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1 ISSN Working Paper Series 174 Foreign Exchange Marke Volailiy Informaion: an invesigaion of real-dollar exchange rae Frederico Pechir Gomes, Marcelo Yoshio Takami and Vinicius Raon Brandi Augus, 008

2 ISSN CGC / Working Paper Series Brasília n. 174 Aug 008 p. 1 36

3 Working Paper Series Edied by Research Deparmen (Depep) Edior: Benjamin Miranda Tabak Ediorial Assisen: Jane Sofia Moia Head of Research Deparmen: Carlos Hamilon Vasconcelos Araújo The Banco Cenral do Brasil Working Papers are all evaluaed in double blind referee process. Reproducion is permied only if source is saed as follows: Working Paper n Auhorized by Mário Mesquia, Depuy Governor for Economic Policy. General Conrol of Publicaions Banco Cenral do Brasil Secre/Surel/Dimep SBS Quadra 3 Bloco B Edifício-Sede 1º andar Caixa Posal Brasília DF Brazil Phones: (5561) and Fax: (5561) edior@bcb.gov.br The views expressed in his work are hose of he auhors and do no necessarily reflec hose of he Banco Cenral or is members. Alhough hese Working Papers ofen represen preliminary work, ciaion of source is required when used or reproduced. As opiniões expressas nese rabalho são exclusivamene do(s) auor(es) e não refleem, necessariamene, a visão do Banco Cenral do Brasil. Ainda que ese arigo represene rabalho preliminar, ciação da fone é requerida mesmo quando reproduzido parcialmene. Consumer Complains and Public Enquiries Cener Address: Secre/Surel/Diae Edifício-Sede º subsolo SBS Quadra 3 Zona Cenral Brasília DF Brazil Fax: (5561) Inerne: hp://

4 Foreign Exchange Marke Volailiy Informaion: an invesigaion of real-dollar exchange rae Frederico Pechir Gomes * Marcelo Yoshio Takami Vinicius Raon Brandi Absrac The Working Papers should no be repored as represening he views of he Banco Cenral do Brasil. The views expressed in he papers are hose of he auhor(s) and do no necessarily reflec hose of he Banco Cenral do Brasil. Price disribuions esimaion has become a relevan subjec for risk and pricing lieraure. Special concern resides on ail probabiliies, which usually presens more severe observaions han hose prediced by Normal disribuions. This work aims o verify wheher he volailiy implied in dollar-real opions conains useful informaion abou unexpeced largemagniude reurns. Implied volailiy is also checked as a predicor for realized volailiy. Our resuls indicae ha implied volailiies indeed provide useful informaion on unusual reurns and also work as a good predicor for observed volailiy. Finally, we implemen an early-warning sysem and implied volailiies seem o signalize large-magniude reurns. Keywords: Informaional conen, predicive power, early warning. JEL Classificaion: D40, F31, G14 * Banco Cenral do Brasil addresses: frederico.pechir@bcb.gov.br; marcelo.akami@bcb.gov.br and vinicius.brandi@bcb.gov.br 3

5 Inroducion Academics, regulaors and marke players all agree on he benefis derived from a sable financial sysem, capable of recognizing, measuring and conrolling financial risks. As Pownall and Koedijk (1999) poin ou, several regulaory changes have been recenly pu ino pracice worldwide in order o achieve his goal. Their purpose is o ouline he advanages associaed wih he use of risk managemen ools in financial sysems, reducing he poenial damages originaed by banking crises and sysemic shocks. The auhors divide hese regulaory changes in caegories: he minimum capial requiremens for financial insiuions, recommended by he Basel Commiee 1, and he disseminaion of risk culure among marke paricipans, including he adopion of he widespread Value-a-Risk echnique as a risk managemen echnique. Neverheless, banking crises observed in recen years indicae ha risk managemen ools were no able o assess he real magniude of he risks presen in urbulen periods. As saed by Blejer and Schumacher (1998), his migh be relaed o he fac ha mos of he risk models were developed under naïve modeling assumpions, such as he assumpion of he normaliy of asse reurns disribuion. I is well known, however, ha fa-ailness consiss on a sylized fac of financial ime series disribuions. As a consequence, he probabiliy of a negaive resul may be underesimaed in he ail, where accuracy should be even more demanded, due o higher severiy of he corresponding evens. The relevan issue is, herefore, how o overcome hose drawbacks, in a way ha exreme movemens could be beer modeled and ail bias avoided. Among he several echniques available, i is worh menioning Sress Tesing, which examines he effecs on porfolios of huge and unusual movemens (high severiy and low frequency) in financial variables and is ofen deal wih he use of he resuls from he Exreme Value Theory (EVT). In his regard, i is worh menioning he developmen of mehodologies applied o he anicipaion of crises and o he search for early warning signals is a fasgrowing field of sudy. In general, hose echniques are focused on he analysis of macroeconomic variables. Berg and Paillo (1998), Frankel and Rose (1996) and Kaminsy, Lizondo and Reinhar (1998), among ohers, posulae ha he monioring of macroeconomic figures, 4

6 such as curren accoun balance, level of inernaional reserves, deb o GDP raio, can be useful when he purpose is o predic he occurrence of financial crises. Alernaively, here has recenly been a growing lieraure concerned on he informaion conained in marke prices. In shor, suppored by marke efficiency and compleeness assumpions, some auhors believe ha asse prices provide relevan and valuable informaion abou fuure prices behavior, especially in he near erm. Tha is he case, for insance, of hose who exrac marke informaion using he echnique firs presened by Breeden and Lizenberger (1978), implemened hrough he esimaion of risk-neural densiies (RND). The auhors sae ha in a risk-neural environmen one could imply a sae-price densiy from opions conracs ha could be inerpreed as he probabiliy densiy over he underlying asse price. Craig and Keller (004), for example, find ha RND exraced from American-syle opions on foreign exchange funcion quie well as an esimaor for he period over which he opions are hickly raded. Moreover, hey find ha simple opion valuaion models fi he densiies as good as he more sophisicaed ones. The purpose of he curren work is o es one echnique creaed o obain, from he informaion conained in financial asse prices, useful informaion abou unusual fuure price movemens. More specifically, he aim is o verify if dollar-real (BRL, he Brazilian currency) opions implied volailiies provide useful informaion abou largemagniude reurns in he fuure. Besides esing his informaional conen, he implied volailiies' predicive power is also checked. As in Andrade and Tabak (001), i is verified if he informaion abou subsequen realized volailiy conained in implied volailiy ouperforms he informaion provided by pas reurns. Finally, as cied earlier, i is proposed a pracical warning sysem o capure he informaional conen of implied volailiies in dollar-real opions, as in Malz (000). The choice of implied volailiy as he observed variable is based on earlier lieraure findings 3 characerizing his price as a predicor 4 for realized volailiy. Besides, Malz (000) suggess ha he informaion conained in opion prices may properly work as a signal for sress evens once hese insrumens provide marke paricipans wih he possibiliy of hedging heir posiions agains huge price changes. 5

