IMPLIED VOLATILITY LINKAGES AMONG MAJOR EUROPEAN CURRENCIES

Transcription

1 IMPLIED VOLATILITY LINKAGES AMONG MAJOR EUROPEAN CURRENCIES Juss Nkknen *, Petr Sahlström, Sam Vähämaa Department of Accountng and Fnance Unversty of Vaasa, Fnland December 28, 200 Abstract Ths paper examnes lnkages n expected future volatltes among major European currences. For that purpose, volatlty expectatons mpled by currency optons on the euro, Brtsh pound, and Swss franc quoted aganst the U.S. dollar are analysed. Vector autoregressve modellng s appled to ascertan the dynamcs of the mpled volatltes across currences. The results show that the market expectatons of future exchange rate volatltes are closely lnked among major European currences. Furthermore, t s found that the mpled volatlty of the euro sgnfcantly affects the volatlty expectatons of the Brtsh pound and the Swss franc. JEL classfcaton: F; G; G5 Keywords: exchange rates, volatlty lnkages, mpled volatlty * Correspondng author. Unversty of Vaasa, Department of Accountng and Fnance, P.O. Box 700, FIN-650 Vaasa, Fnland; Tel ; Fax: ; E-mal address: jn@uwasa.f

2 IMPLIED VOLATILITY LINKAGES AMONG MAJOR EUROPEAN CURRENCIES Abstract Ths paper examnes lnkages n expected future volatltes among major European currences. For that purpose, volatlty expectatons mpled by currency optons on the euro, Brtsh pound, and Swss franc quoted aganst the U.S. dollar are analysed. Vector autoregressve modellng s appled to ascertan the dynamcs of the mpled volatltes across currences. The results show that the market expectatons of future exchange rate volatltes are closely lnked among major European currences. Furthermore, t s found that the mpled volatlty of the euro sgnfcantly affects the volatlty expectatons of the Brtsh pound and the Swss franc. JEL classfcaton: F; G; G5 Keywords: exchange rates, volatlty lnkages, mpled volatlty

3 2. INTRODUCTION Over the last two decades, consderable attenton has been devoted to the volatlty of exchange rates. Gven that the foregn exchange market s by far the largest fnancal market n the world, understandng the dynamcs of exchange rate volatlty s of hgh mportance. Undsputedly, exchange rate volatlty has mportant mplcatons for the economy. Exchange rate volatlty, for nstance, creates uncertanty for the prces of exports and mports, and thereby sgnfcantly affects nternatonal trade flows (see e.g., Caporale and Doroodan, 994; Rose, 2000). Several studes have shown that exchange rate volatlty has a major mpact on the proftablty of multnatonal frms, and consequently, also on stock prces (see e.g., Joron, 990; Baley and Chung, 995; Dumas and Solnk, 995; Baum et al., 200). Moreover, snce ncreasng exchange rate volatlty tends to dscourage nvestment decsons, t may also have an adverse effect on ndustral producton and employment (see e.g., Belke and Gros, 2002). Exchange rate volatlty may be a major concern for global fnancal stablty, as Robert Mundell noted n hs Nobel Lecture (Mundell, 2000). The ERM crss of 992 and the Asan currency crss n the autumn of 997 are recent notorous examples of the potental mpact of exchange rate volatlty on the economy. Especally the Asan currency crss demonstrated how uncertanty n one currency may frst spread to other currences and fnally cause a chan reacton of contagon throughout the global fnancal markets (see e.g., Tuluca and Zwck, 200; Cartapans et al., 2002; Baur, 200). These currency crses clearly ndcate that exchange rate volatltes are affected not only by country specfc economc fundamentals and monetary polcy but also by common uncertanty factors. In other words, volatltes tend to be lnked across

