DISCUSSION PAPER SERIES EURO AT RISK: THE IMPACT OF MEMBER COUNTRIES CREDIT RISK ON THE STABILITY OF THE COMMON CURRENCY FINANCIAL ECONOMICS ABCD

Transcription

1 DISCUSSION PAPER SERIES EURO AT RISK: THE IMPACT OF MEMBER COUNTRIES CREDIT RISK ON THE STABILITY OF THE COMMON CURRENCY FINANCIAL ECONOMICS ABCD

2 Euro a Risk: The Impac of Member Counries Credi Risk on he Sabiliy of he Common Currency* Absrac In his paper, we empirically invesigae he impac of he credi risk of Eurozone member counries on he sabiliy of he Euro. In pracice, in he absence of eurobonds, euro-area credi risk is induced hough he credi defaul swaps of he member counries. The sabiliy of he euro is examined by decomposing dollar-euro exchange rae opions ino he momens of he risk-neural disribuion. We argue ha sovereign capial srucure arbirage ensures ha new informaion on sovereign disress risk affecs he currency. In paricular, we documen ha during he sovereign deb crisis changes in he crediworhiness of member counries have significan impac on he sabiliy of he euro. An increase in member counries credi risk resuls in an increase of volailiy of he dollar-euro exchange rae along wih soaring ail risk induced hrough he risk-neural kurosis. We find ha member counries credi risk is a major deerminan of he euro crash risk as measured by he risk-neural skewness. We propose a new indicaor for currency sabiliy by combining he risk-neural momens ino an aggregaed risk measure and show ha our resuls are robus o his change in measure. During he sovereign deb crisis, he crediworhiness of counries wih vulnerable fiscal posiions is ypically he main risk-endangering facor of he euro-sabiliy. Ineresingly, however, he marke perceives Greece no o be sysemically relevan. Keywords: European sovereign deb crisis, currency opions, credi defaul swaps, currency sabiliy, crash risk, ail risk, sovereign capial srucure arbirage. JEL-Classificaion: G13, F31 1

3 1. Moivaion In view of he curren sovereign deb crisis, undersanding he dynamics of he credi risk of he euro-area counries proves urgen so as o preven dire scenarios. A wors, he defaul of a major counry would unleash he currency break-up, ravage he European banking sysem and ulimaely engender a global economic slump. In his sudy, we view he Eurozone sovereign deb crisis hrough he win lenses of sovereign credi swaps and currency opion markes. In he absence of Eurobonds, we empirically examine he impac of he credi risk of member counries on he sabiliy of he Euro. The credi risk of a counry can be measured hrough is sovereign credi defaul swap (CDS) 1. Marke prices of CDS spreads reflec he percepion of financial markes abou he economicpoliical sabiliy of a counry, and hus abou he crediworhiness of a given sovereign. As shown by Pan and Singleon (008), he changes in credi risk premiums of sovereign markes which ranslae ino changes in sovereign CDS spreads, do no emanae from changes in fundamenals of he underlying economies. Raher, hese variaions mirror a change in he risk appeie of marke paricipans in erms of credi exposure. A negaive change in he crediworhiness of a sovereign ineviably ranslaes ino a depreciaion of is currency along wih soaring currency volailiy. Furhermore, currency opion prices are insrumens which are capable of predicing he changes in he realized volailiy of currency reurns. Based on daa from he Mexican and Brazilian Markes, Car and Wu (007) esablish a relaionship beween sovereign CDS spreads and currency reurn volailiies induced hrough implied-volailiies of currency opions and risk reversals. Their resuls indicae ha he sovereign CDS spreads covary subsanially wih he risk reversals. In he same spiri, Hui and Fong (011) repor similar resuls while focusing on he inerconneciviy beween he US and Japan sovereign CDS markes and he currency opion marke characerized by risk reversals of opions on he dollar-yen exchange rae. Compared o Japan, The US sovereign credi risk is shown o have a significan impac on 1 A sovereign CDS conrac provides proecion agains he non-paymen of sovereign deb. Typically, i involves one counerpary agreeing o sell proecion o anoher. The "proeced" pary pays a yearly premium known as he CDS spread in exchange for a guaranee ha in he even of a defaul, he seller of proecion will provide compensaion. Risk reversal is he difference in volailiy (dela) beween similar ou-of-he-money call and pu opions. A posiive risk reversal implies ha marke paricipans are expecing an appreciaion raher han a depreciaion of he local currency. The risk reversal conveys informaion abou he skewness of he exchange rae disribuion.

4 he risk reversal. Therefore i is deemed o play a more significan role in he way markes form expecaions on he dollar-yen exchange rae. Turning o he European conex, Hui and Chung (011) documen informaion ransmission from he sovereign CDS marke o he currency opion marke. Using implied volailiies of opions on he dollar-euro exchange rae as a measure of crash risk, hey conclude ha he credi risk of he Eurozone is a disinc facor which deermines he prices of he ou-of-he-money euro pu opions prices. The recen Eurozone crisis is viewed from various angles by he lieraure. Azeri e al. (011) and Alfonso e al. (011) use he perspecive of credi raing agencies and show ha sovereign raing announcemens have spillovers effec on he European financial markes. They firsly sudy he response of sovereign CDS spread, banking sock index, insurance sock index and counry sock while hey secondly focus on he response of governmen yield spreads. Eiher way news abou downgrades is found o have significan spillover effecs. However, he linkages wih currency opion markes are no considered. Anoher perspecive is ha of Calice e al. (011) who analyse he Eurozone crisis by modelling liquidiy in he sovereign CDS markes. They find evidence ha he liquidiy of CDS markes of sruggling counries such as Greece, Porugal and Ireland has a subsanial impac on sovereign deb spreads. An earlier srand of lieraure ackles he quesion of currency crash risk from a macro-economic angle and explains currency crash risk by economic fundamenals. I provides empirical evidence from developing counries of a relaionship beween macro-economic indicaors and weak currencies. Counries wih weak fundamenals are less likely o be able o defend heir currencies agains speculaive aacks (Wolff (1987), Eichengreen e al. (1996); Frankel and Rose (1996); Kaminsky e al. (003) are a few examples). Our sudy also relaes o a recen srand of lieraure which aemps o link currency crash risk o he disribuion of exchange rae. Nowihsanding he sound models and explanaions esablished by his srand, i does no ake ino accoun sovereign credi risk. Brunnermeier e al. (009) deec negaive skewness in he movemens of exchange raes involving a low-level ineres rae currency and a high-level one. This boils down o saying ha carry rade sraegies are exposed o crash risk. The auhors argue ha he skewness is riggered when such sraegies ake place in an abrup manner reflecing lower risk appeie and higher liquidiy consrains. 3