7 The remaining par of his work is organized as follows. Secion describes he daa used o implemen he sudy and deail he mehodology chosen o compue implied volailiy. In Secion 3, he informaional conen of implied volailiies is checked and he predicive power es is presened. In Secion 4, he pracical warning sysem is described and is resuls discussed. Finally, Secion 5 presens our concluding remarks. 1. Daa Descripion The dollar-real opions are raded a Bolsa de Mercadorias e Fuuros (BM&F), he Brazilian derivaives exchange 5. They are European-syle calls and he underlying asse is he foreign exchange spo rae (amoun of BRL per USD 1,000). The conracs do no conemplae physical delivery since he Brazilian FX regulaion prohibis he delivery of a foreign currency. Opions on dollar-real fuures are also raded a BM&F, bu were no used in his sudy because of he lack of liquidiy. All he daa are daily and cover he period from June 1 s, 1999 o May 31 s, 005. The daa from 1994 o 1999 were avoided as he economy hen operaed under a nominal exchange rae peg, wih consan inervenion by he Brazilian Cenral Bank. Afer January 1999, he Brazilian auhoriies decided o adop a free floa regime. In he case of he signaling es, presened in Secion 4, i only begins on June 1 s, 000, approximaely a year afer he sar dae in June To obain implied volailiies from he dollar-real calls, he following daa are necessary: a) dollar-real fuures (F), as he amoun of BRL per USD 1,000 mauring on he same day he opion expires; b) he srike exchange rae (K), also as he amoun of BRL per USD1,000; c) number of business days as a fracion of a 5-day year (); d) he coninuously compounded domesic risk free ineres rae (r), obained from he DI fuures conracs 6 ; and e) he price of he las raded call (c). Due o differences in mauriies and srike prices, several calls on dollar-real exchange rae are raded on a daily basis a BM&F. As a resul, differen implied volailiies are obained for he same underlying asse. However, i is well known ha, for a given asse, only one volailiy applies. In order o solve his problem, Lemgruber (1995) recommends alernaives: (i) o calculae a weighed-average implied volailiy; and (ii) o use he implied volailiy associaed wih he a-he-money (ATM) opion. As suggesed by Beckers (1981), ATM opions are beer han any oher approaches based 6

8 on weighed-averages. Addiionally, hese opions are usually he mos raded insrumens, bes reproducing marke expecaions. For ha reason, Jorion (1995) chooses he ATM calls and pus o compue implied volailiies. However, considering ha pu opions are very illiquid insrumens in he Brazilian derivaives marke, we decided o use solely call opions. The analysis here discussed was implemened based on hree differen esimaes for he implied volailiy: (i) he average of he daily implied volailiies weighed by he number of rades; (ii) he average of he daily implied volailiies weighed by each opion's gamma, defined as he as he sensiiviy of dela o he underlying asse price changes; and (iii) he implied volailiy associaed wih he ATM opion 7. Some filers were included before he calculaion of he implied volailiies. Traded calls wih ime o mauriy inferior o 6 business days were eliminaed in order o avoid disorions in volailiy, as indicaed by Malz (000). Anoher reason is documened in Maos, Kapoas and Schirmer (004), where hey show ha Brazilian ypical dollar-real opions behave like Asian opions 8, as mauriy ges closer. Such paricular feaure arises due o conrac specificaions, because he underlying asse is referred o an official exchange rae compued by he Brazilian Cenral Bank as a weighed-average of marke prices on acual rades PTAX 800. Besides, he analysis was resriced o he more liquid series. Because he series wih longer mauriies are very illiquid, only he wo shorer mauriies were used in he calculaion of he implied volailiies chosen o perform he informaional conen es. In order o perform he predicive power es, only he shores mauriy was considered. Wih he daa filered, he implied volailiy was calculaed based on he Garman and Kohlhagen (1983) formula, as shown in Secion.1. Once he implied volailiies were obained, he negaive ones were eliminaed, given he fac ha his would represen an arbirage opporuniy. Wih he remaining daa, he calculaion of he daily average is implemened. The gamma (Γ) used as a weighing facor was obained hrough he use of he following formula for a European-syle call: Γ = ' N ( d 1 ) Sσ T, (1) 7

9 wih ' N ( d ) = 1 1 e π d1 / () and d 1 ln( F / K) σ = +, (3) σ From June 1 s, 1999 o May 31 s, 005, 1,47 implied volailiies on dollar-real opions were obained. These observaions were used o perform boh he informaional conen and signaling ess. For he predicive power es, he number of observaions is 1,05 for he firs mauriy. I is imporan o noice ha he underlying asse is raded during some days when he derivaives marke is closed (e.g. December, 31 s ). 1.1 Compuing Implied Volailiies Afer he original derivaion of Black and Scholes (197), Meron (1973) was he firs one o derive a formula o value European opions on asses paying a coninuous dividend yield. Assuming ha currency posiions provide yields similar o dividends, equal o he risk-free rae in he foreign currency, Garman and Kohlhagen (1983) show ha he same formula can be used in he currency opion marke. Using analogous raionale, Black (1976) demonsraes ha fuure prices presens a sochasic behavior similar o socks paying a coninuous dividend yield and derive a pricing formula for opions on currency fuures. Hull (003) shows ha fuures and spo opions prices wih similar feaures should be equally priced whenever fuure opions maure a he same ime as is underlying fuure conrac. Despie comprising many simplisic assumpions abou model s parameers, hose B&S-based pricing models are sill very popular among praciioners. Neverheless, he lieraure has been generalizing some of hem and more recen works have suggesed alernaive sophisicaed modeling wih he aim o incorporae more realisic assumpions. Hillard, Madura and Tucker (1991) model foreign and domesic ineres raes following Vasicek (1977) and presen an alernaive approach o assess fuure prices 8