4 currences n the sense that movements n one currency may affect other currences beyond the mpact of macroeconomc fundamentals. These volatlty lnkages across exchange rates have mportant practcal mplcatons for nternatonal nvestors, multnatonal frms, rsk managers, bank supervson authortes, and monetary polcy makers. Internatonal nvestors, for nstance, need to consder the mpact of exchange rate volatlty lnkages on portfolo dversfcaton. From the vewpont of monetary polcy makers, volatlty lnkages may be dsquetng, as they mply that exchange rates are affected by global uncertanty factors whch are beyond the control of local monetary polcy. Ths paper focuses on volatlty lnkages among major European currences. In partcular, the purpose of ths paper s to examne lnkages n market expectatons of future exchange rate volatlty. Although not drectly observable, these volatlty expectatons are mplct n the market prces of currency optons, and can thus be estmated gven an opton prcng model. In ths paper, volatltes mpled by currency optons on the euro, Brtsh pound, and Swss franc quoted aganst the U.S. dollar are used to nvestgate lnkages n expected exchange rate volatltes. Impled volatlty may be regarded as market partcpants forecast of the average future volatlty of the underlyng asset over the remanng lfe of the opton contract. Provded that market partcpants are ratonal, mpled volatlty should ncorporate all the avalable nformaton that s relevant for formng expectatons about the future volatlty. Therefore, mpled volatlty may be consdered as the best avalable estmate of market uncertanty. By focusng on lnkages n expected exchange rate volatltes as mpled by opton prces, ths paper provdes new evdence on the exchange rate volatlty dynamcs.

5 4 Although exchange rate volatlty has been a focus of extensve research over recent years, surprsngly lttle s known about volatlty lnkages across exchange rates. The lterature on volatlty transmsson n the foregn exchange markets was poneered by Engle et al. (990). They examned exchange rate volatlty lnkages across market segments and noted that volatlty tends to spll over from one marketplace to another. 2 Volatlty lnkages across exchange rates have prevously been examned n Najand et al. (992), Alexander (995), Laopods (998), Kearney and Patton (2000), and Speght and McMllan (200). A common feature of these papers s the use of autoregressve condtonal heteroskedastcty (ARCH) modellng to assess volatlty lnkages across exchange rates. In bref, these prevous studes demonstrate that volatltes tend to be lnked across currences. Najand et al. (992) use data on the Brtsh pound, Canadan dollar, Japanese yen, German mark, and Swss franc futures quoted aganst the U.S. dollar to show that volatlty n one currency s transmtted to other currences. In partcular, they show that the German mark sgnfcantly nfluences the other four currences. Regardng the European currences, Najand et al. (992) show that the volatlty of the Brtsh pound s sgnfcantly affected both by the German mark and the Swss franc. Alexander (995) documents that the volatltes of the European Monetary System (EMS) currences, ncludng the German mark, are consderably affected by the Brtsh pound and the Japanese yen. These results are contradcted by Kearney et al. (2000), who show that Consderable lterature has examned volatlty lnkages n stock markets (see e.g., Ln et al., 994; Koutmos and Booth, 995; Booth et al., 997; Kearney, 2000) and among nterest rates (see e.g., Laopods, 2002; Zhou, 200). 2 Smlar fndngs have been subsequently documented e.g. n Balle and Bollerslev (99), Ito et al. (992), Kanas and Kouretas (200, 2002), and Melvn and Peers Melvn (200).