5 Currency risk wih respec o Carry rade sraegies are also examined in work by Fahri e al. (009).The main risk of hese sraegies emerges from he value of he exchange rae a he end. The auhors propose an exchange model o disinguish beween disaser and Gaussian premia in he currency opion markes. The model enails a srong relaionship beween ineres raes, changes in exchange raes and levels of risk reversals. The main empirical implicaion indicaes ha disaser premium explains 5% of carry rades reurns. In ohers words, crash risk drives currency reurns considerably. Oher papers, which find a similar resul by analyzing crash risk from he perspecive of currency opions include he work of Jurek (009) and Burnside e al. (011). Moreover, our sudy is relaed o he lieraure examining he linkage beween corporae CDS and sock opion markes and he informaion ransmission inheren o hese markes. Examples include work by Acharya and Johnson (007), which presens empirical evidence on he exisence of informaion ransmission from he corporae CDS o he sock marke. This phenomenon is deeced for firms which were subjec or are likely o be subjec o negaive credi news and which mainain srong ies wih banks. The analysis of he relaion beween CDS spreads and implied-volailiies in he work of Cao e al. (010) shows ha he informaion embedded in he implied volailiies of deep ou of he money pu opions is able o explain he variaions in CDS spreads. The skew of he implied volailiies is also compued so as o examine is effec on CDS spreads. Imporan o noe is he fac ha his implied volailiy is relaed o he negaive ail of he risk neural probabiliy. Besides, he informaion embedded in i reflecs boh fuure volailiy and risk premium. In an effor o shed more ligh on he curren sovereign deb crisis, our sudy proposes he use of a sound and sae-o-he ar measure o assess he sabiliy of he Euro. Based on he framework of Bakshi e al. (003), he sabiliy of he euro is examined by decomposing dollar-euro 3 exchange rae opions ino he momens of he risk-neural disribuion. The mehod is parly used in he recen empirical opion pricing lieraure (see e.g. Bams e al. (009) and Neumann and Skiadopoulos (01)). In paricular, we compue model-free risk-neural volailiy, skewness and kurosis measures from he cross-secion of currency opion prices, which allow us o 3 The quoaion dollar-euro refers o he amoun of dollars needed o obain one uni of euro. 4

6 evaluae he sabiliy of he euro. Skewness is ypically inerpreed as he euro crash risk, while risk-neural kurosis as he ail risk of he exchange rae disribuion. The firs measure gives an indicaion in which direcion marke paricipans are expecing he dollar-euro exchange rae o move. A negaive skewness reflecs concerns abou a depreciaion of he euro, which ranslaes ino he willingness of invesors o pay a higher risk premium for pu opions relaive o call opions in order o obain proecion for he poenial drop in value. Tail risk refers o he exreme evens whose probabiliy is low bu whose impac on prices is large should hey maerialize. In paricular, during he European sovereign deb crisis, we expec ha possible concerns abou he sabiliy of he euro should be refleced in a negaive skewness of he dollar-euro exchange rae opions. The focus of his sudy is o examine he impac of he credi risk of Eurozone member counries on he sabiliy of he Euro. We documen ha changes in he crediworhiness of a member counry on one day have a significan impac on he sabiliy of he euro on he following day. On he one hand, an increase in member counries credi risk resuls in an increase of he volailiy of he dollar-euro exchange rae along wih soaring ail risk induced hrough he risk-neural kurosis. On he oher, we find ha member counries credi risk is a major deerminan of he euro crash risk as measured by he risk-neural skewness. Based on hose resuls, we propose a new indicaor for currency sabiliy by combining he risk-neural momens ino an aggregaed risk measure and show ha our resuls are robus o his change in measure. Noiceable is he fac he crediworhiness of counries wih vulnerable fiscal posiions is he main, bu no he only riskendangering facor of he euro-sabiliy. While he crediworhiness of he laer counries has a significan impac on he skewness measure (i.e. crash risk) and he sabiliy indicaors, healhier counries equally drive he relaionship beween he crediworhiness and he volailiy as well as he kurosis (i.e. ail risk) of he risk-neural disribuion. The remainder of his paper is srucured as follows: The nex secion oulines he concepual framework. Secion 3 describes he daa and presens some summary saisics. Then, he mehodologies wih respec o he opion pricing aspecs and he regression analyses are explained. Subsequenly, he empirical resuls are oulined and discussed. The las secion conains concluding remarks. 5

7 . A Concepual Framework In his secion, we aemp o provide a concepual explanaion for he channels hrough which he sovereign CDS marke migh impinge on he currency opion marke. We build on he coningen claim balance shee framework of (Gray e al. (007)), which is an adapaion of Meron s coningen claim analysis o he sovereign conex. Under his srucure, he sovereign balance shee in Figure 1, represening a combined balance shee of he governmen and he moneary auhoriy, can be expressed in erms of foreign currency unis (here US Dollar) o analyze he values of asses and liabiliies in an inernaional conex. [Figure 1] Sovereign asses consis of foreign reserves, ne fiscal asses and oher public asses. The iem - guaranees resuls from subracing he guaranees o oo-big-o-fail eniies from boh sides of he balance shee. The value of local currency liabiliies in foreign currency erms,, which comprises local-currency deb and base money, can be viewed as a call opion on sovereign asses (in foreign currency erms),. The srike price for his opion,, is he disress barrier for foreign currency-denominaed deb, which is derived from he ineres paymens and promised paymens on foreign currency deb up o ime T in he fuure. Similar o he Black-Scholes- Meron pricing framework for equiy, his call opion can be expressed as: $ $ ) wih d 1 ln(a = $Sov / B ) + f σ ( r r + 0.5σ ) f $ Sov T d $ Sov T and d ln(a = $Sov / B ) + f σ ( r r 0.5σ ) f $ Sov T d $ Sov T. Where r f and r d are he foreign and local ineres raes, respecively, and σ $Sov is he volailiy of sovereign asses in foreign currency erms. The local currency deb and money are claims on sovereign asses. In principle, governmens can always inflae or dilue local currency deb in case of disress, insead of defauling on foreign currency deb. Therefore, foreign currency deb can be assumed o be more senior compared o local currency deb. In his line of hinking, local 6