10 volailiies. Their resuls indicae greaer efficiency when compared o a consan dividend yield model. Cunha Jr. and Lemgruber (003) apply similar mehodology o he Brazilian currency opions marke and find ha heir resuls consiue an evidence ha he proposed modeling provides beer adjusmen o marke prices han hose of radiional fixed dividend yield approaches. Hull and Whie (1987), Sco (1987) and Wiggings (1987) are examples of works ha have addressed he valuaion of opions on asses presening sochasic volailiy 9. Duan (1995), in he same line, derived an opion model where he price reurns follow a GARCH diffusion process. Melino and Turnbull (1991) examine currency opions on G-7 exchange raes and conclude ha sochasic volailiy models are bes fied o marke prices han B&S wih ime series parameers esimaors. I is worh menioning ha Chesney and Sco (1989), however, develop a similar analysis using implied volailiies insead of hisorical ones. Their resuls lead o an opposie conclusion, wih a worse fi provided by sochasic volailiy models. The approaches menioned above involve high compuaional coss relaed o he numerical soluion of parial differenial equaions. For ha reason, Sein and Sein (1991) and Heson (1993) addressed he problem proposing he use of analyical answers. Da Cosa and Yoshino (004) es he adequacy of he Heson (1983) model for he Brazilian currency opions marke. The analyical formula is calibraed hrough he minimizaion of he quadraic error when compared o marke prices. The auhors sugges ha he simples models may work very well for ATM opions. For deep-ou-ofhe-money opions, hey say, even he Heson (1993) sophisicaed approach fails o explain marke prices. In his work, we use Black (1976) model for European opions on fuures, which may be similar o Garman-Kohlhagen (1983) whenever fuure values are priced a heir fair values. The implied volailiies are obained by making marke prices equal o he one obained by using he opion pricing formula: [ F N d ) K N( )] r c = e (4) ( 1 d d = d 1 σ (5) 9

11 where F is he fuure price, K is he srike price, is he ime o opion expiraion, r is he risk free rae and σ is he asse volailiy.. Informaional Conen and Forecasing Accuracy.1 Informaional Conen One of he mos preliminary invesigaions beween realized volailiy and heir expecaions measured hrough opions conracs is classified by Jorion (1995) as informaional conen analysis. Following Day and Lewis (199), he auhor regress one-week-ahead realized volailiy in he foreign exchange marke agains implied volailiy. I is imporan o noice ha, since he mauriies of boh volailiies mismach, he slope coefficien will no necessarily indicae forecasing accuracy. Though, whenever i indicaes posiive significance, his will sugges ha opion prices may carry relevan and useful informaion abou fuure volailiies. In his work es for presence of informaion conen on he implied volailiy agains wo oher compeing volailiies (GARCH(1,1) and he sample sandard deviaion), according o Andrade and Tabak (001): R IV GARCH = α + α σ + α ˆ ε + ν (6) R GARCH IV GARCH = β + β σ + β ˆ ε + η (7) R IV SD = γ + γ σ + γ ˆ ε + ζ (8) R SD IV SD = θ + θ σ + θ ˆ ε + ξ (9) SD where R+ 1 is he one-day-ahead log-reurn, σ is he sandard deviaion esimae 10, σ is he condiional sandard deviaion GARCH(1,1), σ IV is he implied GARCH volailiy, εˆ is he esimaed residual 11 of he GMM regression GARCH σ + GARCH IV GARCH = δ 0 + δ1σ ε ; 10

12 εˆ is he esimaed residual of he GMM regression IV GARCH IV GARCH IV GARCH σ = λ0 + λ1σ + ε ; SD εˆ is he esimaed residual of he GMM regression SD IV SD σ = ϕ0 + ϕ1σ + ε and εˆ is he esimaed residual of he GMM IV SD regression IV SD IV SD σ = φ0 + φ1σ + ε. The previous regressions were applied by means of he GMM (Generalized Mehod of Momens). I provides a robus esimaor in ha i does no require informaion of he exac disribuion of he disurbances and was used essenially for: i) idenificaion problem 1 reamen and ii) heeroskedasiciy and auocorrelaion consisen covariance esimaion. The GMM esimaor selecs parameer esimaes so ha he correlaions beween he insrumens and disurbances are as close o zero as possible, i.e., he momen condiions are expressed by E[ε.Z ] = 0, where Z = [1 σ i,-1 ]. Furhermore, by choosing he weighing marix in he crierion funcion appropriaely, GMM can be made robus o heeroskedasiciy and/or auocorrelaion of unknown form. We used he firs lag of each explanaory variable as insrumenal variables. Table 1 presens he coefficien esimaes for equaions (6) hrough (9) using he ATM (a-he-money) esimaion of implied volailiies (IV). The resuls are nonconclusive regarding he explanaory power, i.e., hey indicae ha he explanaory power of he implied volailiies are no superseded by and do no supersede he sandard deviaion esimae s or he condiional sandard deviaion GARCH(1,1) s. TABLE 1. INFORMATIONAL CONTENT ANALYSIS Coefficiens, sandard errors and R-squared of equaions (6) hrough (9) for he ATM implied volailiy. Sandard errors are shown in parenhesis. Equaion α 0,β 0,γ 0,θ 0 α 1,β 1,γ 1,θ 1 α,β,γ,θ R-sqr ( ) * ( ) ( ) ( ) * ( ) (0.043) ( ) * (0.0058) ( ) ( ) * ( ) ( ) 0.04 Values wih * represen significanly posiive esimaes a he 1% significance level. 11

13 Moreover, we aim o assess he informaional conen of implied volailiies based on Malz (000) approach, which applies Granger causaliy es in order o capure lagged relaionship higher han one-day lengh. Despie he fac ha Granger causaliy does no provide a noion of causaliy in an economic sense, i may be very useful o indicae he lead-lag relaionship beween wo variables. We deermined maximum lengh of 10 business days and he opimal lag lengh is chosen by AIC (Akaike Informaion Crieria) using univariae VAR (Vecor Auo Regressive) model. We obained a lag equal o 7 business days for every regression, which is close o he lag of 5 arbirarily chosen by Malz (000), assuming ha price adjusmens occur wihin one rading week. The Granger causaliy es basically verifies wheher he condiional forecas variance of a dependen variable can be reduced significanly by including pas informaion of anoher variable in he equaion along lagged values of he dependen one iself. As shown in Greene (003), ess comparing resriced and unresriced equaions can be based on a simple F es in he single equaions of he VAR model. The resriced equaion is defined as below; comprising only lagged values of he dependen variable. The use of squared reurns, as proposed by Malz (000), is inended o capure large magniude reurns, focusing on kurosis raher han skewness of he reurn disribuion: k = i r i i = 1 r γ + v (10) The unresriced equaion is defined as: k k IV = α i r i + β i σ i i = 1 i = 1 r + u (11) The es saisic is defined as follows: T v u = 1 = 1 T k 1 λ = (1) T u k = 1 T 1

