An Analysis of the Determinants of the itraxx CDS Spreads. using the Skewed Student s t AR-GARCH Model
|
|
- Caroline Barnett
- 6 years ago
- Views:
Transcription
1 An Analysis of he Deerminans of he itraxx CDS Spreads using he Skewed Suden s AR-GARCH Model Yuan-Sung Chu * Nick Consaninou John O Hara Absrac This paper examines he volailiy clusering behaviour beween he changes in he itraxx 5-year Europe Credi Defaul Swap (CDS) index and is heoreical deerminans using he AR-GARCH model wih he skewed suden s disribuion. Financial ime series are known o be condiionally heeroskedasic, fa-ailed, and ofen skewed. I is demonsraed ha he AR-GARCH model wih he skewed suden s marginal densiy funcion provides boh beer in-sample fi and more accurae ou-of-sample forecass han hose based on he symmeric disribued assumpions. Moreover, o es he explanaory power of he heoreical deerminans we perform regression analysis on daa from he pre-crisis ( ) and crisis periods (007-00). We show ha sock reurns and equiy volailiy have saisically significan explanaory power on he itraxx CDS index during each period, while he risk-free ineres rae has no saisically significan effec on he itraxx CDS index during he crisis period. JEL: G0, G7, C, C46 Keywords: itraxx; CDS; Credi defaul swap; AR-GARCH; Skewed Suden s. Inroducion The credi derivaives marke has grown rapidly over he las five years. A credi defaul swap (CDS), one of he mos imporan credi derivaives, is creaed o help banking and non-banking insiuions efficienly diversify credi exposure. Principally, CDSs can be classified ino wo ypes: single-name and muli-name conracs. Single-name CDSs involve only one underlying eniy whereas muli-name CDSs (e.g. CDS indices) comprise of a se of underlying eniies in a porfolio pool. Our work focuses on CDS indices ha are more efficien and liquid han holding a group of * Cenre for Compuaional Finance and Economic Agens (CCFEA), Universiy of Essex, Wivenhoe Park, Colcheser CO4 3SQ, UK. ychud@essex.ac.uk Essex Business School, Universiy of Essex, Wivenhoe Park, Colcheser CO4 3SQ, UK. ncons@essex.ac.uk. Cenre for Compuaional Finance and Economic Agens (CCFEA), Universiy of Essex, Wivenhoe Park, Colcheser CO4 3SQ, UK. johara@essex.ac.uk
2 single-name CDS conracs as hey allow invesors o shor or long he indices in order o adjus heir credi risk exposure. The Dow Jones itraxx family, one of he mos liquid families of CDS indices, includes global companies wih he excepion of hose based in Norh America. The mos widely raded CDS index of he Dow Jones itraxx family is he Dow Jones itraxx Europe index, a porfolio made up of he 5 mos liquid invesmen grade European companies in accordance wih CDS volume raded. Each company has equally weighed credi exposure (noional principal). Undersanding he relaionship beween CDS spreads and is heoreical deerminans has become an imporan issue. There are wo pricing models for CDSs, srucural form and reduced form models, of which our work focuses on he former o invesigae he deerminans of he mos liquid itraxx Europe 5-year CDS index spreads. Srucural form models (or firm s value models) originaed from he opion pricing heory of Black and Scholes (973), and were firs formulaed by Meron (974), and subsequenly exended by researchers such as Black and Cox (976), Geske (977), Leland and Tof (996), Zhou (00), Collin-Dufresne e al.(00), and amongs ohers. The core concep of a srucural form models is ha an obligor defauls when he asse value of a company his a specific hreshold level. Based on he srucural form models, several earlier empirical sudies have been applied o defaul swap markes. Collin-Dufresne e al.