8 currency liabiliies can be considered o be similar o equiy issued by firms and muliplied by he exchange rae being he marke cap of he sovereign 4. The wo unknowns ha canno be observed, bu need o be compued are implied sovereign asses, $ and asse volailiyσ $Sov. Asse volailiy σ $Sov can be derived by applying Io s lemma o he pricing formula of he call opion, suggesing a relaionship wih he volailiy of sovereign equiy, $ : $ σ $ $ σ $ ) The local currency liabiliies $, can be direcly compued from he sovereign balance shee daa using acual exchange raes. The volailiy of local currency liabiliies, σ $, is a funcion of he volailiy of he money base and local currency deb, as well as exchange rae volailiy. In case he exchange rae is floaing, exchange rae volailiy is he major par of uncerainy. The model can be implemened similarly o he Meron model, solving he wo equaions wih wo unknown variables. The probabiliy of defaul of he sovereign is given by N(-d). In order o find he model-implied credi spread, we firs need o find he curren value of he risky deb wih promised paymens B f. From he balance shee of he sovereign, he value of risky deb D f can be expressed as he difference beween he asse value, $, and he value of he local currency liabiliies $. Then he yield-o-mauriy of he risky deb is fair value of he credi spread is equal o s = y r f. and he model-implied The sovereign CCA model provides a framework for valuing sovereign foreign-currency deb, local-currency deb, foreign currency value of base money and local-currency deb. However, he CCA model is no only useful for he valuaion of he differen consiuens of a sovereign s capial srucure, bu also for he valuaion of oher claims such as CDS on foreign currency deb. The book-based fair esimaes can be compared wih marke-based spreads of sovereign CDS s and relaive value sraegies can be employed. This makes i possible o benefi from capial 4 One can easily make he analogy beween he value of local currency deb and he value of equiy for a firm. If he marke value of asses a ime is he sum of he marke value of equiy and marke value on deb, hen equiy is modeled as a call opion on he asses wih srike price, which represens he promised deb paymens. 7

9 srucure arbirage sraegies using various insrumens, FX opions and sovereign CDS, in paricular. Similarly o he relaionship beween he volailiy skew implied by equiy opions and CDS spreads, a rade sraegy on he sovereign capial srucure is o rade currency agains he CDS. A fair value CDS spread can be obained from he coningen claims model using currency marke informaion. If currency volailiy is expensive relaive o observed CDS spreads, resuling in a fair value CDS spread being oo high compared o he observed spread, a sraegy is o sell currency volailiy (e.g. a sraddle) and o buy proecion. If volailiy declines or spreads widen he sraegy earns money. Anoher sraegy, if currency volailiy is cheap relaive o he observed CDS spreads, he sraegy is o buy currency volailiy and o sell proecion. If volailiy increases or spreads decline he sraegy earns money. Many differen sovereign capial srucure arbirage rading sraegies are possible using a variey of insrumens, including FX spo and forwards, FX opions, local-currency deb, foreign-currency deb, CDS on foreign-currency deb, and inflaion or indexed deb. These sraegies are reasonable because exchange raes (which affec he value of local currency liabiliies) end o co-move wih he credi spreads of foreign currency deb. As a resul, sovereign capial srucure arbirage also ensures ha relevan informaion from he sovereign CDS marke is ransmied ino he currency opions marke. For example, if he sovereign CDS spread increases, he fair value modelimplied spreads appears o be cheap or he foreign currency appears o be undervalued, he sraegy is o buy a pu on he local currency and o sell proecion. If he local currency subsequenly depreciaes he sraegy earns money. In he European conex, i suggess, ha relevan informaion regarding sovereign disress risk migh affec he sabiliy of he Euro. However, one migh argue ha here are several reasons why he sovereign CCA model is no applicable o European counries. Firs, counries have direc access o large and liquid markes o issue deb in heir domesic currency and ha is why European counries have only a relaively small amoun of foreign currency deb. Moreover, counries from he Economic and Moneary Union (EMU) have only limied conrol over he money supply of he European Cenral Bank (ECB) and, herefore, he analogy beween local currency liabiliies and equiy is no complee. However, counries like Greece are indebed in erms of a currency (he euro) ha hey canno prin on demand. This makes heir local currency deb similar o foreign currency deb. Furhermore, he recen inervenions of he European Cenral Bank give rise o he 8

10 percepion ha he member counries joinly ook over some conrol over he money supply. As a resul, deb of he member counries can be parly considered o be senior deb, equivalen o foreign currency deb, and parly o be junior deb, equivalen o local currency deb. This suggess ha he CCA framework can be used as an ad-hoc model for relaive value sraegies like sovereign capial srucure arbirage. 3. Daa & Summary Saisics Daa We collec daa on daily 5-year sovereign CDS spreads for 11 counries: Belgium, France, Germany, Neherlands, Ausria, Finland, Greece, Spain, Ialy, Ireland, Porugal. The source used o obain he sovereign CDS quoes is Bloomberg s CMAT poral. In addiion, we obain a complee cross-secion of daily over-he-couner dollar/euro opion prices ogeher wih he underlying spo exchange raes, as well as ineres raes for Europe and he US hrough Thomson Reuers Tick Hisory sysem. Our daa sample covers he period from Sepember 10 h 007 o January 31 s Our daa underwen a rigorous cleaning process in order o obain he final daase. Currency opion prices We obain OTC European ype dollar/euro opion prices quoed in implied volailiies a fixed mauriies. We used he 1, 3, 6 and 9 monhs mauriy opions, because hey are he mos frequenly raded ones. The opion quoes are in erms of implied volailiies for paricular pu and call delas caegories, which is a common indusry pracice. The differen dela caegories cover he complee moneyness range of he currency opions, e.g ou-of-he-money calls and pus a dela and a-he-money-opions a 50-dela. Using he available dela- and mauriy caegories of all opion conracs, on each day, we fi a funcional form o he observed implied volailiies of he opions, which allows us o obain implied volailiies for every possible dela-mauriy combinaion. Tha allows us o calculae call and pu opion prices 5 However, we had o reduce he sample period for he regression analysis due o lack of reliable sovereign CDS daa for cerain counries before Sepember 5 h 008. Noneheless, our sample period sill covers he subprime and he sovereign deb crises. 9