14 where u and v are he residuals from he unresriced and resriced regressions, respecively and T is he sample size. The saisic λ has an asympoic F (k, T-k - 1) disribuion. If he criical value of he F disribuion for a specified confidence level is lower han λ he es will rejec he null hypohesis saing ha he new independen variable included in he unresriced regression fails o Granger cause he dependen variable. Table conains he resuls for eq.(10) and eq.(11) comparison. In all he hree cases, Granger causaliy is verified a a very low significance level, corroboraing previous resuls on one-day ahead regressions, which sugges ha implied volailiies provide useful informaion on he predicion of fuure, squared log-reurns. The adjused R-squared, also displayed in he able, indicae ha previous squared reurns in conjuncion wih implied volailiies esimaes presen significan explanaory power on fuure squared reurns. TABLE. GRANGER CAUSALITY TEST FOR EQ. (10) AND (11). λ p-value R-sqr adj. ATM 1,7 7,47E-16 0,50 GAMMA 1,7 7,47E-16 0,53 NT 1,7 7,47E-16 0,43 Anoher es is proposed in order o idenify he addiional value of implied volailiies over hisorical GARCH esimaes. The unresriced equaion includes boh GARCH (1,1) and IV esimaes as endogenous variables in he VAR model, along wih he squared reurn: k k k GARCH IV = α i r i + β iσ i + β iσ i i = 1 i = 1 i = 1 r + u (13) Resriced equaion is defined as follows: k k GARCH = α i r i + β iσ i i = 1 i = 1 r + v (14) Table 3 conains he resuls for eq. (13) and eq. (14) comparison. Granger causaliy is also verified a a very low significance level, in line wih previous resuls, 13

15 corroboraing ha implied volailiies provide addiional valuable informaion raher han ime series esimaes. The adjused R-squared of unresriced regressions indicaes he significance of he variables and he expeced increase in he explanaory power when compared o he above-menioned resuls. TABLE 3. GRANGER CAUSALITY TEST FOR EQ. (10) AND (11). λ p-value R-sqr adj. ATM 5,9 9,76E-07 0,8 GAMMA 5,9 9,76E-07 0,8 NT 4,4 8,8E-05 0,76. Predicive Power Iniially, we applied he same approach used by Jorion (1995), in which he realized volailiy is regressed agains he ATM implied volailiy (eq. 15) and agains he adjused GARCH(1,1) (eq. 16): σ + IV, T = δ0 + δ1σ η (15) σ garch + ν, T = θ0 + θ 1 (16) where σ, T is he realized volailiy beween and he expiraion dae T, measured as he IV sandard deviaion of daily reurns σ is he implied volailiy in dae for he period beween and T and garch is he adjused GARCH(1,1). From he parameers esimaion of a GARCH(1,1) in he previous secion, we compued he in-sample forecas of he average condiional variance garch (we used garch in equaions 16 and 18) over he remaining life of he opion, according o Heynen e al. (1994) and likewise Andrade and Tabak (001): α ˆ 1 τ ( α β+ 1 ) ( 1 α β ) 0, + 1 0, + 1 garch = + h α + 1 β+ 1 1 α + 1 β+ 1 τ α where R = + ε, ε ~ N(0, h ), h = α 0, + α. ε 1 + β. h 1 μ and τ is he mauriy. 14

16 We used he firs lag of he explanaory variable as insrumenal variable and he resuls of he GMM regressions (15) and (16) are presened in Table 4. TABLE 4. PREDICTIVE POWER ANALYSIS Coefficiens, sandard errors and R-squared of eq. (15) and (16). Sandard errors are shown in parenhesis. Equaion δ 0,θ 0 δ 1,θ 1 R-sqr * ( ) (0.0048) ( ) * (0.173) Values wih * represen significanly posiive esimaes a he 1% significance level. The resuls of Table 4 show ha here is no evidence of superioriy of one compeing volailiy agains he oher. Therefore, we applied an encompassing es likewise he approach underaken in he informaion conen analysis. Now, he aim is o compare he predicive performance of he implied volailiy only agains GARCH(1,1) aking he realized volailiy as he dependen variable: σ = α + α σ + α ˆ ε + η IV GARCH, T 0 1 (17) σ = γ + γ garch + γ ˆ ε + ν IV, T 0 1 (18) Where: εˆ is he esimaed residual of he GMM regression GARCH garch = 1 IV GARCH δ 0 + δ σ + ε and IV εˆ is he esimaed residual of he GMM IV regression σ λ + λ garch + ε IV = 0 1 ; We used he firs lag of each explanaory variable as insrumenal variables and he resuls of he GMM regressions (15) and (16) are presened in Table 5. The ATM implied volailiy is found o be an efficien volailiy predicor a he 5% significance level, i.e., one canno rejec ha he ATM implied volailiy may conain incremenal informaion regarding he GARCH(1,1), as α 1 and γ are significanly differen from zero a he 5% significance level, while α is non-significan. 15

17 TABLE 5. ENCOMPASSING TEST Coefficiens, sandard errors and R-squared of equaions (17) and (18). Sandard errors are shown in parenhesis Equaion α 0,γ 0 α 1,γ 1 α, γ R-sqr * (0.0574) ( ) (0.7199) ( ) * ( ) ** ( ) 0.46 Values wih * represen significanly posiive esimaes a he 1% significance level. Values wih ** represen significanly posiive esimaes a he 5% significance level. 3. Signaling for Tail Evens In he previous secions we have shown ha implied volailiy on dollar-real opions conains relevan informaion abou fuure large-magniude reurns. From now on, our inenion is o use his informaion o build a pracical ool ha may work as a warning sysem for sress evens. More specifically, he goal here is o follow Malz (000) and measure he probabiliy of a week-ahead large movemen in dollar-real exchange rae condiional o observed high and rising implied volailiy, and hen verify wheher or no here is independence beween signal and fuure even. The signaling ool consiss, basically, of verifying he independence beween wo disinc evens. The firs one, which deermines he subse of weeks A, is relaed o he occurrence of high and rising implied volailiy in he one week. Once i is verified he occurrence of his even, a signal is considered o have been sen. The second even, which deermines he subse B, refers o he occurrence of high absolue reurns of he underlying asse (dollar-real exchange rae) one week ahead. Because of he resuls presened in he predicive power secion, where ATM opions implied volailiies are highly superior in erms of R-squared when compared o he oher esimaes of implied volailiy, he signaling es is performed based only on he ATM esimae. The signaling is esed always based on weekly daa observed every Wednesday 13, as suggesed by Malz (000) in order o avoid he day-of-he-week bias. Therefore, o define a high implied volailiy, a series of daily implied volailiies is used o calculae, for each day, he average and he sandard deviaion of he previous 5 observaions. If 16