(00), Longsaff e al. (005), and Zhang e al. (006) use linear regression o invesigae he link beween he key economic variables and bond yields. Recenly, work has focused on exending earlier empirical sudies on he itraxx CDS marke since itraxx Europe CDS indices are more liquid han oher relevan credi defaul insrumens. Bysröm (005), he firs sudy exended o muli-name CDS spreads, ess he link beween itraxx spread changes and sock marke using linear regression. This analysis shows ha he itraxx CDS marke ends o be led by he sock marke. Furhermore, he also demonsraes a significanly posiive auocorrelaion in he itraxx marke. Alexander and Kaeck (008) and Ericsson e al. (009) find ha he changes in he CDS spreads are no only significanly affeced by he firm s equiy value, bu also influenced by he equiy volailiy and risk-free ineres raes. They observe ha he higher he equiy volailiy, he higher he firm s value volailiy, resuling in an upward rend in he CDS spread. Moreover, a low risk-free rae increases he defaul probabiliy in he itraxx CDS marke. However, all hese earlier empirical sudies assume he error erm of he linear regression model is normally disribued. Financial ime series are ypified by volailiy clusering behaviour; hence he auoregressive condiional heeroskedasiciy (ARCH) model proposed by Engle (98) and he generalized auoregressive condiional heeroskedasiciy (GARCH) inroduced by Bollerslev (986) are very popular for modelling financial volailiy.
3 These models are also being used o develop a more flexible and robus model o forecas financial ime series in order o provide an explanaion for volailiy clusering and, implicily, heavy-ailedness. However, numerous empirical sudies show ha financial ime series ofen show skewed disribuion condiionally as well as uncondiionally, which implies ha very large changes in reurns occur wih a higher frequency han under he symmerically disribued assumpion. A common assumpion in applying sandard GARCH models o financial ime series is ha he reurn series is condiionally symmerically disribued (i.e. normally or suden s disribued), which are rarely able o accommodae he excess of skewness. In his sudy he AR-GARCH model wih he skewed suden s disribuion proposed by Hansen (994) is implemened o invesigae he volailiy clusering feaure of he itraxx Europe CDS index variaion agains is deerminans. The skewed suden s disribuion involves higher-order feaures of he condiional disribuion, allowing he asymmeric behaviours of he error erm o be capured. The symmeric suden s disribuion can be seen as a special case in which he skewness parameer is se o zero. As more skewness is imposed, he skewed suden s disribuion can be used o describe various combinaions of asymmeric ail behaviours. The res of he paper is organized as follows. In Secion, he heoreical deerminans of CDS spreads are discussed. In Secion 3, he AR-GARCH model wih differen disribued assumpions and economic mehodology of volailiy forecasing performance will be inroduced. In Secion 4, we summarize he empirical analyses and resuls using he AR-GARCH wih differen marginal densiy funcions. Conclusions are presened in Secion 5.. The Theoreical Deerminans of CDS Spreads Theoreically, he main economic deerminans of srucural form pricing models are firm value, equiy volailiy, and he risk-free ineres rae. Numerous srucural form models have been exended from he basic srucural form model suggesed by Meron (974), and all he exended sudies are cenral o hese hree key deerminans. Hence, in his sudy, we use linear regression analysis o invesigae he relaionship beween he itraxx spread changes wih hese hree key variables, raher han including all sysemaic facors suggesed by oher exensive sudies. A decrease in he marke value of underlying eniy resuls in an increase in he defaul probabiliy, since he underlying eniy is approaching he defaul barrier. However, esimaing he value of firm asses and liabiliies is no easy because invesors can no ge all he informaion analogous o ha of he company s managers. Since he changes in he firm s sock price can reflec on he condiion of he firm s 3
