently wth optons maturty (source: Datastream). The choce s made both for comparablty wth other studes (n partcular Capelle-Blancard and Chaudhury (2)) and because alternatve choces (e.g. an IRS rate) would not affect results, gven that these types of rates are not sgnfcantly dfferent n the perod under nvestgaton. Transacton costs, although very dffcult to estmate, are of ultmate mportance n ths knd of emprcal tests. Indeed, there are many components that have to be consdered (commssons, tradng and clearng fees, costs dervng from bd and ask prces, short sellng costs etc.) and each of them depends on the knd of strategy, on the sze of transactons and on the nvestors type (e.g. retals vs. arbtrageurs) and tends to vary over tme. Nevertheless, on the Italan market clearng fees are neglgble (see also Cavallo and Mammola (2)) and the same s true for short-sellng costs, snce that repo and rsk free nterests rates are very low and smlar. Hence, as far as transacton costs are concerned, we wll focus just on commsson costs and the costs dervng from the bdask opton spread. By nspecton of optons trade commssons on the IDEM, the Italan opton market appears remarkably dversfed. Commssons depend on the type of nvestors as well as on the means of trade: for example, arbtrageurs usually face low commssons because of the hgh yearly volume of transactons they realze, even though retal nvestors who mplement tradng on lne can obtan low commssons too. On the bass of ths latter 7 These flters mples that only a few of the 2297 orgnal observatons were kept. More precsely, for the call (put) spread we retan 2,4% (,59%) of the total orgnal data set, for the call (put) butterfly spread 2,73% (2,67%) and,39% for the box spreads, equal to of the orgnal observatons. The sensble dsparty n the number of observaton retaned s essentally due to the dfferent number of optons nvolved n the arbtrage relatonshps: two n the spreads, three n the butterfly spread and four n the box spreads. 8

10 observaton, we carry out our emprcal study of the no arbtrage relatonshps () (6) assumng four dfferent commssons levels, whch we attrbute to four dfferent types of traders:. MINIMUM, equal to for opton traded, whch s ntended to represent arbtrageurs who realze yearly hgh volume of transactons; 2. MEDIUM-LOW, equal to, whch s ntended to represent professonal nvestors wth low volume of transactons or partcularly actve retal nvestors; 3. MEDIUM-HIGH, equal to 25, whch s ntended to represent retal nvestors who trade optons on lne; 4. HIGH, equal to 4 for opton traded, whch s ntended to represent retal nvestors who trade optons only occasonally. As for bd and ask Mbo quotatons, snce they are not avalable n our orgnal dataset, they also have to be estmated. To ths end, we create a sutable dataset downloadng the bd and ask Mbo quotatons avalable on the Fnance secton of n each tradng day of open Exchange, from 3 February to 7 March Then, on the bass of ths sample, we estmate the average opton bd-ask spread (as suggested by Phllps and Smth (98)) and we assume t constant over tme, as t s common n lterature (see also Capelle-Blancard and Chaudhury (2)). We fnd that the mean bd (ask) prce resulted about.923 (.62) tmes the tradng prce. Thus, multplyng the tradng prces avalable n our data set by these values, we get the estmated bd (ask) optons quotatons. 5. Emprcal results In order to better emphasze the role of market frctons n absorbng most of the arbtrage opportuntes, we wll present our results under three dfferent scenaros: scenaro A, n whch we assume a frctonless market; scenaro B, n whch we nclude only the costs dervng from the opton bd-ask spread and fnally scenaro C, n whch we take nto account the bd-ask costs as well as the commsson costs. 8 Even though ths perod does not correspond wth the one under nvestgaton, we can assume that the average bd-ask spread of ndex opton prces has not remarkably changed, gven that we assume t constant over tme. 9