18 he esimae for a specific Wednesday is one sandard deviaion higher han he average, boh compued for ha specific dae, he implied volailiy is considered o be high. To obain a rising implied volailiy i was necessary o compue log variaions of implied volailiies beween Wednesdays. Those values are hen compared o he produc of and he sandard deviaion of las 5 daily implied volailiy log variaions, scaled up o week dimension hrough he square roo rule. This las sandard deviaion encompasses he concep of vol of vol (volailiy of volailiy), which in cerain way reveals he magniude of he variabiliy of he daily implied volailiy esimaions in recen observaions. If he implied volailiy calculaed from Wednesday o Wednesday is higher han his las produc, i is considered o be rising. Afer ha, weekly reurns on he underlying asse, measured beween Wednesdays, are considered o be high whenever is absolue value is higher han.33 (99 h percenile) imes he sandard deviaion of he las 5 daily log reurns, scaled up ino week dimension by he squared roo rule. Independence is verified hrough Chi-square and Fisher s Exac ess based on he x coningency able presened below. Boh of hem ess for he null hypohesis of independence beween evens A and B. Therefore, he rejecion of he null hypohesis lead o he inerpreaion ha he implied volailiy does provide a good warning signal for large magniude reurns. TABLE 7. SIGNALING TEST Observed values for subses A and B, exraced from he implied volailiies on ATM dollar-real opions. N(A) corresponds o he number of evens of he subse A (implied volailiy high and rising). N(B) corresponds o he number of evens of subse B (high reurns). N(~A) and N(~B) are he denials of subses A and B. Observed N(B) N(~B) Toal N(A) 5 7 N(~A) Toal The es saisic of he chi-square es has an asympoic chi-square disribuion wih 1 degree of freedom and is obained as follows: 17

19 wih N j. N. k ( N jk ) χ = N, (19) N j= 1 k= 1 j. N. k N N jk as he number of elemens in he jk h cell and wih he dos indicaing oals of columns and cells. The χ value for he above coningency able is 9,85, wih an associaed p-value of , suggesing ha implied volailiy signals for dollar-real large magniude reurns a a 99.83% confidence level. Fisher (19) has shown ha Chi-square es, due o is asympoic feaure, provides inaccurae resuls when he expeced numbers for he coningency able are small. Alernaively, he auhor recommends he applicaion of a hypergeomeric es, which p-value associaed wih he null hypohesis of independence is given by he following hypergeomeric probabiliy funcion: a + b c + d a c p = (0) n a + c Accordingly, as menioned before, we have also performed he Fisher s exac es for independence and wih a p-value of 3.1% he es rejecs he null hypohesis of independence a he 5% significance level. Nowihsanding he above resuls, we share Malz (000) concerns ha he ess performed in his secion have major limiaions when applied o financial ime series. Daa sample frequency and volailiy clusering, which is a broadly acknowledged sylized fac for financial reurns, may bias he sample or sugges for spurious relaionship. Hence, alhough we inerpre our resuls as srong evidence for marke signaling, we undersand ha furher developmen on he implemenaion of signaling ools in financial markes mus be done. 4. Concluding Remarks The purpose of he curren work is o es one of he echniques creaed o obain, from he informaion conained in financial asse prices, useful informaion abou unusual 18

20 fuure price movemens. Is specific aim is o verify if dollar-real opions implied volailiies can provide useful informaion abou large-magniude reurns in he fuure. Besides esing his informaional conen, he implied volailiies' predicive power is also checked. Finally, i is proposed, based on Malz (000), a pracical warning sysem o capure he informaional conen of implied volailiies in dollar-real opions. Wih regards o he informaional conen analysis, Granger causaliy is verified a a very low significance level, corroboraing previous resuls on one-day ahead regressions, which suggess ha implied volailiies provide useful informaion abou large-magniude reurns in he fuure. In he case of he predicive power es, all implied volailiies measures are found o be efficien volailiy predicors a he 1% significance level. This resul demonsraes he capabiliy of implied volailiies o predic fuure realized price variaions on he underlying asses. Finally, he signaling es indicaes ha he monioring of implied volailiies on dollar-real opions can be used o build an efficien and pracical warning sysem for sress evens in he fuure. 19

21 References Ahoniemi, Kaja. Modeling and forecasing implied volailiy: An economeric analysis of he VIX index. Helsinki School of Economics, Discussion Paper 19, Ocober, 006. Amin, K, Jarrow, R.A;. Pricing Foreign Currency Opions under Sochasic Ineres Raes. Journal of Inernaional Money and Finance, 10, p , Andrade, S.C., Tabak, B.M. (001). Is i worh racking dollar/real implied volailiy?, Revisa de Economia Aplicada, 5, n.3. Becker, J.L; Lemgruber, E.F. Uma Análise de Esraégias de Negociação no Mercado Brasileiro de Opções: evidências a parir das opções de compras mais negociadas durane o Plano Cruzado. In BRITO. Gesão de Invesimenos. Ediora Alas, Beckers, S., 1981, Sandard Deviaions Implied in Opions Prices as Predicors of Fuure Sock Price Volailiy, Journal of Banking and Finance 5, Berg, Andrew; Paillo, Caherine. Are Currency Crises Predicable? A Tes. IMF Working Paper Series. n. 98/154, November Black. F. and Scholes, M. The Valuaion of Opion Conracs and a Tes of Marke Efficiency. Journal of Finance 7, 197. Black, F. The Pricing of Commodiy Conracs. Journal of Financial Economics, 4, p , Jan/Mar Blejer, M. I.; Schumacher, L. Cenral Bank Vulnerabiliy and he Credibiliy of Commimens: A Value-a-Risk Approach o Currency Crises. IMF Working Paper Series. n. 98/65, May Breeden, D. T.; Lizenberger, R. H. Prices of Sae coningen Claims Implici in Opion Prices, Journal of Business, 51, 61-65, Casro, P. C. Opções sobre Dólar Comercial e Expecaivas a Respeio do Comporameno da Taxa de Câmbio. Banco Cenral do Brasil, Brasília, 00. 0