11 hrough he Black-Scholes model. Thereafer, on a daily frequency, we are able o derive he momens of he risk-neural disribuion of he dollar-euro exchange rae opions. Sovereign CDS spread The sovereign credi defaul swaps, expressed in basis poins, are raded a various mauriies of up o 30 years. We rerieve he 5-years mauriy quoes for he 11 euro-area counries in he analysis since hey are he mos liquid. Summary Saisics Table 1 porrays he summary saisics of individual counries CDS spreads. We repor summary saisics for he subprime crisis period and he sovereign deb crisis period separaely. In line wih previous research (Hui and Chung (011)), we assume ha Ocober 14 h 009 was he onse of he European sovereign deb crisis. Therefore, he subprime crisis covers he period from Sepember 5 h 008 unil Ocober 13 h 009. The period saring on Ocober 14 h 009 and ending a January 31 s 01 represens he sovereign deb crisis period. [Table 1] Panel A shows he overall saisics for he full sample and reveals he obvious difference in he crediworhiness of he Euro member counries. Based on he CDS daa, one migh wan o characerize cerain counries as healhy counries wih sable economic condiions and vulnerable counries wih fragile economic condiions. Following his logic, France, Germany, Neherlands, Finland and Ausria would belong o he group of healhy counries. In conras, Ireland, Spain, Porugal, Greece and Ialy would belong o he group vulnerable counry. We leave Belgium due o is poliical insabiliy unclassified, while is CDS spread would sugges ha i could be included in one of he groups. Panel B and Panel C allow us o compare he CDS spreads during he subprime crisis period and during he sovereign deb crisis. The summary saisics reveal subsanial differences in he CDS spreads across counries. These differences are in paricular pronounced during he sovereign deb crisis. While he average CDS spreads for he healhy counries shows only a sligh increase during he subprime crisis, he increase in 10

12 spreads was subsanial for he vulnerable counries. As shown by panel C, he average value is 39bps for Finland and 1359 bps for Greece. Tables and 3 repor summary saisics of he dollar-euro opion prices quoed in erms of 10- dela and 5-dela implied-volailiies of calls and pus. The a-he-money opions saisics are only repored once ogeher wih he pu saisics. Summary saisics are presened for four differen mauriies. The saisics are compued over a sample period covering he subprime- and sovereign deb crisis period, ranging from Sepember 5 h 008 unil January 31 s 01. Overall, he implied volailiies for calls and pus increase wih mauriy and hey are on average higher during he sub-prime crisis. [Table and 3] Figure shows he dollar-euro opion smile on February 14 h 01 for mauriies of up o 9 monhs. The graph nicely characerizes he exreme shape of he smile, which characerizes he European sovereign deb crisis period. The smirk-ype shape, ypically observed for equiy opions, refers o he negaive skewness in he risk-neural disribuion of he dollar-euro exchange rae and, herefore, proxies he crash risk of he euro. [Figure ] 4. Mehodology I is indusry pracice o quoe currency opions in erms of implied volailiies a paricular delas. The Black-Scholes delas of European-syle call and pu opions are given by r q T qt ln( Se / K) + 0. σ T dela = e N C σ T (1) r q T qt ln( Se / K) + 0. σ T dela = e N P 1 5 σ T () 11

13 where S is he dollar-euro exchange rae, K is he exercise, σ is he implied volailiy of he opion, r and q are he US and European risk-free ineres raes corresponding o he ime o mauriy (T) of he opion and N(.) is he cumulaive normal disribuion. Esimaing he implied volailiy surface For he empirical analysis, we firs use a modificaion of he prominen ad-hoc Black-Scholes model of Dumas, Fleming and Whaley (1998) o esimae he implied volailiy surface of our currency opions. We use all available informaion conen in currency opion prices for differen moneyness (delas) and differen mauriies. The aim is o consruc a ime series of sandardized measures (e.g. risk neural volailiy, skewness and kurosis) ha characerize he cross-secion of prices and can be compared over ime. Raher han averaging he wo conracs ha are closes o a-he-money or closes o one monh mauriy, we fi he modified ad-hoc Black-Scholes model o all opion conracs on a given day and subsequenly obain he desired funcional form of he implied volailiy surface. This sraegy successfully eliminaes some of he noise from he daa (see Chrisoffersen e al. (010)). We allow each opion o have is own Black-Scholes implied volailiy depending on he opions dela and ime o mauriy T. We use he following funcional form for he opions implied volailiy: IV i, j = α 0 + α1dela C + α i j dela C + α T i j 3 j + α 4T,, j + α 5dela C i, j T j, (3) where IV ij denoes he observed implied volailiy and dela C,i,j, he dela of a call opion for he i- h moneyness and j-h mauriy, defined in Equaion (1) 6. T j denoes he ime o mauriy of an opion for he j-h mauriy. I is common pracice o esimae he parameers using sandard OLS. For every call opion dela (or pu opion dela) and mauriy, we can compue he implied volailiy and derive opion prices using he Black-Scholes model. For example, he implied volailiy for an a-he-money shor erm call opion wih hree monh mauriy can be derived by seing dela equal o 0.5 and ime o mauriy T equal o 3/1. Calculaing he momens of he risk-neural disribuion 6 For pu opions, we use he corresponding call dela in he implied volailiy regression. 1