11 Scenaro A In ths scenaro we test the no arbtrage condtons ()- (6), whereby the followng assumptons are taken: TC a C = TC P C = C = C a b P = P = P b = wth C and P transacton prces. [Table about here] Table reports the results obtaned n ths frst scenaro. As for spreads and butterfly spreads, the frequency of volatons s very low, even under the hypothess of frctonless market. In fact, over the whole sample we observe only.8% (.27%) cases of volatons for the call (put) spread and.34% (.47%) for the call (put) butterfly spread. On the other hand, the percentages of the volatons of the box spreads no-arbtrage condtons are much hgher than those reported above for spreads and butterfly spreads. Ths result s only apparently surprsng. In fact, n ths frst scenaro where no commsson costs nor bd ask spread are taken nto account, the l.h.s. of relatonshp (6) s just the negatve of the l.h.s. of equaton (5). As a consequence, the percentages reported n the two fnal lnes of Table nevtably need to sum up to one. [Table 2 about here] Table 2 reports the average values (n ) of the arbtrage opportuntes for each relatonshp n ths scenaro. Some values are consderable (see call spreads and box spreads (b)). However, overall they are not relable ndcators of the potental arbtrage opportuntes exstng on the Italan Index Opton Market, gven that they can be eroded by commsson costs and/or bd ask spreads. Scenaro B Tests n ths scenaro gnore the commsson costs but consder the bd ask spread on opton prces, whch also n lterature s referred to as the most mportant among the

12 mplct transacton costs (e.g. Demsetz (968), Phllps and Smth (98) and Stoll (989)). More precsely, we mpose: TC C = TC P = and, as llustrated n Secton 3, we assume the followng: a b =.62 C C =.923* C C * a b =.62 P P =.923* P P * Table 3 and Table 4 report, respectvely, the frequency and the average amount of the volatons to the no arbtrage relatonshps. [Table 3 and Table 4 about here] A few comments are here n order. As expected, the ncluson of the bd-ask spread sgnfcantly reduces the frequency of the volatons of the put spread, the butterfly spreads and the box spreads. As for the call spread, the frequency s unchanged but the average arbtrage proft reduces by more than 4%. Moreover, the mean profts of butterfly spreads have also reduced, whle the average amount of arbtrage gans stemmng from put spreads and box spread has sgnfcantly ncreased. A possble explanaton of ths rests on the fact that the bd-ask opton spreads, whch are not consderable, wpe away those arbtrage opportuntes assocated to small profts, whle leavng those assocated to consderable profts. Thus an ncrease n the average proft follows. Scenaro C By ncludng the costs dervng from both the bd ask spread and the commsson costs, the most realstc scenaro can be obtaned. As dscussed n Secton 3, four dfferent commsson levels are assumed,.e.: TC C = TC P =,, 25, 4 and as n Scenaro B the followng bd-ask prce relatonshps are assumed: a b =.62 C C =.923* C C * a b =.62 P P =.923* P P * Table 5, 6 and 7 report the results obtaned n ths last scenaro for call and put Spreads, butterfly spreads and box spreads respectvely.

13 [Table 5,6 and 7 about here] Overall, the ncluson of commsson costs further reduces the frequency of volatons wth respect to the prevous scenaro. In partcular, as for call butterfly spreads and box spreads (5), arbtrage opportuntes completely dsappear. The mportance of transacton costs s once agan stressed by the results obtaned for put butterfly spread. Table 6 n fact shows how the frequency of arbtrage opportuntes decreases, as the level of the transacton costs rases. On the other hand, as far as call and put spreads and box spread (6) are concerned, some more cases of volatons stll persst, even for retal nvestors. However, the cases of volatons are absolutely exceptonal: respectvely only 5, 2, and 3 cases of arbtrage opportuntes recorded over the whole four-month perod. The average devatons from the no-arbtrage condtons () (6), reported n Table 8, ndcate sgnfcant arbtrage opportuntes by means of both call and put spreads and box spread (6).In other words, although very exceptonal, the arbtrage opportuntes exstng on the Italan ndex opton market can be szeable, even for retal nvestors. [Table 8 about here] In order to dentfy possble common features of the optons volatng the no-arbtrage condtons, an exploratve analyss of the cases of arbtrage opportuntes has been conducted. Overall, the most relevant arbtrage opportuntes, namely all the 5 cases of volatons of the call spread no-arbtrage relatonshp, nvolve optons wth maturty longer than three months. Ths result ponts at hghlghtng some nfluence of tme to maturty on the frequency of volatons and yet has to be nterpreted wth cauton, gven that only a few volatons are detected over the whole sample and hence the analyss s based on a few observatons only. The tests descrbed so far are normally addressed to as ex-post tests. A few authors (e.g. Capelle-Blancard and Chaudhury (2), Mttnk and Reken (2a), Ackert and Tan (2)) dscuss the mportance of performng also ex-ante tests, whch are essentally meant to check whether the detected arbtrage opportuntes persst long enough to be 2