22 Chesney Marc, Sco L. Pricing European Currency Opions: A Comparison of he Modified Black-Scholes Model and a Random Variance Model. Journal of Financial and Quaniaive Analysis, Chrisensen, B. and J. Prabhala, N.R. The Relaion Beween Implied and Realized Volailiy. Journal of Financial Economics. v.50, n.3, p , Craig, Ben R.; Keller, Joachim G. The Forecas Abiliy of Risk-Neural Densiies of Foreign Exchange, Federal Reserve Bank of Cleveland, WP 04-09, 004. Cunha JR., D. and Lemgruber, E.F.Opções de Dólar no Brasil com Taxas de Juro e de Cupom Esocásicos. III Enconro Brasileiro de Finanças. FEA USP, Julho, 003. Da Cosa, M.N. and Yoshino, J.A. Calibração do Modelo de Heson para o Mercado Brasileiro. IV Enconro Brasileiro de Finanças, 004. Day, T. and C. Lewis. Sock marke volailiy and he informaion conen of sock index opions. Journal of Economerics 5, 67-87, 199. Dickey, D.A. and W.A. Fuller. Disribuion of he esimaors for auoregressive ime series wih a uni roo. Journal of he American Saisical Associaion 74, , Doran, James S. and Ronn, Ehud I. The Bias in Black-Scholes/Black Implied Volailiy: An Analysis of Equiy and Energy Markes. Florida Sae Universiy Working Paper, 006. Duan, J. The GARCH opion pricing model. Mahemaical Finance, 5(1), 13-3, Feiger, G; B. Jacquilla. Currency Opion Bonds, Pus and Calls on Spo Exchange and he Hedging of Coningen Foreign Earnings. Journal of Finance, 34, p , Dec Fisher, R.A. (19). "On he inerpreaion of χ from coningency ables, and he calculaion of P". Journal of he Royal Saisical Sociey 85(1): Frankel, Jeffrey A.; ROSE, Andrew K. Currency Crashes in Emerging Markes: An Empirical Treamen. Journal of Inernaional Economics. v.41, p , Garman, M, Kohlhagen, S. Foreign Currency Opions Values. Journal of Inernaional Money and Finance,,p , Dec

23 Geske, R. The Pricing of Opions wih Sochasic Dividend Yield. The Journal of Finance, 33, p , Gomes, F. P. Volailidade Implícia Anecipada de Evenos de Sress: Um ese para o Mercado Brasileiro. Deparameno de Esudos e Pesquisas, Banco Cenral do Brasil, Brasília, 00. Grabbe, J. O. The Pricing of Call and Pu Opions on Foreign Exchange. Journal of Inernaional Money and Finance,, p , Granger, C.W.J. Invesigaing causal relaions by economeric mehods and crossspecral mehods. Economerica, 34, Greene, W.H. Economeric Analysis. Prenice Hall, 5 h ed, 003. Heson, S. A Closed-Form Soluion for Opions wih Sochasic Volailiy wih Applicaions o Bond and Currency Opions,The Review of Financial Sudies,6(), Heynen, R., Kemna, A., Vors, T. Analysis Of The Term Srucure Of Implies Volailiies. Journal of Financial Quaniaive Analysis, 9, Hilliard, J.E, J.Madura E A.L.Tucker. Currency Opion Pricing wih Sochasic Domesic and Foreign Ineres Raes. Journal of Financial and Quaniaive Analysis, 6,, p , Jun Hull, J. Opions, Fuures and Oher Derivaives Securiies, 5. ed, Prenice Hall, New Jersey, 003. Hull, J., and Whie A. The Pricing of Opions on Asses wih Sochasic Volailiies," Journal of Finance, 4, , Jorion, Philippe. Predicing Volailiy in he Foreign Exchange Marke. The Journal of Finance. v.50, n., p , June Kaminsky, G.; Lizondo, S.; Reinhar, C. Leading Indicaors of Currency Crises. IMF Saff Papers. v.45, n.1, p.01-48, March Lemgruber, Eduardo F. Avaliação de Conraos de Opções. Edição Revisada e Ampliada. São Paulo: BM&F, p.

24 Malz, A. M. Do Implied Volailiies Provide Early Warning of Marke Sress? RiskMerics Journal. v.1, n.1, p.41-60, 000. Maos, J.A., Kapoas, J.C. and Schirmer, P.P. Pricing and Hedging Brazilian Currency Opions IV EBF 004 Melino A. and Turnbull S.M. The Pricing of Foreign Currency Opions. Canadian Journal of Economics, Canadian Economics Associaion, vol. 4(), pages Meron, R.C. Theory of Raional Opion Pricing. Bell Journal of Economics 4, p , Spring Navae, P.; Villa, C. The Informaion Conen of Implied Volailiy, Skewness and Kurosis: Empirical Evidence from Long-Term CAC 40 Opions. European Financial Managemen. v.06, n.1, p.41-56, 000. Neeley, C. Forecasing foreign exchange volailiy: Why is implied volailiy biased and inefficien? And does i maer?, Federal Reserve Bank of S. Louis Working Paper, 004. Pownall, R.A.J.; Koedijk, K.G. Capuring Downside Risk in Financial Markes: he Case of he Asian Crisis. Journal of Ineranional Money and Finance. 18, p , Sco, L. Random Variance Opion Pricing. Advances in Fuures and Opions Research, 5, , Sco, L.O. The informaion conen of prices in derivaive securiy markes. IMF Saff Papers 39, , 199. Sein E.M. and Sein J.C. Sock Price Disribuions wih Sochasic Volailiy, The Review of Financial Sudies, 4 (4), Vasicek, O. An Equilibrium Characerizaion of The Term Srucure, Journal of Financial Economics, 5, , Wiggins, J. Opion Values under Sochasic Volailiy: Theory and Empirical Esimaes. Journal of Financial Economics, 19, ,

25 Noes 1 The Basel Commiee on Banking Supervision, esablished a he end of 1974, is composed of members from Belgium, Canada, France, Germany, Ialy, Japan, Luxembourg, he Neherlands, Spain, Sweden, Swizerland, Unied Kingdom and Unied Saes. The Commiee encourages convergence owards common approaches and common sandards regarding he supervision of financial sysems. See Malz (000) for more deails. 3 Chrisensen and Prabhala (1998), Jorion (1995) and Navae and Villa (000). 4 As noed by Ahoniemi (006), predominan sudies rejec he hypohesis of an unbiased predicor. According o Neeley (004), common answers for he bias may be overlapping daa, he use of low frequency daa or he non-pricing of volailiy premia. See Doran and Ronn (006) for furher debae on he subjec. 5 According o a repor released in 004 by he Fuures Indusry Associaion, BM&F is he 6 h derivaives exchange in he world when considered only he rading of fuures conracs. 6 Fuure conracs on he Brazilian iner-bank rae. Unlike wha happens wih ineres rae fuures in he US and Europe, where he underlying asse is a fixed income securiy mauring afer he fuures mauriy, in Brazil our main ineres rae fuure conrac, DI fuures, may be considered similar o a fixed income securiy negoiaed in he spo marke wih daily adjusmens (mark o marke). 7 The ATM opion here is he one wih he presen value of K closes o he spo price (S). 8 Asian opions have heir payoff dependen on he average price of he underlying asse during a predefined period. 9 Jorion (1995) reminds ha if volailiy is indeed sochasic, he arbirage argumen behind B&S will no sand and, herefore, B&S opion pricing model shall be considered inconsisen. 10 Sample sandard deviaion of he previous 1 daily log-reurns. 11 GARCH εˆ accouns for he GARCH(1,1)-volailiy s movemens no explained by he impliedvolailiy s. This procedure avoids bias, inefficiency and inconsisency of he parameer esimaors of regressions in (6). 1 one or more explanaory variables may be correlaed o he disurbance and his resuls in biased esimaors 13 In he case he marke is closed on Wednesday, daa from Tuesdays are used. 14 Represening he 75 h percenile of he sandard Normal disribuion. 4