6 5 the volatlty of the German mark tends to be transmtted to the other EMS currences, thereby suggestng that the German mark s the domnant currency wthn the EMS. Ths paper contrbutes to the lterature on exchange rate volatlty n several respects. The man novelty of ths paper s the focus on lnkages n expected exchange rate volatltes. Whereas the prevous studes by Najand et al. (992), Alexander (995), Laopods (998), Kearney et al. (2000), and Speght et al. (200) use ex post volatlty estmates to examne volatlty lnkages across exchange rates, ths paper uses ex ante volatlty estmates extracted from opton prces. Ths approach has several advantages. Most mportantly, mpled volatlty may be consdered as the best avalable estmate of market uncertanty. It s well known that market uncertanty may change consderably from day to day. Such changes n uncertanty should be mmedately reflected n opton prces, and hence, also n mpled volatltes. On the contrary, volatlty estmates obtaned va ARCH modellng are based on past observatons, and hence, are by constructon constraned to reflect only past market reactons rather than current or expected future market uncertanty. For most practcal purposes, lnkages n future exchange rate volatltes are of nterest. As a consderable body of lterature has confrmed the superorty of mpled volatlty to other volatlty estmates n forecastng future volatlty, these lnkages n expected future volatltes across exchange rates may be most approprately assessed usng mpled volatltes. By examnng mpled volatlty lnkages across exchange rates, ths paper extends the lterature on mpled volatlty dynamcs n the foregn exchange markets. Although several studes have examned mpled volatltes n stock markets (see Mayhew, 995 for a revew), only lttle s known about the dynamcs of mpled volatltes derved from currency optons. Prevously, propertes of mpled volatltes

7 6 n the foregn exchange markets have been examned n Xu and Taylor (994), Campa and Chang (995), Bonser-Neal and Tanner (996), Ederngton and Lee (996), Km and Km (200), and Sarwar (200). Ths paper extends the above lterature by focusng on the cross-dynamcs of mpled volatltes. Regardng the predctve power of mpled volatltes, Shastr and Tandon (986), Joron (995), and Xu and Taylor (995) show that mpled volatlty s superor to other volatlty estmates n forecastng future exchange rate volatlty. Snce knowledge of potental causal relatonshps may mprove volatlty forecasts (Najand et al., 992), ths paper also contrbutes to the volatlty predcton lterature by provdng nformaton regardng the lead-lag relatonshps between mpled volatltes. Fnally, ths paper provdes new evdence regardng the role of the euro among European currences by focusng on the mpled volatlty lnkages. Indsputably, the ntroducton of the euro s one of the most mportant events n the fnancal markets over recent years. Before the ntroducton of the euro, Mundell (998) prophesed that the dollar-euro exchange rate s lkely to become the most mportant prce n the world. Detken and Hartmann (2000) and Frsch (200) have later concluded that the euro became the second most wdely used currency n nternatonal fnancal markets mmedately after ts ntroducton. Gven the mportance of the euro to the nternatonal monetary system, understandng the dynamcs of the euro s certanly a hgh prorty task. The remander of ths paper s organzed as follows. Secton 2 descrbes the mpled volatlty data used n the emprcal analyss. Secton presents the methodology used to examne lnkages n expected exchange rate volatltes. The

8 7 emprcal fndngs on the mpled volatlty lnkages among major European currences are reported n Secton 4. Fnally, concludng remarks are provded n Secton DATA The emprcal analyss n ths paper s performed usng daly data on mpled volatltes of the major three European currences, the euro (EUR), the Brtsh pound (GBP), and the Swss franc (CHF), quoted aganst the U.S. dollar. The sample perod used n the analyss extends from January 2, 200 to September 29, 200. The euro, Brtsh pound, and Swss franc are selected for the analyss snce they are by far the most mportant European currences, as measured both by the daly tradng volume and the sze of the economy. The euro accounts for about 5.4 % of the global foregn exchange market turnover aganst the U.S. dollar whle the Brtsh pound and Swss franc account for 8.5 % and 5.4 % respectvely (see Bank for Internatonal Settlements, 2002). Furthermore, the mportance of these currences s also reflected n the dervatves tradng volumes. For nstance, as measured by the number of contracts traded and premums pad, optons on the euro are dstnctly the most actvely traded currency optons on the Phladelpha Stock Exchange (PHLX), whch s wdely consdered as the world s leadng marketplace for exchange-traded currency optons. The mpled volatltes used n ths paper are derved from the prces of currency optons traded on the Phladelpha Stock Exchange. The PHLX currency optons are quoted n U.S. cents per unt of the underlyng foregn currency. Exercsed currency For comparson, the Japanese yen accounts for about 24.8 % and the Canadan dollar for about 4.6 % of the global turnover aganst the U.S. dollar.