14 exploted by an nvestor. Ex-ante tests are performed as follows: frst, an arbtrage opportunty s sngled out, then all the avalable transacton prces wthn the next predefned executon wndow 9 for the same group of optons are consdered. However, Capelle-Blanchard and Chaudhury stress that, when the number of ex-post volatons s too small, whch s the case n ther study and n the present work, the ex-ante tests are less nformatve. Despte ths observaton, we have conducted the ex-ante tests and observed that the arbtrage opportuntes detected are both very rare and not repeated n a reasonable executon wndow (up to two weeks). Therefore, none of the volatons detected s actually explotable for the nvestors. 6. Comparson wth other studes As stressed n the Introducton, most of the lterature on ndex opton market effcency focuses on the noton of cross-market effcency, but for Capelle-Blancard and Chaudhury (2) and Ackert and Tan (998, 2) who perform an analyss of the nternal market effcency too. Therefore, n ths secton we wll compare our results manly wth those reported n the latter two studes. Moreover, t has to be stressed that Capelle-Blancard and Chaudhury (2) perform ther analyses under dfferent transacton costs scenaros, whch are very close to ours; furthermore, they use a dataset that s very smlar to ours both for data frequency (hgh frequency ntraday prces) and for number of observaton n the sample. As a consequence, the French study represents the most comparable work. On the other hand, Ackert and Tan (998, 2) nvestgate US market effcency n one sngle scenaro and consderng one sngle level of transacton costs. For ths reason, n the followng ther results are compared wth our results n scenaro C (.e. professonal arbtrageurs wth mnmum level of transacton costs). 9 As for the length of the executon wndow, n lterature dfferent choces are made: Capelle-Blancard and Chaudhury (2) take a ffteen-mnute wndow, whle Mttnk and Reken (2a) take dfferent lengths rangng from one mnute to one day. It should be stressed that the assumpton taken by of Ackert and Tan (2) corresponds ther man objectve,.e. to assess whether effcency of the S&P 5 ndex opton market has been enhanced by the ntroducton of Stnadard and Poor s Depostory Recept (SPDRs),.e. traded stock baskets whch should ease the replcaton of the underlyng ndex. 3