4 operaion, we use he Dow Jones Euro STOXX 600 index o represen he performance of he Euro zone equiy marke. The Dow Jones Euro STOXX 600 reflecs he performance of he 600 larges marke capialized companies in he European economic region. The variaion of credi risk premia is an increasing funcion of equiy volailiy, since he likelihood of hiing he defaul barrier will increase while he flucuaion of firm value widens. The equiy volailiy can be esimaed using eiher hisorical daa or implied volailiy based on sock opions. Benker (004) demonsraes ha explaining he variaion in CDS spreads using implied volailiy has a sronger impac han using hisorical volailiy. However, considering he lack of raded opions on some reference eniies of he itraxx Europe CDS index and illiquidiy on some raded opions, he implied volailiy consruced by all available single-name underlying eniies may no reflec all he curren business risk in he European marke. In his sudy, we choose he opion-implied volailiy index, he Dow Jones Euro VSTOXX 50 index, as a proxy of equiy volailiy insead. The Dow Jones Euro VSTOXX 50 index is based on Dow Jones Euro STOXX 50 opions prices, which is designed o reflec near-erm volailiy marke expecaions by deermining he implied volailiy across all underlying equiy opions wih a given ime o mauriy. The heoreical argumens suppor ha he credi defaul spread is inversely relaed o he risk-free ineres rae (see Duffie, 999). The risk-free rae deermines he risk neural drif in firm value, ha is, an increase in he risk-free ineres rae ends o lower he risk-neural defaul probabiliy. Houweling and Vors (005) use he swap rae as a proxy of he risk-free ineres rae and find a sronger impac of he swap rae on he CDS marke han ha of he Treasury rae. Thus, in our approach we use he -year Euro Swap middle raes as a proxy for risk-free raes, which may provide near-erm expecaions on he European economic and credi environmen. 3. Volailiy Modelling and Evoluion of Volailiy Forecass 3. The AR-GARCH Model wih Differen Disribued Assumpions An auoregressive (AR) model is chosen for he condiional mean o allow for possible auocorrelaion in he lagged itraxx index spreads. The condiional mean equaion of a univariae ime series y can be expressed as: y s = Ai y i= i + ε ε = σ z, z ~ N(0,) () () where z is a sequence of independenly idenically disribued random variables, 4
5 σ is condiional variance, and ε denoes he error erm of he ime series. Therefore, he condiional variance equaion of Bollerslev (986) can be expressed as: where ω, α i and q p = + i i i= j= σ ω + α ε β σ, (3) j j q p β j are non-negaive inegers wih α i + i= j= β < o ensure he saisfacion wih he sufficien sable condiion of sricly saionary in he GARCH process. Moreover, p and q are also resriced o be non-negaive inegers. The inabiliy of he symmeric GARCH model o accommodae he excess of skewness in financial series is well-known. The skewed suden s densiy funcion proposed by Hansen (994) has he addiional benefi of including igher-order feaures of he condiional disribuion. Therefore, he skewed suden s densiy funcion, presen in Equaion (4), will be used o accoun for he excess of skewness in his sudy: j g ( ν, λ) b + a bc( + ( ) ) ν λ = b + a bc( + ( ) ) ν + λ ( ν + ) ( ν + ) a < b a b (4) wih a, b, and c defined as: ν a = 4λc( ), ν (5) b = + 3λ a, (6) ν + Γ( ) c =, (7) ν π ( ν ) Γ( ) where ν is he ail index and λ is he skewness parameer, which are used o conrol he differen shape of he densiy funcion and Γ ( ) is he gamma funcion. The wo shape parameers need o be resriced wih ν > and < λ < respecively. If < λ < 0 he densiy funcion skews oward o he righ, conversely if 0 > λ > he densiy funcion skews oward o he lef. Furhermore, he skewed suden s disribuion ransforms o he normal disribuion by seing ν = and λ = 0 and o symmeric suden s disribuions by seing λ = 0. 5