26 Banco Cenral do Brasil Trabalhos para Discussão Os Trabalhos para Discussão podem ser acessados na inerne, no formao PDF, no endereço: hp:// Working Paper Series Working Papers in PDF forma can be downloaded from: hp:// 1 Implemening Inflaion Targeing in Brazil Joel Bogdanski, Alexandre Anonio Tombini and Sérgio Ribeiro da Cosa Werlang Políica Moneária e Supervisão do Sisema Financeiro Nacional no Banco Cenral do Brasil Eduardo Lundberg Moneary Policy and Banking Supervision Funcions on he Cenral Bank Eduardo Lundberg 3 Privae Secor Paricipaion: a Theoreical Jusificaion of he Brazilian Posiion Sérgio Ribeiro da Cosa Werlang 4 An Informaion Theory Approach o he Aggregaion of Log-Linear Models Pedro H. Albuquerque 5 The Pass-Through from Depreciaion o Inflaion: a Panel Sudy Ilan Goldfajn and Sérgio Ribeiro da Cosa Werlang 6 Opimal Ineres Rae Rules in Inflaion Targeing Frameworks José Alvaro Rodrigues Neo, Fabio Araújo and Mara Balar J. Moreira 7 Leading Indicaors of Inflaion for Brazil Marcelle Chauve 8 The Correlaion Marix of he Brazilian Cenral Bank s Sandard Model for Ineres Rae Marke Risk José Alvaro Rodrigues Neo 9 Esimaing Exchange Marke Pressure and Inervenion Aciviy Emanuel-Werner Kohlscheen 10 Análise do Financiameno Exerno a uma Pequena Economia Aplicação da Teoria do Prêmio Moneário ao Caso Brasileiro: Carlos Hamilon Vasconcelos Araújo e Renao Galvão Flôres Júnior 11 A Noe on he Efficien Esimaion of Inflaion in Brazil Michael F. Bryan and Sephen G. Cecchei 1 A Tes of Compeiion in Brazilian Banking Márcio I. Nakane Jul/000 Jul/000 Jul/000 Jul/000 Jul/000 Jul/000 Jul/000 Sep/000 Sep/000 Nov/000 Mar/001 Mar/001 Mar/001 5

27 13 Modelos de Previsão de Insolvência Bancária no Brasil Marcio Magalhães Jano 14 Evaluaing Core Inflaion Measures for Brazil Francisco Marcos Rodrigues Figueiredo 15 Is I Worh Tracking Dollar/Real Implied Volailiy? Sandro Canesso de Andrade and Benjamin Miranda Tabak 16 Avaliação das Projeções do Modelo Esruural do Banco Cenral do Brasil para a Taxa de Variação do IPCA Sergio Afonso Lago Alves Evaluaion of he Cenral Bank of Brazil Srucural Model s Inflaion Forecass in an Inflaion Targeing Framework Sergio Afonso Lago Alves 17 Esimando o Produo Poencial Brasileiro: uma Abordagem de Função de Produção Tio Nícias Teixeira da Silva Filho Esimaing Brazilian Poenial Oupu: a Producion Funcion Approach Tio Nícias Teixeira da Silva Filho 18 A Simple Model for Inflaion Targeing in Brazil Paulo Springer de Freias and Marcelo Kfoury Muinhos 19 Uncovered Ineres Pariy wih Fundamenals: a Brazilian Exchange Rae Forecas Model Marcelo Kfoury Muinhos, Paulo Springer de Freias and Fabio Araújo 0 Credi Channel wihou he LM Curve Vicorio Y. T. Chu and Márcio I. Nakane 1 Os Impacos Econômicos da CPMF: Teoria e Evidência Pedro H. Albuquerque Decenralized Porfolio Managemen Paulo Couinho and Benjamin Miranda Tabak 3 Os Efeios da CPMF sobre a Inermediação Financeira Sérgio Mikio Koyama e Márcio I. Nakane 4 Inflaion Targeing in Brazil: Shocks, Backward-Looking Prices, and IMF Condiionaliy Joel Bogdanski, Paulo Springer de Freias, Ilan Goldfajn and Alexandre Anonio Tombini 5 Inflaion Targeing in Brazil: Reviewing Two Years of Moneary Policy 1999/00 Pedro Fachada 6 Inflaion Targeing in an Open Financially Inegraed Emerging Economy: he Case of Brazil Marcelo Kfoury Muinhos 7 Complemenaridade e Fungibilidade dos Fluxos de Capiais Inernacionais Carlos Hamilon Vasconcelos Araújo e Renao Galvão Flôres Júnior Mar/001 Mar/001 Mar/001 Mar/001 Jul/001 Abr/001 Aug/00 Apr/001 May/001 May/001 Jun/001 Jun/001 Jul/001 Aug/001 Aug/001 Aug/001 Se/001 6