14 Having characerized he implied volailiy surface of he dollar-euro exchange rae opions, we calibrae he momens of he resuling risk-neural disribuion. Bakshi e al. (003) derive a model-free measure of risk-neural variance, skewness and kurosis based on all opions over he complee moneyness range for a paricular ime o mauriy T. Variance, skewness and kurosis of he T-monh risk-neural disribuion can be compued by where rt Variance ( T ) = e V( T ) µ e Skewness ( T ) = e Kurosis ( T ) = rt rt W( T ) 3µ ( T ) e X( T ) 4µ ( T ) e rt V( T ) + µ ( T ) 3 rt [ e V( T ) µ ( T ) ] rt W( T ) + 6e rt rt [ e V ( T ) ( T ) ] µ 3 µ ( T ) V( T ) 3µ ( T ) 4 (4) rt rt rt rt e e e µ ( T ) = e 1 V( T ) W( T ) X( T ) 6 4 V ( T ) = S qt (1 ln( K / S K )) c ( T, K) dk + (1 + ln( S qt qt qt S 0 qt 6 ln( K / S )) 3 W ( T ) = qt S K 6 ln( S / K)) 3 ln( qt qt S 0 1 ln( K / S qt X ( T ) = qt S K K qt ( ln( K / S )) qt ( S / K) ) )) 4 K qt ( ln( K / S )) qt ( ln( S / K) ) / K)) p ( T, K) dk c ( T, K ) dk p ( T, K) dk 3 c ( T, K ) dk qt qt S 1 ln( S / K)) 4 + p ( T, K) dk. 0 K 3 (5) The parameers correspond o he ones used in Equaion (1) and (). c and p refer o call and pu prices. Again, raher han averaging he observed implied volailiies of all conracs ha are closes o one paricular mauriy (e.g. 3 monh), we derive he Bakshi e al. (003) risk-neural 13

15 momens using he esimaed implied volailiy surface and he corresponding call and pu prices. In he empirical analysis, we focus on he 3 monhs horizon and calculae he momens of he 3- monhs risk-neural disribuion. Regression analysis The firs sep in our analysis is o regress daily changes in credi defaul spreads of counry i on conemporaneous and lagged changes in he various momens ha we use o characerize he risk-neural disribuion as well as on lagged changes in credi defaul spreads in order o exrac he residual componen, hence, we esimae he following equaions 7 CDS 5 5 Vol Vol Vol CDSVol, i, = ω i + υ i, k Vol k + ψ i, k CDS i, k + εi, k= 0 k= 1 (6a) CDS CDS 5 5 Skew Skew Skew CDS, Skew i, = ω i + υ i, k Skew k+ ψ i, k CDS i, k + εi, k= 0 k= Kur Kur Kur CDS, Kur i, = ω i + υ i, k Kur k+ ψ i, k CDS i, k + εi, k= 0 k= 1 (6b) (6c) We do his for up o five lags o absorb any conemporaneous informaion ransmission and any lagged informaion ransmission. In his way, we are able o idenify he informaion arriving in he CDS marke, which is no based on informaion ha has been revealed in he dollar-euro opions marke. The resuling residuals ε can be inerpreed as innovaions in he CDS marke relaive o he risk-neural momens ha characerize he marke condiions in he currency opions marke. Subsequenly, for each counry i, we run a regression of changes in he momens of he riskneural disribuions on lagged innovaions in he CDS marke and lagged changes in he variable iself, hence, we esimae Vol 5 Vol 5 CDS, Vol Vol Vol i k Vol = τ i + λ i, kε i, k + θ, Vol k + µ i, k = 1 k = 1 (7a) 7 We use log-changes for CDSs and simple changes for he oher variables, which allow us o compare he resuls across counries. 14

16 Skew 5 Skew 5 CDS, Skew Skew Skew i k Skew = τ i + λ i, kε i, k + θ, S kew k + µ i, (7b) k = 1 k= 1 Skew 5 Kur 5 CDS, Kur Kur Skew i k Skew = τ i + λ i, kε i, k + θ, Kur k + µ i, k = 1 k = 1 (7c) For each of he risk-neural momens, we examine β Vol i = 5 k = 1 λ Vol i, k, β Skew i = 5 k = 1 λ Skew i, k and 5 Kur β Kur i = λ i, k as measures of impac of counries i credi risk on he risk-neural momens k = 1 of he dollar-euro exchange rae and, herefore, on he sabiliy of he euro. A moivaion and deailed discussion of he usefulness of his approach for esing ransmission effecs can be found in Acharya and Johnson (007) and Bernd and Osrovnaya (008). 5. Empirical resuls Figure 3 shows he annualized volailiy of he daily 3-monh risk neural disribuion ogeher wih he dollar-euro exchange rae over he period from Sepember 10 h 007 o January 31 s 01. Figure 4 shows he daily risk-neural skewness and kurosis of 3 monh opions calculaed according o Bakshi e al. (003). Ineresingly, during he subprime crisis, he skewness is mainly posiive and urns negaive during he subsequen European sovereign deb crisis, wih a urning poin in Ocober 009, ypically found o be he sar of he sovereign deb crisis. Kurosis was much higher and more volaile during he subprime crisis and reaches is peak in December 008. [Figure 3 and 4] Clearly, our risk neural skewness measure is able o disinguish beween urbulen imes. During he subprime crisis, our measure is posiive reflecing a possible depreciaion (crash risk) of he Dollar. Towards mid-ocober 009, he skewness measure urns negaive, suggesing a change in he marke expecaions of he euro vis-à-vis he dollar. Tha is, markes expec he euro o depreciae, which ranslaes ino buying pu opions of he dollar-euro exchange rae. The lower kurosis exhibied during he sovereign deb crisis is synonymous o hinner ails of he risk- 15