9 8 optons are settled by the delvery of the spot currency. In ths paper, the European-style md-month optons are used to compute the mpled volatltes. The expraton months for the md-month currency optons are March, June, September, and December as well as the two addtonal near-term months, so that sx contract maturtes are always avalable for tradng. The md-month currency optons expre on the Frday before the thrd Wednesday of the contract month. The mpled volatltes are extracted from the observed currency opton prces usng the Garman-Kohlhagen (98) verson of the Black-Scholes (97) / Merton (97) model. In the Black-Scholes framework, volatlty of the underlyng asset prce s the only unobservable determnant of opton prce. Consequently, gven the other varables, the prce of an opton, c t, at tme t can be expressed as a functon of volatlty, c t = f(), where denotes the volatlty of the underlyng asset prce. Provded that opton prces are observable on the market, volatlty mpled by opton prces, v, can be obtaned by nvertng the prcng functon, v = f - (c t ), where f - s the nverse functon of f. Ths mpled volatlty estmate s the market s assessment of the future volatlty over the remanng lfe of the opton. Snce mpled volatltes tend to vary across strke prces and maturtes (see e.g., Taylor and Xu, 994; Xu and Taylor, 994), constant maturty at-the-money mpled volatlty tme-seres of the euro, Brtsh pound, and Swss franc aganst the U.S. dollar are constructed. Frst, mpled volatltes are estmated for each tradng day n the data set, for the two closest-to-money call and put optons, and for two near-term expraton months. These call and put mpled volatltes are then nterpolated n order to obtan at-the-money mpled volatltes. Subsequently, the at-the-money call and put mpled volatltes are averaged, and then fnally nterpolated between the two adjacent maturty

10 9 volatlty estmates. As a result, at-the-money mpled volatlty tme-seres wth a constant maturty of one month are obtaned. 4 These constant maturty mpled volatltes on a gven day reflect market expectatons of future exchange rate volatlty over the next month. By usng one-month at-the-money mpled volatlty tme-seres to examne volatlty lnkages, the well-known Black-Scholes bases can be mnmzed. Whle the Black-Scholes model systematcally msprces n-the-money and out-of-the-money optons, broad evdence suggests that t prces short-term at-the-money optons correctly. For nstance, Corrado and Mller (996) show that for short maturty at-themoney optons the mpled volatltes derved from the Black-Scholes model are vrtually dentcal wth the volatltes based on stochastc volatlty models. In addton, snce short-term at-the-money and near-the-money optons are the most actvely traded opton contracts, the mpled volatltes derved from these optons should most accurately reflect market expectatons about the future volatlty of the underlyng asset. (nsert Fgure about here) Fgure plots the developments n the one-month at-the-money mpled volatlty tme-seres of the euro, Brtsh pound, and Swss franc over the perod from January 200 to September 200. Fgure demonstrates that the mpled volatltes are varyng consderably over tme. All exchange rates have been partcularly volatle n the 4 These mpled volatlty seres are essentally smlar to the U.S. and German stock market volatlty ndces, VIX and VDAX, respectvely.

11 0 aftermath of the September th terrorst attack. The substantal ncrease n exchange rate volatlty expectatons n the summer of 2002 s concurrent wth the begnnng of the dollar deprecaton after the long dollar surge. Furthermore, turnng the focus to the volatlty lnkages, Fgure ndcates that the three mpled volatlty seres tend to move together rather closely. (nsert Table about here) Table reports descrptve statstcs of the mpled volatlty tme-seres. It can be noted that the mpled volatltes have ranged from about 5 % to almost 6 % durng the sample perod. Interestngly, the mean mpled volatlty estmates show that the Brtsh pound tends to be less volatle than the euro and the Swss franc. The consderable correlatons reported n Panel B of Table confrm that market expectatons of future volatlty are closely lnked across currences.. FRAMEWORK OF ANALYSIS The choce of econometrc methodology depends on the tme-seres propertes of the mpled volatltes. Dependng on the statonarty of the mpled volatlty tmeseres, vector autoregressve (VAR) modellng wth levels or frst dfferences, or vector error correcton (VEC) modellng are the applcable methodologcal canddates for examnng mpled volatlty lnkages. In order to determne the statonarty of the mpled volatltes tme-seres, the augmented Dckey-Fuller and Phllps-Perron unt