15 Call & Put Spread Ackert and Tan (2), usng daly closng prces of the S&P 5 Optons, fnd that the call (put) spread no-arbtrage relatonshp s volated n 2.5 (.4) % of cases over the whole decade under analyss ( ). As for the amount of volatons, Ackert and Tan (2) fnd for both these relatonshps very low levels of arbtrage opportuntes: only.5 $ and.3 $ respectvely. Ths means that the proftable arbtrage opportuntes on the Italan Index Opton Market are defntvely more sporadc than on the Us Market, even though ther sze s on average much more consderable. On the Cac 4 Index Opton Market, Capelle-Blancard and Chaudhury (2) fnd, under the hypothess of a completely frctonless market, a frequency of call (put) spread volatons of.34% (.%), qute smlar to our results: respectvely.8% (.27%). On the other hand, once the transacton costs are ncluded, Capelle-Blancard and Chaudhury (2) observe that all the volatons present on the market dsappear, whle n our analyss very few cases (only 5) of volaton stll persst. In any case, the detected frequences of volatons of the no-arbtrage condtons under analyss are very smlar, under all the scenaros consdered, thus confrmng a strong smlarty between the two European markets. Nevertheless, a dfference emerges as far as the average amount of the arbtrage opportuntes s concerned: n fact, Capelle-Blancard and Chaudhury (2) fnd that, once all transacton costs are taken nto account, a retal nvestor can acheve on average only a.84 performng a call spread strategy and 6.7 performng a put spread strategy, whle we fnd that n a smlar scenaro on the Italan Index Opton Market a retal nvestor can acheve much hgher profts (see Table 8). Call & Put Butterfly Spread Ackert and Tan (2) fnd that the call (put) butterfly spread are volated n 3.8% (.9%) of the cases, whle n our study we detect only.6% for put butterfly spread and no volaton for call butterfly spread. Ths confrms agan that the arbtrage opportuntes are much more frequent on the Us Market than on the Italan Index Opton Market. Capelle-Blancard and Chaudhury (2) report ther results n ndex ponts, whch we have transformed n monetary amounts by consderng that on the Monep each ndex pont s equal to. 4

16 However, Ackert and Tan (2) fnd that the average amount of profts attanable performng both these strateges s around $, whch s much a smaller value than the one we fnd for put butterfly spread (26.69 ) 2. In the scenaro wthout transacton costs, Capelle-Blancard and Chaudhury (2) fnd.34% (2.47%) cases of volatons of the call (put) butterfly spreads, whle, n a smlar scenaro, we observe even lower frequences:.34% (.47%) over the whole sample. Once transacton costs are taken nto account, both the French and the present study fnd that all the arbtrage opportuntes attanable by means of a call butterfly spread are completely swept away. As far as the put butterfly spread s concerned, we obtan better results than Capelle-Blancard and Chaudhury (2): they report 8 cases of arbtrage opportuntes for retal nvestors (correspondng to.6% of ther sample observatons), whle we observe no case of arbtrage opportuntes at all for the same knd of nvestors. In ths scenaro we observe only two arbtrage opportuntes for professonal arbtrageurs and one sngle case when a medum-low level of transacton costs s accounted for (respectvely.33% and.6% of the avalable observatons over the whole sample). Box Spread In the exstng lterature, box spreads have been more often emprcally analysed than other types of spreads. For example, Bllngsley and Chance (985) nvestgate the box spreads usng daly data on equty Amercan optons, Ronn and Ronn (989) study the proftablty of box spreads usng CBOE stock optons data, Marchand, Lndley and Followll (994) use S&P5 futures opton data to test long box spread, whch corresponds to the no- arbtrage relatonshp (5) n the present study. The overall fndng s that arbtrage profts emerge only f transacton costs are excluded or set at very low levels. However, none of the above cted studes s actually useful for a comparson, gven that optons wth dfferent underlyng (equty or futures) are used n the emprcal analyss. Thus, we compare our results only wth Capelle-Blancard and Chaudhury (2), Ackert and Tan (2) and Ackert and Tan (998), where the effcency of the Toronto 35 Index Opton Market s nvestgated. 2 Ths s the mean proft when the mnmum level of transacton costs s consdered; as transacton costs for retal are ncluded no arbtrage opportunty perssts, so that the average proft attanable turns out to be zero. 5