17 neural disribuion of he dollar-euro exchange rae. Therefore, he ail risk of he wo currencies seems o be priced in he US. The subprime crisis saring wih he burs of he housing bubble in he US had a major impac on he US economy. Figure shows ha during he subprime crisis, no only he volailiy of he dollar-euro exchange rae subsanially increased, bu he kurosis of he risk-neural disribuion, our proxy for ail risk, increased as well. However, during he sovereign deb crisis period he volailiy increased, bu he ail risk of he wo currencies is relaively sable a a low level. [Table 4] Summary saisics of he dollar-euro exchange rae and he risk-neural momens are displayed in Table 4. The skewness measure is posiive over he sub-prime crisis (0.47) bu becomes negaive during he sovereign deb crisis (-0.37) reflecing concerns of marke paricipans abou he sabiliy of he euro. Wih respec o he kurosis measure, he lower kurosis exhibied during he sovereign deb crisis (5 versus 8 in he prior period) is synonymous o hinner ails of he risk-neural disribuion of he dollar-euro exchange rae and, herefore, lower ail risk. Table 5 summaries our regression analysis resuls. The repored beas refer o he sum of regression coefficiens based on equaions (7a) (7c) and can be inerpreed as a measures of impac of counries i credi risk on he risk-neural momens of he dollar-euro exchange rae and, herefore, on he sabiliy of he euro. For he complee sample period, he resuls sugges ha member counries crediworhiness affecs he volailiy of he dollar-euro exchange rae. An increase in he CDS spreads, indicaing worsening credi condiions, has a posiive impac on he volailiy of he exchange rae. However, he resuls for skewness and kurosis are ypically insignifican. Once we separae he period ino a subprime crisis period and a sovereign deb crisis period, we observe significan differences over ime. Looking a he subprime crisis period, our esimaes have no saisical significance. The inerpreaion is ha he credi risk of he euroarea member counries as measured by heir CDS spreads does no affec he sabiliy of he euro induced hrough he skewness (Skew) and kurosis (Kur) of he risk-neural disribuion of he dollar-euro exchange rae ogeher wih he risk-neural volailiy. In conras, he resuls during he sovereign deb crisis period are quie pronounced. An increase in member counries credi risk resuls in an increased risk-neural volailiy of he dollar-euro exchange rae along wih 16

18 soaring ail risk induced hrough he risk-neural kurosis. Furhermore, he impac for healhy counries is significanly no differen o he impac for vulnerable counries. As resul, boh vulnerable and healhy counries have an impac on he sabiliy of he euro in he way ha higher levels of volailiy are accompanied by lower levels of he exchange rae, and in urn, a weaker euro. However, we find ha member counries credi risk is a major deerminan of he euro crash risk as measured by he risk-neural skewness. Overall, he relaionship is negaive, suggesing ha an increase in counries credi risk has a negaive impac on he sabiliy of he euro. [Table 5] Wih respec o he skewness measure, we find saisical significance only among counries belonging o he vulnerable group, namely: Ireland, Spain, Porugal and Ialy. These coefficiens are subsanially negaive, which enails ha he sruggling counries drive he euro crash risk. I can be shown ha he beas for he healhy counries and he ones of he vulnerable counries are significanly differen form each oher a he 1% level. Addiionally, we performed a principal componen analysis on he CDS spreads changes of he healhy counries vis à vis he vulnerable counries. PCA H refers o he firs principal componen of he firs group and PCA V refers o he firs principal componen of he second group. Resuls presened in Table 5 confirm previous findings and sugges ha during he sovereign deb crisis period only he sruggling counries drive he euro crash risk. Conrary o wha one would expec, he crediworhiness of Greece does no seem o play a looming role in he sabiliy of he common currency. This reflecs he fac ha currency opion markes do no perceive he credi risk of Greece as a major deerminan or risk facor for he sabiliy of he euro. I is ineresing o confron hese findings wih figures published by he Bank for Inernaional Selemens (BIS). On a regular basis BIS publishes cross-border claims of BIS reporing European banks. The Eurozone member counries are inerlinked hroughou he foreign claims heir naional banks hold. Given his exposure, a defaul of one counry would cause a spread of he crisis o he res of he member counries. The speed and magniude of hose conagious 17

19 effecs depend on he amoun of deb he defauling counry owes o he res of Eurozone counries as well he way i is conneced o heir respecive banks. Pu anoher way, he higher he foreign exposure of a given counry o he banks of oher Eurozone counries, he sronger he poenial conagion effecs. Looking a he BIS figures for he hird quarer of 009, he onse of he sovereign deb crisis, he daa sugges ha oher vulnerable counries like Ireland, Porugal, Spain and Ialy accoun for nearly 16% of foreign claims in European banks 8, while Greece only accouns for a bi more han 1%. Ineresingly, we find ha he crediworhiness of counries like Ireland, Porugal, Spain and Ialy have an impac on he sabiliy of he euro, while he resuls for Greece are insignifican. Addiionally, Figure 5 illusraes he Eurozone deb srucure as of he end of June 011. [Figure 5] Each cycle represens he foreign exposure of a given Eurozone counry o oher member counries as well as is exposure o major economies. The figure shows how a counry would influence he res in he even of a defaul. The counries of ineres are: Greece, Spain, Porugal, Ialy and Ireland. Wih n euro of gross foreign deb, Ialy has he highes exposure owards naional banks of he Eurozone counries, and hose of he U.S, Japan, and he UK. Spain comes second wih 1.9n, followed by Ireland 1.7n and finally Porugal and Greece a he same indebedness level of 0.4 n. Given hese amouns and he inerlinkages of each counry wih naional banks of he oher counries, he crediworhiness of Ialy, Ireland and Spain seem o be he main sources of worry regarding he common currency, which is in line wih our empirical resuls. French and German banks ogeher hold 49bn, 43.7bn, 105,8 bn of Ialian, of Spanish and Irish deb respecively, whereas hey only hold 57.3 of Greek claims. This lends furher credence o our resuls which do no display significance for Greece. In he case of defaul, France and Germany would be in posiion o absorb he shock more easily han if Ialy, Spain or Ireland were o defaul. Furhermore, while Porugal and Greece have similar levels of deb, 8 European banks refer o domesically owned banks of Ausria, Belgium, Finland, France, Germany, Greece, Ireland, Ialy, he Neherlands, Norway, Porugal, Spain, Sweden, Swizerland, Turkey, and he UK. 18