12 root tests are performed. 5 The results of the unt root tests are reported n Table 2. The lag length used n the tests s decded based on the Schwartz nformaton crteron. The test results n Table 2 ndcate that the mpled volatlty tme-seres are statonary, as the null hypothess of a unt root can be soundly rejected for all three mpled volatlty seres. (nsert Table 2 about here) Gven that the unt root tests ndcate statonarty of the mpled volatlty tmeseres, vector autoregressve (VAR) modellng may be appled to ascertan the causal dynamcs of the mpled volatltes. Hence, t s assumed that the mpled volatlty dynamcs of the euro, Brtsh pound, and Swss franc exchange rates aganst the U.S. dollar are descrbed by the followng unrestrcted trvarate VAR(p) model p = α Φ ε () t t t where =,, ) s a covarance statonary vector of mpled t ( t t CHF, t volatlty tme-seres contanng 7 observatons, α s a vector of ntercepts, {Φ,, 2,, p} s a matrx of autoregressve coeffcents, ε t s a vector of 5 Due to the nature of volatlty, t s assumed that there s no tme trend n the mpled volatlty seres n the long run. However, the unt root tests were also performed wth a tme trend and the results reman unchanged. Moreover, the test results are not senstve to the number of lags used.

13 2 whte nose wth zero mean and postve defnte covarance matrx, and p denotes the lag order of the system. In ths paper, the VAR(p) system gven by Equaton () s used to ascertan possble lead-lag relatonshps between the mpled volatlty seres and, addtonally, to examne the transmsson of shocks n the mpled volatlty of one exchange rate on the other mpled volatltes n the system. The unrestrcted trvarate VAR(p) model allows for unbased testng of Granger causalty and for relable analyss of the shock transmsson mechansm between the varables n the system. Therefore, the VAR modellng provdes a sutable framework for analysng mpled volatlty lnkages among European currences. Granger causalty tests, mpulse response analyss and varance decompostons are appled to nterpret the estmated VAR(p) system. Granger causalty tests are used to dentfy potental lead-lag relatonshps between the mpled volatltes and the drecton of causaltes. The Granger causalty tests are conducted based on the unrestrcted trvarate VAR(p) system, and hence, the causalty results should be more general and relable than n a standard bvarate settng. Impulse response analyss s used to trace the mpact of a shock n mpled volatlty of one exchange rate on the future values of tself and the other mpled volatltes n the system. Moreover, mpulse response analyss reveals the persstence of shocks n the system, and hence, enables the assessment of the tme structure of volatlty transmsson. In order to avod problems wth the orderng of the varables n the system, the generalzed mpulses proposed by Pesaran and Shn (998) are appled n the mpulse response analyss. Fnally, varance decomposton analyss s used to assess the fracton of varaton n mpled volatlty of one exchange rate caused by nnovatons n the other mpled volatltes n the system.