17 In ths latter work, the authors observe, before the ntroducton of the TIPs (Toronto Index Partcpaton Unts, launched n 99), qute frequent box spreads volatons on the Canadan Index Opton Market, even when transacton costs are accounted for: 7.39% and 8.4% for no-arbtrage condtons (5) and (6) respectvely. However, the mean profts they observe are, on average, under.3 $ for each strategy. As for Ackert and Tan (2), by takng the transacton costs nto account, they fnd sgnfcant volatons of box spreads based on S&P 5 Index Optons. In partcular, they observe that (5) s volated n 2.2% of case, whle (6) s volated by 23.78% of all the avalable observatons. The mean proft detected s, also n ths case, very low and around $. In both cases, the volatons are much more frequent on the US Index Opton Market than on the Italan Market, on whch, once the transacton costs are taken nto account, only three volatons persst; but the average profts attanable makng use of these very rare arbtrage opportuntes are much hgher on the Italan Market (around 34 ). In the frctonless scenaro Capelle-Blancard and Chaudhury (2) fnd 43.26% and 56.74% cases of volatons of the box spread relatonshps 3. However, wth modest transacton costs (Scenaro 2 n the French study), the box spread volaton frequences drop around 3% and % and further drops to around % and 8% n Scenaro 3. As for retal nvestors, they do not detect any arbtrage opportunty at all. In our study, we fnd very smlar results: under the hypothess of a completely frctonless market, we observe very hgh frequences of volatons for both the box spreads no arbtrage condtons, whle once the transacton costs are taken nto account only three proftable arbtrage opportuntes stll persst. Thus, consderng transacton costs, our results ndcate a smlar hgh level of nternal optons market effcency (n terms of frequency of volaton) n the Italan and French ndex optons market that, n both cases, s sgnfcantly greater than n the US Market. If the frequency of volatons of no-arbtrage relatonshps on the Italan Index Opton Market s lower than n other studes, the sze of the devatons from these condtons s clearly bgger. The average amount of arbtrage opportuntes detected by Capelle- Blancard and Chaudhury (2) once the transacton costs are taken nto account s less 3 Recall that n ths scenaro, where no transacton cost s consdered, the l.h.s. of relatonshp (6) s just the negatve of the l.h.s. of equaton (5) and thus also the percentages reported by Capelle-Blancard and Chaudhury (2) sum up to one. 6

18 than 4 performng both strategy (5) and (6), whle on the Italan Index Opton Market a retal nvestor can gan on average about 85 performng the strategy (6). 7. Conclusons In ths paper we examne the nternal market effcency of the Italan ndex opton market, whch s based on tests of arbtrage prcng relatonshp nvolvng optons only. Specfcally we test call/put spreads, call/put butterfly spreads and box spreads nvolvng Mbos n the perod September 3 December 22. When we gnore transacton costs and bd-ask spreads, we report volatons whch dsplay a low frequency and a dsparate average amount dependng on the specfc strategy under analyss. These results contrast those obtaned by Ackert and Tan (998, 2) for North Amercan markets, whereby hgher frequences are reported, and are very much n lne wth the study by Capelle-Blanchard and Chaudhury (2) on the French ndex opton market. In the most realstc scenaro ncludng both transacton costs and the bd-ask spread, the results we obtan for the Italan market dsplay a common pattern. Agan the frequences are much lower than those on the US or Canadan markets and very smlar to those charactersng the French market. By contrast, the average amount of the volatons s on the Italan market hgher than on both the North Amercan and the French market. Gven the lmted number of arbtrage volatons a deep analyss of the determnants of the volatons s not vable. However, based on an exploratve analyss of the optons allowng for arbtrage opportuntes a possble determnant s the opton maturty, whereby longer maturty optons are generally assocated wth arbtrage opportuntes wth an mportant average amount of profts. On the other hand, the ex-ante analyss hghlghts that the arbtrage opportuntes do not normally survve long enough to be really exploted. In sum, the present study completes prevous research-work on the cross-market effcency of the Mbo market and ponts at a hgh level of nternal effcency. Ths renforces the effcency results obtaned n prevous studes. 7