28 8 Regras Moneárias e Dinâmica Macroeconômica no Brasil: uma Abordagem de Expecaivas Racionais Marco Anonio Bonomo e Ricardo D. Brio 9 Using a Money Demand Model o Evaluae Moneary Policies in Brazil Pedro H. Albuquerque and Solange Gouvêa 30 Tesing he Expecaions Hypohesis in he Brazilian Term Srucure of Ineres Raes Benjamin Miranda Tabak and Sandro Canesso de Andrade 31 Algumas Considerações sobre a Sazonalidade no IPCA Francisco Marcos R. Figueiredo e Robera Blass Saub 3 Crises Cambiais e Aaques Especulaivos no Brasil Mauro Cosa Miranda 33 Moneary Policy and Inflaion in Brazil ( ): a VAR Esimaion André Minella 34 Consrained Discreion and Collecive Acion Problems: Reflecions on he Resoluion of Inernaional Financial Crises Arminio Fraga and Daniel Luiz Gleizer 35 Uma Definição Operacional de Esabilidade de Preços Tio Nícias Teixeira da Silva Filho 36 Can Emerging Markes Floa? Should They Inflaion Targe? Barry Eichengreen 37 Moneary Policy in Brazil: Remarks on he Inflaion Targeing Regime, Public Deb Managemen and Open Marke Operaions Luiz Fernando Figueiredo, Pedro Fachada and Sérgio Goldensein 38 Volailidade Implícia e Anecipação de Evenos de Sress: um Tese para o Mercado Brasileiro Frederico Pechir Gomes 39 Opções sobre Dólar Comercial e Expecaivas a Respeio do Comporameno da Taxa de Câmbio Paulo Casor de Casro 40 Speculaive Aacks on Debs, Dollarizaion and Opimum Currency Areas Aloisio Araujo and Márcia Leon 41 Mudanças de Regime no Câmbio Brasileiro Carlos Hamilon V. Araújo e Geúlio B. da Silveira Filho 4 Modelo Esruural com Seor Exerno: Endogenização do Prêmio de Risco e do Câmbio Marcelo Kfoury Muinhos, Sérgio Afonso Lago Alves e Gil Riella 43 The Effecs of he Brazilian ADRs Program on Domesic Marke Efficiency Benjamin Miranda Tabak and Eduardo José Araújo Lima Nov/001 Nov/001 Nov/001 Nov/001 Nov/001 Nov/001 Nov/001 Dez/001 Feb/00 Mar/00 Mar/00 Mar/00 Apr/00 Jun/00 Jun/00 Jun/00 7

29 44 Esruura Compeiiva, Produividade Indusrial e Liberação Comercial no Brasil Pedro Cavalcani Ferreira e Osmani Teixeira de Carvalho Guillén 45 Opimal Moneary Policy, Gains from Commimen, and Inflaion Persisence André Minella 46 The Deerminans of Bank Ineres Spread in Brazil Tarsila Segalla Afanasieff, Priscilla Maria Villa Lhacer and Márcio I. Nakane 47 Indicadores Derivados de Agregados Moneários Fernando de Aquino Fonseca Neo e José Albuquerque Júnior 48 Should Governmen Smooh Exchange Rae Risk? Ilan Goldfajn and Marcos Anonio Silveira 49 Desenvolvimeno do Sisema Financeiro e Crescimeno Econômico no Brasil: Evidências de Causalidade Orlando Carneiro de Maos 50 Macroeconomic Coordinaion and Inflaion Targeing in a Two-Counry Model Eui Jung Chang, Marcelo Kfoury Muinhos and Joanílio Rodolpho Teixeira 51 Credi Channel wih Sovereign Credi Risk: an Empirical Tes Vicorio Yi Tson Chu 5 Generalized Hyperbolic Disribuions and Brazilian Daa José Fajardo and Aquiles Farias 53 Inflaion Targeing in Brazil: Lessons and Challenges André Minella, Paulo Springer de Freias, Ilan Goldfajn and Marcelo Kfoury Muinhos 54 Sock Reurns and Volailiy Benjamin Miranda Tabak and Solange Maria Guerra 55 Componenes de Curo e Longo Prazo das Taxas de Juros no Brasil Carlos Hamilon Vasconcelos Araújo e Osmani Teixeira de Carvalho de Guillén 56 Causaliy and Coinegraion in Sock Markes: he Case of Lain America Benjamin Miranda Tabak and Eduardo José Araújo Lima 57 As Leis de Falência: uma Abordagem Econômica Aloisio Araujo 58 The Random Walk Hypohesis and he Behavior of Foreign Capial Porfolio Flows: he Brazilian Sock Marke Case Benjamin Miranda Tabak 59 Os Preços Adminisrados e a Inflação no Brasil Francisco Marcos R. Figueiredo e Thaís Poro Ferreira 60 Delegaed Porfolio Managemen Paulo Couinho and Benjamin Miranda Tabak Jun/00 Aug/00 Aug/00 Se/00 Sep/00 Se/00 Sep/00 Sep/00 Sep/00 Nov/00 Nov/00 Nov/00 Dec/00 Dez/00 Dec/00 Dez/00 Dec/00 8

30 61 O Uso de Dados de Ala Freqüência na Esimação da Volailidade e do Valor em Risco para o Ibovespa João Maurício de Souza Moreira e Eduardo Facó Lemgruber 6 Taxa de Juros e Concenração Bancária no Brasil Eduardo Kiyoshi Tonooka e Sérgio Mikio Koyama 63 Opimal Moneary Rules: he Case of Brazil Charles Lima de Almeida, Marco Aurélio Peres, Geraldo da Silva e Souza and Benjamin Miranda Tabak 64 Medium-Size Macroeconomic Model for he Brazilian Economy Marcelo Kfoury Muinhos and Sergio Afonso Lago Alves 65 On he Informaion Conen of Oil Fuure Prices Benjamin Miranda Tabak 66 A Taxa de Juros de Equilíbrio: uma Abordagem Múlipla Pedro Calhman de Miranda e Marcelo Kfoury Muinhos 67 Avaliação de Méodos de Cálculo de Exigência de Capial para Risco de Mercado de Careiras de Ações no Brasil Gusavo S. Araújo, João Maurício S. Moreira e Ricardo S. Maia Clemene 68 Real Balances in he Uiliy Funcion: Evidence for Brazil Leonardo Soriano de Alencar and Márcio I. Nakane 69 r-filers: a Hodrick-Presco Filer Generalizaion Fabio Araújo, Mara Balar Moreira Areosa and José Alvaro Rodrigues Neo 70 Moneary Policy Surprises and he Brazilian Term Srucure of Ineres Raes Benjamin Miranda Tabak 71 On Shadow-Prices of Banks in Real-Time Gross Selemen Sysems Rodrigo Penaloza 7 O Prêmio pela Mauridade na Esruura a Termo das Taxas de Juros Brasileiras Ricardo Dias de Oliveira Brio, Angelo J. Mon'Alverne Duare e Osmani Teixeira de C. Guillen 73 Análise de Componenes Principais de Dados Funcionais uma Aplicação às Esruuras a Termo de Taxas de Juros Geúlio Borges da Silveira e Ocavio Bessada 74 Aplicação do Modelo de Black, Derman & Toy à Precificação de Opções Sobre Tíulos de Renda Fixa Ocavio Manuel Bessada Lion, Carlos Albero Nunes Cosenza e César das Neves 75 Brazil s Financial Sysem: Resilience o Shocks, no Currency Subsiuion, bu Sruggling o Promoe Growh Ilan Goldfajn, Kaherine Hennings and Helio Mori Dez/00 Fev/003 Feb/003 Feb/003 Feb/003 Fev/003 Fev/003 Feb/003 Feb/003 Feb/003 Apr/003 Maio/003 Maio/003 Maio/003 Jun/003 9