14 Hence, varance decompostons provde nformaton about the relatve mportance of one mpled volatlty n affectng the other mpled volatltes n the VAR. (nsert Table about here) Determnaton of an approprate lag order, p, for the VAR system s an emprcal ssue. In ths paper, the order of the VAR s defned based on the standard lag length crtera and lkelhood rato tests. In addton, gven that the resduals of the VAR should exhbt no seral correlaton f there are enough lags n the model, the resdual seral correlatons are analysed to confrm the adequacy of the lag order. Table reports Akake s, Schwartz s and Hannan-Qunn nformaton crtera and Lütkepohl s (99) modfed lkelhood rato test for the lag order selecton. All the nformaton crtera reported n Table suggest settng p=2 whle the lkelhood rato test suggests p=. In addton, the Breusch-Godfrey LM test ndcates sgnfcant seral correlaton n the resduals of the VAR(2) model. Therefore, the VAR(2) system s augmented wth one addtonal lag. Model dagnostcs suggest that ths specfcaton s adequate. Consequently, the emprcal analyss n ths paper s based on the VAR system gven by Equaton () wth p=. 4. RESULTS Table 4 reports summary statstcs of the VAR() estmaton results. The F- statstcs ndcate that the estmated VAR() model s statstcally hghly sgnfcant. Moreover, the R 2 s relatvely hgh for all equatons, rangng from for the Swss

15 4 franc to for the euro. The Ljung-Box statstc for 2 lags shows no sgn of resdual seral correlaton n the model, thereby suggestng that the selected lag order s adequate. (nsert Table 4 about here) The contemporaneous resdual correlatons of the estmated VAR() model are shown n Table 5. The reported resdual correlatons between the mpled volatlty seres ndcate nstantaneous relatonshps between the volatlty expectatons of the major European currences. All resdual correlatons n Table 5 are postve and statstcally hghly sgnfcant. The hghest resdual correlaton s found between the euro and the Swss franc, wth the correlaton coeffcent of The resdual correlatons are somewhat lower between the euro and the Brtsh pound and between the Swss franc and the Brtsh pound, correlaton coeffcents beng 0.2 n both cases. These resdual correlatons ndcate that the market expectatons of future exchange rate volatltes are contemporaneously and postvely lnked among the major European currences. (nsert Table 5 about here) Granger causalty tests are performed n order to ascertan potental lead-lag relatonshps between the mpled volatlty seres. Table 6 presents the Granger causalty test results based on the trvarate VAR() specfcaton. The results ndcate that the euro s the domnant European currency, as the mpled volatlty of the euro s

16 5 found to Granger cause the volatlty expectatons of both the Brtsh pound and the Swss franc. In contrast, the Granger causalty test results suggest that the volatlty expectatons of the euro are not affected by the other major currences. In addton, the results show weak volatlty transmsson (p-value of 0.079) from the pound to the franc. In general, the Granger causalty test results n Table 6 clearly show that the euro s the leadng source of volatlty expectatons among the major European currences. (nsert Table 6 about here) In order to trace the mpact of a shock n mpled volatlty of one exchange rate on the future values of tself and the other mpled volatltes n the VAR system, mpulse response analyss s accomplshed. Gven the Granger causalty test results, the man focus n the analyss s on the dynamcs of responses of the Brtsh pound and Swss franc volatlty expectatons to shocks n the volatlty expectatons of the euro. The mpulse response analyss s performed usng generalzed one standard devaton shocks on the mpled volatltes (see Pesaran and Shn 998). The mpulse response functons and the Monte Carlo smulated 95 percent confdence bounds (dashed lnes) are presented n Fgure 2. The mpulse response functon of the mpled volatlty of the pound to a shock n the mpled volatlty of the euro ndcates that after the contemporaneous (day one) effect, the mpled volatlty of the pound stll ncreases on the next day (day two), and afterwards, the effect seems to settle down. A smlar pattern can also be observed for the mpulse response functon of the mpled volatlty of the franc to a shock n the mpled volatlty of the euro. In bref, the mpulse