19 References Ackert L.F., Tan Y.S. (998) The Introducton of Toronto Index Partcpaton Unts and Arbtrage Opportuntes n the Toronto 35 Index Optons Markets," Journal of Dervatves 5, Ackert L.F., Tan Y.S. (2) Effcency n ndex optons markets and tradng n stock baskets, Journal of Bankng and Fnance, 25, Bllngsley R. S., D. M. Chance (985) "Optons market effcency and the box spread strategy", The Fnancal Revew, 2, Black F., Scholes M. (973) The prcng of optons and corporate labltes, Journal of Poltcal Economy, 8, Brunett M., Torrcell C. (23) The Put-Call Party n the Index Optons Markets: further results for the Italan Mb3 optons market, Materal d Dscussone, Dpartmento d Economa Poltca, Unverstà d Modena e Reggo Emla, N. 436, luglo. Brunett M., Torrcell C. (26) Put-Call Party and cross-market effcency n the Index Optons Markets: evdence from the Italan market, Internatonal Revew of Fnancal Analyss, Vl.5,, to appear. Capelle-Blancard G., Chaudhury M. (2) Effcency tests of the French ndex (CAC 4) optons market, Workng paper, McGll Fnance Research Center, SSRN Cavallo L., Mammola P. (2) Emprcal tests of effcency of the Italan ndex optons market, Journal of Emprcal Fnance, 7,

20 Chance D. M. (985) "Emprcal Tests of the Prcng of Index Call Optons." Advances n Futures and Optons Research,, Chesney M., Gbson R., Loubergé H. (995) Arbtrage tradng and ndex opton tradng at Soffex: an emprcal study usng daly and ntradaly data, Fnancal Markets and Portfolo Management, 9, Demsetz H. (968) The cost of transactng, Quarterly Journal of Economcs, 82, Evnne J., Rudd A. (985) Index optons: the early evdence, Journal of Fnance, 4, Kamara A., Mller T.W.Jr. (995) Daly and ntradaly tests of European put-call party, Journal of Fnancal and Quanttatve Analyss, 3, Marchand P., Lndley J., Followll R.A. (994) "Further Evdence on Party Relatonshps n Optons on S&P 5 Index Futures", Journal of Futures Markets, 4, Mttnk S., Reken S. (2a) Put-call party and the nformatonal effcency of the German DAX-ndex optons market, Internatonal Revew of Fnancal Analyss, 9, Mttnk S., Reken S. (2b) Lower boundary volatons and market effcency: evdence from the German DAX-ndex optons market, The Journal of Futures Markets, 2, Phllps S.M., Smth C.W.Jr. (98) Tradng costs for lsted optons The mplcatons for market effcency, Journal of Fnancal Economcs, 8, Puttonen V. (993) Boundary condtons for ndex optons: evdence from the Fnnsh market, Journal of Futures Market, 3,

21 Ronn A.G., Ronn E.I. (989) " The box spread arbtrage condtons: theory, tests, and nvestment strateges", Revew of Fnancal Studes, 2, 9-8. Stoll H.R (969) The relatonshp between put and call opton prces, Journal of Fnance, 24, Stoll H.R (989) Inferrng the components of the bd-ask spread: theory and emprcal tests, Journal of Fnance, 44,

22 Fgure Mbo contracts traded every year from 995 to 22 Data source: Borsa Itala S.p.A Fgure 2 Isoα and Mbo contracts per year: volumes Data source: Borsa Itala S.p.A Fgure 3 Isoα and Mbo contracts per year: notonal values Data source: Borsa Itala S.p.A 2

23 Table : Frequency of volatons n Scenaro A, by month*. Call Spread Put Spread Call Butterfly spread Put Butterfly spread Box Spread (a) Box Spread (b) September October November December 5 (.%) (.4%) (.%) (.%) (.58%) (.3%) (.8%) (.42) (.68%) (.25%) (.4%) (.2%) (.84%) (.43%) (.24%) (.36%) (2.2%) (.%) (7.%) (8.39%) (87.88%) (89.88%) (92.99%) (9.6%) Whole sample 5 (.8%) 72 (.27%) 2 (.34%) 29 (.47%) 85 (9.6%) 8 (9.4%) * = The table reports, for each month of the perod under analyss and for the whole sample, the number and the percentage (n parenthess) of volatons recorded for each no-arbtrage condton tested. Table 2: Average amount of volatons of ()-(6) relatonshps, n Scenaro A*. Spread Butterfly spread Box Spread Call Put Call Put (a) (b) * = The table reports the average amount of the volatons (expressed n ), for each no arbtrage condton tested. 22