20 Porugal proves more unseling because i is more inimaely linked o anoher sruggling counry like Spain. A new indicaor for currency sabiliy In he following, we combine he hree risk neural momens ino one aggregaed risk indicaor ha characerizes he complee risk-neural disribuion. This allows us o derive one single marke-based indicaor ha measures currency sabiliy from he cross-secion of exchange rae opions. During he sovereign deb crisis period, his indicaor would measure he euro insabiliy. However, he comovemens of hese hree momens are supposed o have a nonlinear impac on he risk-neural disribuion as a whole. Some popular risk measures in risk managemen, such as Value a Risk (VaR) and Expeced Shorfall (ES) consruced from his risk-neural disribuion are expeced o be a good indicaor of he euro sabiliy. The Gram- Charlier and Cornish-Fisher expansions are ools ofen used o compue VaR and ES in he conex of skewed and lepokuric reurn disribuions. These approximaions use he higher momens of he unknown arge disribuion o compue an approximae disribuion and quanile funcions. Simonao (011) compare hese mehods wih he Johnson Sysem of disribuions which also uses he momens as main inpus bu is capable of accommodaing all possible skewness and kurosis. In his sudy, we consider an alernaive approach based on he Pearson Sysem (Pearson (1895)), which can be used o model a wide scale of disribuions wih various skewness and kurosis. The Pearson Sysem is a family of probabiliy densiy disribuions which includes a unique disribuion corresponding o every valid combinaion of he momens of a disribuion. I is possible o find he disribuion in he Pearson sysem ha precisely maches he momens of he risk-neural disribuion and o generae a random sample. We calculae he VaR and ES for boh lower ail and upper ail a he 1%-quanile from he generaed random samples. We consruc wo euro sabiliy indicaors by relaing he upper ail of he risk-neural disribuion o he lower ail, e.g. he absolue VaR of he upper 1%-quanile divided by he absolue VaR of he lower 1%-quanile. Clearly, hese indicaors nicely summarize he imbalances of exreme values of he risk-neural disribuion overall and can be considered o reflec currency sabiliy. For example, a raio below one indicaes a faer lef ail of he 19

21 disribuion compared o he righ ail and, herefore, suggess euro insabiliy. Figure 5 shows he sabiliy indicaors for he complee period. [Figure 5] We replicae he -sep regression analysis oulined in Equaions (6) and (7) by replacing e.g. he skewness measure by he differen sabiliy indicaors. The resuling beas are shown in Table 6. VaR raio refers o he indicaor based on he Value-a-Risks measure and ES raio refers o he indicaor based on he expeced shorfall measure. [Table 6] The resuls sugges ha our previous findings are robus o a change of measure for euro sabiliy. Mos of he coefficiens are insignifican excep he ones for he sovereign deb crisis sub sample. During ha period, all coefficiens are subsanially negaive, which enails ha member counries credi risk have a negaive impac on he sabiliy of he euro. Bu again, during he sovereign deb crisis period he sruggling counries drive he insabiliy of he common currency. I can be shown ha he beas for he healhy counries and he ones of he vulnerable counries are significanly differen form each oher a he 5% level for boh indicaors. The principal componen analysis again suppors hose conjecures. In line wih previous findings and conrary o wha one would expec, he crediworhiness of Greece does no seem o affec he sabiliy of he common currency significanly. 6. Conclusions In his paper, he recen Eurozone sovereign deb crisis is viewed hrough he win lenses of sovereign credi swaps and currency opion markes. We empirically invesigae he impac of 0

22 he credi risk of Eurozone member counries on he sabiliy of he Euro. The credi risk of a counry can be measured hrough is sovereign credi defaul swap (CDS). Marke prices of CDS spreads reflec he percepion of financial markes abou he economic-poliical sabiliy of a counry, and hus abou he crediworhiness of a given sovereign. The sabiliy of he euro is examined by decomposing dollar-euro exchange rae opions ino he momens of he risk-neural disribuion. We documen ha changes in he crediworhiness of a member counry on one day have a significan impac on he sabiliy of he euro on he following day. On he one hand, an increase in member counries credi risk resuls in an increase of he volailiy of he dollar-euro exchange rae along wih soaring ail risk induced hrough he risk-neural kurosis. On he oher hand, we find ha member counries credi risk is a major deerminan of he euro crash risk as measured by he risk-neural skewness. We propose a new indicaor for currency sabiliy by combining he risk-neural momens ino an aggregaed risk measure and show ha our resuls are robus o his change in measure. In line wih previous research, hese findings apply o he period of he sovereign deb crisis bu no necessarily o he subprime crisis period. Noiceable is he fac he crediworhiness of counries wih vulnerable fiscal posiions is he main, bu no he only risk-endangering facor of he euro-sabiliy. While he crediworhiness of he laer counries has a significan impac on he skewness measure (i.e crash risk) and he sabiliy indicaors, healhier counries equally drive he relaionship beween he crediworhiness and he kurosis (i.e ail risk). As one would expec, Ireland, Porugal, Spain and Ialy play a prominen role. However, his does no seem o be he case for Greece, which can be parly explained by he only marginal foreign exposure of European banks o Greece. 1

23 References Acharya, V., Johnson, T., 007, Insider rading in credi derivaives, Journal of Financial Economics 84 (1), Afonso, A., Fureci, D., Gomes, P., 011. Sovereign credi raings and financial markes linkages: applicaion o European daa, ECB Working Paper Series No Azerki, R., Candelon, B., Sy, A.-N.R., 011, Sovereign raing News and Financial Markes Spillovers: Evidence from he European deb crisis, Inernaional Moneary Fund WP/11/68. Bakshi, G., Kapadia, N. Madan, D., 003, Sock Reurn Characerisics, Skew Laws, and Differenial Pricing of Individual Equiy Opions, Review of Financial Sudies 16, Bams, D., Lehner, T., Wolff, C., 009. Loss Funcions in Opion Valuaion: A Framework for Selecion. Managemen Science 55 (5), Bernd, A., Osrovnaya, A., (008). Do equiy markes favour credi marke news over opions marke news? Carnegie Mellon Universiy. Working Paper. Brunnermeier, M.K., Nagel, S., Pedersen, L.H., 009. Carry rades and currency crashes, NBER Macroeconomics Annual 008. Burnside, C., Eichenbaum, M., Kleshchelski, I., Rebelo, S., 011, Do peso problems explain he reurns o he cary rade?, Review of financial Sudies 4 (3), Calice, G., Chen, J., Williams, J.,011. Liquidiy spillovers in sovereign bond and CDS markes: An analysis of he Eurozone sovereign deb crisis.working Paper. Cao, C., Yu, F., Zhong, Z., 01. The informaion conen of opion-implied volailiy for credi defaul swap valuaion, Journal of Financial Markes 13(3), Carr, P., Wu, L., 007. Theory and evidence on he dynamic ineracions beween sovereign credi defaul swaps and currency opions, Journal of Banking and Finance 31 (8), Chrisoffersen, P., Heson, S., Jacobs, K., 010. Opion Anomalies and he Pricing Kernel. Working Paper. Cochrane, J.H., 005, Asse Pricing, Princeon Universiy Press, New Jersey.