17 6 response functons shown n Fgure 2 ndcate that a shock n the volatlty expectatons of the euro sgnfcantly affects volatlty expectatons of the pound and the franc. The mpact of a shock n the mpled volatlty of the euro seems to be ncorporated nto the volatlty expectatons of the Brtsh pound and the Swss franc durng the frst two days. (nsert Fgure 2 about here) Fnally, varance decomposton analyss s appled to ascertan the relatve mportance of one mpled volatlty n affectng the other mpled volatltes n the VAR system. The varance decompostons are presented n Fgure. The dashed lnes around each varance decomposton present 95 percent confdence bounds obtaned va Monte Carlo smulaton. Fgure clearly demonstrates that the forecast varance of the mpled volatlty of the euro s solely caused by nnovatons n tself. Hence, also the varance decomposton analyss mples that the volatlty expectatons of the euro are not affected by the Brtsh pound and the Swss franc. However, volatlty expectatons of the euro appear to have a consderable mpact on the volatlty expectatons of the pound and the franc. About % of two days ahead and about 26 percent of ten days ahead varance forecasts of the pound s attrbutable to nnovatons n the volatlty expectatons of the euro. For the volatlty expectatons of the Swss franc, the correspondng fgures are 20 % and %, respectvely. Therefore, the varance decompostons suggest that the expected future volatltes of the Brtsh pound and the Swss franc are sgnfcantly affected by the expected volatlty of the euro.

18 7 (nsert Fgure about here) 5. CONCLUSIONS Ths paper examnes lnkages n expected future volatltes among major European currences. The man novelty of ths paper s the focus on lnkages n expected exchange rate volatltes. Whereas the prevous studes (see Najand et al., 992; Alexander, 995; Laopods, 998; Kearney et al., 2000; Speght et al., 200) use ex post volatlty estmates to examne volatlty lnkages across exchange rates, ths paper uses ex ante volatlty estmates extracted from opton prces. Provded that market partcpants are ratonal, opton-mpled volatlty estmates should ncorporate all the avalable nformaton that s relevant for formng expectatons about the future volatlty. Therefore, mpled volatltes provde a sutable framework for assessng lnkages n expected exchange rate volatltes. The emprcal analyss n ths paper s performed usng daly data on volatltes mpled by currency optons on the euro, Brtsh pound, and Swss franc quoted aganst the U.S. dollar. Vector autoregressve (VAR) modellng s appled to ascertan the causal dynamcs of the mpled volatltes across currences. Granger causalty tests, mpulse response analyss and varance decompostons are used to nterpret the VAR estmaton results. In bref, the results of ths paper ndcate that the market expectatons of future exchange rate volatltes are closely lnked among the major European currences. In partcular, the results show that the euro s the domnant European currency, as the mpled volatlty of the euro s found to sgnfcantly affect the volatlty expectatons

19 8 of the Brtsh pound and the Swss franc. Moreover, the results suggest that the volatlty expectatons of the euro are not affected by the other currences. The results of ths paper have mportant practcal mplcatons, for nstance, to fnancal market practtoners and monetary polcy makers. Knowledge of the causal relatonshps between exchange rate volatltes may be useful e.g. for asset prcng, portfolo selecton, and rsk management purposes. In partcular, the leadng role of the euro may be utlzed for constructng better volatlty forecasts whch are needed n numerous fnancal applcatons. From the vewpont of monetary polcy makers, the documented volatlty lnkages may be dsquetng, as they mply that the exchange rates are affected by common uncertanty factors whch are beyond the control of local monetary polcy. Consderng that the U.K. and Swtzerland are relatvely large economes, but stll the volatlty expectatons of the euro sgnfcantly affect uncertanty n the Brtsh pound and Swss franc, smaller European currences such as the Dansh and Swedsh kronas are lkely to be even more vulnerable to the mpact of the euro.