24 Table 3: Frequency of volatons n Scenaro B, by month*. Call Spread Put Spread Call Butterfly spread Put Butterfly spread Box Spread (a) Box Spread (b) September October November December 5 (.%) (.7%) (.%) (.%) (.%) (.%) (.%) (.%) (.%) (.%) (.%) (.7%) (.6%) (.7%) (.%) (.%) (.%) (.%) (.%) (.%) 2 (.38%) (.%) (.27%) (.%) Whole sample 5 (.8%) 2 (.8%) (.6%) 2 (.33%) (.%) 3 (.34%) * = The table reports, for each month of the perod under analyss and for the whole sample, the number and the percentage (n parenthess) of volatons recorded for each no-arbtrage condton tested. Table 4: Average amount of volatons n Scenaro B*. Spread Butterfly spread Box Spread Call Put Call Put (a) (b) * = The table reports the average amounts of the volatons (expressed n ), for each no arbtrage condton tested. 23

25 Table 5: Frequency of volatons of Call and Put Spreads n Scenaro C, by month*. Sept. Oct. Nov. Dec. Whole sample Call Spreads Put Spreads TC= TC= TC=25 TC=4 TC= TC= TC=25 TC=4 (.%) (.%) (.%) (.%) (.%) (.7%) (.7%) (.7%) (.7%) (.%) (.%) (.%) (.%) (.%) (.%) (.%) (.%) (.%) (.%) (.%) (.8 (.8 (.8 (.8 (.8 %) %) %) %) %) (.%) (.%) (.%) (.%) (.%) (.%) (.%) (.%) (.%) (.%) (.%) (.%) (.8 (.8 (.8 %) %) %) * = The table reports, for each month and for the whole sample, the number and the percentage (n parenthess) of volatons recorded testng the arbtrage prcng relatonshps () and (2). 24

26 Sept. Oct. Nov. Dec. Whole sample Table 6: Frequency of volatons of Call and Put Butterfly Spreads n Scenaro C, by month*. Call Butterfly Spreads Put Butterfly Spreads TC= TC= TC=25 TC=4 TC= TC= TC=25 TC=4 (.%) (.%) (.%) (.%) (.%) (.%) (.%) (.%) (.%) (.%) (.%) (.%) (.%) (.%) (.%) (.%) (.%) (.%) (.%) (.%) (.6%) (.7%) (.%) (.%) 2 (.33 %) (.%) (.7%) (.%) (.%) (.6 %) (.%) (.%) (.%) (.%) (.%) * = The table reports, for each month and for the whole sample, the number and the percentage (n parenthess) of volatons recorded testng the arbtrage prcng relatonshp (3) and (4). (.%) (.%) (.%) (.%) (.%) Table 7: Frequency of volatons of Box Spreads n Scenaro C, by month*. (5) (6) TC= TC= TC=25 TC=4 TC= TC= TC=25 TC=4 Sept. (.%) (.%) (.%) (.%) (.38%) (.38%) (.38%) (.38%) Oct. (.%) (.%) (.%) (.%) (.%) (.%) (.%) (.%) Nov. (.%) (.%) (.%) (.%) 2 (.25%) 2 (.25%) 2 (.25%) 2 (.25%) Dec. (.%) (.%) (.%) (.%) (.%) (.%) (.%) (.%) Whole sample (.%) (.%) (.%) (.%) (.34%) (.34%) (.34%) (.34%) * = The table reports, for each month and for the whole sample, the number and the percentage (n parenthess) of volatons recorded recorded testng the arbtrage prcng relatonshp (5) and (6). 25

27 Table 8: Average amount of volatons of ()-(6) relatonshps, n Scenaro C*. Spread Butterfly spread Box Spread Transacton costs Call Put Call Put (a) (b) TC= TC= TC= TC= * = The table reports the average amount of the volatons (expressed n ), for each no arbtrage condton tested. 26