24 Dumas, B., Fleming J., Whaley, R.E., 1998, Implied Volailiy Funcions: Empirical Tess, The Journal of Finance 53, Eichengreen, B., Rose, A.K., Wyplosz, C., Exchange marke mayhem: he anecedens and afermah of speculaive aacks, Economic Policy 1, Fahri, E., Fraiberger, S.P., Gabaix, X., Ranciere, R., Verdlhan, A., 009. Crash Risk in Currency Markes, Working Paper 1506, NBER. Frankel, J., Rose, A., Currency crashes in emerging markes: am empirical reamen, Journal of Inernaional Economics 41 (3-4), Jurek, J.W., 009. Crash-neural currency rades, Working Paper, Princeon Universiy. Hui, C.-H, Chung, T.-H., 011. Crash Risk of he Euro in he Sovereign Deb Crisis of , Journal of Banking and Finance 35: Hui, C.-H, Fong T., 011, Informaion flow beween sovereign CDS and Dollar-Yen currency opion markes in he sovereign deb crisis of , HKIMR Working Paper No.40/011. Kaminsky, G., Lizondo, S., Reinhar, C.M., Leading indicaors of currency crises, Inernaional Moneary Fund Saff Papers 45, 1-48 Neumann M. and G. Skiadopoulos, 01. Predicable Dynamics in Higher Order Risk-Neural Momens: Evidence from he S&P 500 Opions, forhcoming: Journal of Financial and Quaniaive Analysis. Pan, J., Singleon, K.J., 008. Defaul and recovery implici in he erm srucure of sovereign CDS spreads, Journal of Finance 63 (5), Pearson, K. (1895) Conribuions o he Mahemaical Theory of Evoluion. II. Skew Variaion in Homogeneous Maerial, Philosophical Transacions of he Royal Sociey A, 186, Simonao, Jean-Guy (011), The Performance of Johnson Disribuions for Compuing Value a Risk and Expeced Shorfall, Journal of Derivaives. Wolff, C., 1987, Forward Foreign Exchange Raes, Expeced Spo Raes and Premia: A Signal- Exracion Approach, Journal of Finance, Vol. 4, no., pp

25 Figure 1. The sovereign balance shee Asses Liabiliies Foreign Reserves Ne Fiscal Asse Oher Public Asses - Guaranees Foreign-currency Deb Local-Currency Deb Base Money Defaul-free value of deb minus pu opion Call opion 4

26 Figure. Dollar-euro opion smile on February 14 h 01 for various mauriies (Source: websie) 5

27 Figure 3. Dollar-euro exchange rae and annualized volailiy of he 3-monhs risk-neural disribuion of opions on he dollar-euro exchange rae Sep-07 Nov-07 Jan-08 Mar-08 May-08 Jul-08 Sep-08 Nov-08 Jan-09 Mar-09 May-09 Jul-09 Sep-09 Nov-09 Jan-10 Mar-10 May-10 Jul-10 Sep-10 Nov-10 Jan-11 Mar-11 May-11 Jul-11 Sep-11 Nov-11 Jan-1 1. Volailiy $/ (righ axis) 6

28 Figure 4. Skewness and kurosis of he 3-monhs risk-neural disribuion of opions on he dollar-euro exchange rae Sep-07 Nov-07 Jan-08 Mar-08 May-08 Jul-08 Sep-08 Nov-08 Jan-09 Mar-09 May-09 Jul-09 Sep-09 Nov-09 Jan-10 Mar-10 May-10 Jul-10 Sep-10 Nov-10 Jan-11 Mar-11 May-11 Jul-11 Sep-11 Nov-11 Jan Skewness Kurosis (righ axis) 7

29 Figure 5. BBC Eurozone deb web: Who owes wha o whom? The circles below summarize daa from he Bank for Inernaional Selemens and show he gross exernal, or foreign, deb of some of he main players in he eurozone as well as oher big world economies. The arrows poin from he debor o he credior and are proporional o he money owed as of he end of June 011. The exposures, represened by he proporional arrows, shows wha banks in one counry are owed by debors - boh governmen and privae - in anoher counry. (Source: BBC websie, hp:// Greece Spain Porugal Ialy Ireland 8

30 Figure 5. Euro sabiliy indicaors Euro sabiliy indicaors based on he 3-monhs risk-neural disribuion of opions on he dollar-euro exchange rae. VaR raio refers o he indicaor based on he Value-a-Risks measure and ES raio refers o he indicaor based on he expeced shorfall measure /10/007 1/8/008 5/7/008 9/4/008 1//009 5//009 8/30/009 1/8/009 4/7/010 8/5/010 1/3/010 4//011 8/0/011 1/18/011 VaR raio ES raio 9

31 Table 1 : Summary Saisics: CDS spreads per counry BE FR DE NL FL A IR ES PT GR IT Overall sample period from 05/09/008 o 31/01/01 Mean Median Maximum Minimum Sd.Dev Skewness Kurosis Q Q Subprime crisis from 05/09/008 o 13/10/009 Mean Median Maximum Minimum Sd.Dev Skewness Kurosis Q Q Sovereign deb crisis from 14/10/009 o 31/01/01 Mean Median Maximum Minimum Sd.Dev Skewness Kurosis Q Q Noe: Enries correspond o Q1 (firs quanile), Q3 (hird quanile), BE (Belgium), FR (France), DE (Germany), NL (Neherlands), FL (Finland), A (Ausria), IR (Ireland), ES (Spain), PT (Porugal), GR (Greece), IT(Ialy). Saisics are compued based on daily daa and are expressed in basis poins excep for Skewness and Kurosis. The oal number of observaions is 88 for he whole sample period, 88 for he firs sub-period and 594 for he second. 30