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25 24 Fgure. Impled volatltes. 8 6 EUR Jan-0 May-0 Sep-0 Jan-02 May-02 Sep-02 Jan-0 May-0 Sep GBP Jan-0 May-0 Sep-0 Jan-02 May-02 Sep-02 Jan-0 May-0 Sep CHF Jan-0 May-0 Sep-0 Jan-02 May-02 Sep-02 Jan-0 May-0 Sep-0

26 25 Fgure 2. Impulse response functons. The graphs present the mpact of a generalzed one standard devaton nnovaton n mpled volatlty of one exchange rate on tself and on the other mpled volatltes n the system. Two standard error confdence bounds are presented around each mpulse response functon Response of EUR to EUR Response of EUR to GBP Response of EUR to CHF Response of GBP to EUR Response of GBP to GBP Response of GBP to CHF Response of CHF to EUR Response of CHF to GBP Response of CHF to CHF

27 26 Fgure. Varance decompostons. The graphs present the percentage of forecast varance of mpled volatlty of one exchange rate caused by nnovatons n tself and n the other mpled volatltes n the system. Two standard error confdence bounds are presented around each varance decomposton Percent EUR varance due to EUR Percent EUR varance due to GBP Percent EUR varance due to CHF Percent GBP varance due to EUR 00 Percent GBP varance due to GBP 00 Percent GBP varance due to CHF Percent CHF varance due to EUR 00 Percent CHF varance due to GBP 00 Percent CHF varance due to CHF

28 27 Table. Descrptve statstcs and contemporaneous correlatons of mpled volatltes. Panel A: Descrptve statstcs EUR GBP CHF Mean Medan Mnmum Maxmum Standard Devaton Skewness Kurtoss No. of Observatons Panel B: Correlatons EUR GBP CHF EUR.00 GBP CHF sgnfcant at the 0.0 level

29 28 Table 2. Unt root tests. The table reports Augmented Dckey-Fuller (ADF) and Phllps-Perron (PP) unt root tests wthout a tme trend for the mpled volatlty seres. The lag length for the unt root tests s decded based on the Schwarz nformaton crteron. The crtcal value for the tests at the % sgnfcance level s.44. ADF p-value PP p-value EUR GBP CHF

30 29 Table. Lag order selecton for the VAR(p) model. The table reports Akake s (AIC), Schwarz s (SIC), and Hannan-Qunn (HQ) nformaton crtera and Lütkepohl s (99) modfed lkelhood rato (LR) test for the lag order selecton. Lag AIC SIC HQ LR

31 0 Table 4. Summary statstcs of the VAR() model. The table reports the summary statstcs of the followng trvarate VAR() specfcaton: t t CHF, t = α = α = α EUR GBP CHF EUR EUR EUR CHF, t t t GBP GBP GBP CHF, t t t CHF CHF CHF CHF, CHF, t CHF, t CHF, t where j,t denotes mpled volatlty of currency j quoted aganst the U.S. dollar at tme t. Q(n) s the Ljung-Box statstc for n lags. ε ε ε t t CHF, t Dependent Varable Adj. R 2 F-Stat. p-value Q(2) p-value EUR GBP CHF

32 Table 5. Resdual correlatons of the VAR() model. The table reports the resdual correlatons of the followng trvarate VAR() specfcaton: t t CHF, t = α = α = α EUR GBP CHF EUR EUR EUR CHF, t t t GBP GBP GBP CHF, t t t CHF CHF CHF CHF, CHF, t CHF, t CHF, t ε ε ε t t CHF, t where j,t denotes mpled volatlty of currency j quoted aganst the U.S. dollar at tme t. EUR.00 EUR GBP CHF GBP CHF sgnfcant at the 0.0 level

33 2 Table 6. Granger causalty tests. The table reports the Granger causalty test results based on the followng trvarate VAR() specfcaton: t t CHF, t = α = α = α EUR GBP CHF EUR EUR EUR CHF, t t t GBP GBP GBP CHF, t t t CHF CHF CHF CHF, CHF, t CHF, t CHF, t where j,t denotes mpled volatlty of currency j quoted aganst the U.S. dollar at tme t. The reported Wald statstc s for the jont sgnfcance of the coeffcents of lagged mpled volatltes of currency k n the mpled volatlty equaton of currency j. Dependent: EUR Wald-stat. ε ε ε t t CHF, t p-value GBP CHF Dependent: GBP EUR CHF Dependent: CHF EUR GBP