6 3. Evaluaion of Volailiy Forecasing Performance 3.. Loss Funcions A common way o compare differen forecas models is given by he minimizaion of a saisic loss funcion. AR-GARCH models describe he evoluion of he condiional mean and condiional variance. Once he parameers of he AR-GARCH models have been esimaed using in-sample period daa, and condiional variance forecass based on hese esimaes can be generaed over he ou-of-sample period. In order o evaluae he forecas accuracy of various compeing models, saisical loss funcions have o be used o measure forecas errors. Mean squared error (MSE) is he mos commonly used loss funcion, however, he MSE crierion is very sensiive o ouliers. Hence, a more robus loss funcion o possible presence of ouliers, mean absolue error (MAE) is aken ino accoun in his sudy. Moreover, he logarihmic loss (LL) funcion, proposed by Pagan and Schwer(990), penalizes volailiy forecass asymmerically in low volailiy and high volailiy periods, which can be used o deal wih he second shorcoming of he MSE crierion. These hree loss funcions are defined as follows: ( ), T n MSE = h σ (8) n + = T + T n MAE = h σ, (9) n + = T + [ ln( ) ln( )], T n LL = h σ (0) n + = T + where n is he number of forecas daa poins, T is he enire in-sample period, h is forecas condiional variance a ime, and σ is realized condiional variance a ime. 3.. Diebold-Mariano Tes (DM Tes) Diebold and Mariano (995) propose a es o evaluae he accuracy of L-seps ahead forecass of one model in comparison o anoher. The null hypohesis of he es is ha wo compeing models have equal forecas accuracy agains he alernaive hypohesis of significan difference in he accuracy of he wo compeing forecass. The DM es is based on a -es ha E( δ ) = 0 where E ( ) is he expecaion A B A B operaor, δ = l l. l, and l are forecas errors of wo compeing models A and B respecively. The DM es saisic can be expressed as: 6
7 δ DM = () V where δ and V (δ ) is mean and variance of forecas errors over he forecasing period respecively. However, δ can no be assumed o be uncorrelaed. The DM es assumes ha he auocorrelaions of order L or higher are zero of δ, so V (δ ) can be esimaed asympoically as: + L V δ γ 0 γ j () n j= ( δ ) ( ) where δ is serially correlaed for n > and γ j denoes he j-h auocovariance of δ. 4. Empirical Analysis 4. Daa Descripion Our daa se on he mos liquid itraxx 5-year Europe CDS index, he STOXX 600 index, he VSTOXX 50 index, and he -year Euro swap rae consiss of 375 daily observaions; i covers he period from Augus 6, 004 o January 8, 00. Alhough he itraxx 5-year Europe CDS index was launched in June 004, our daa se lacks some rading day observaions on he itraxx CDS index before mid-augus 004. As a resul, we use daa from Augus 6, 004 onward in his sudy. Since he new series of he itraxx Europe CDS index is launched every six monhs in order o adjus he underlying companies, we use he mos curren series daa of he itraxx index a any poin in ime o ensure our analysis is always based on he mos liquid underlying eniies. The daa se on -year Euro Swap rae is obained from Daasream, he daa for he STOXX 600 and he VSTOXX 50 indices are obained from Soxx Ld, and he itraxx CDS index daa is available from Marki Group. 4. Descripive Saisics Before invesigaing he relaionship beween he itraxx CDS index and he explanaory variables, we provide summary saisics for he itraxx CDS index and he key variables. We consider he naural logarihmic reurns of all he ime series. In order o deermine he presence of mean reversion in he logarihm of reurns, he uni roo ess (Augmened Dickey-Fuller es (ADF es)) can be used o verify he behaviour of he ime series. The summary saisics and he uni es resuls are 7
8 presened in Table. The resuls in Table show ha he disribuions of log reurns of he itraxx index and is heoreical deerminans are skewed. Moreover, he itraxx CDS and he VSTOXX 50 indices are more volaile han he STOXX 600 index and he Euro swap rae. The ADF es is run on he level of he log reurns of all indices. One can see from he resuls ha all he null hypoheses under he ADF es can be rejeced a he 5% level. The mean-revering coefficiens in he ADF es is saisically significanly negaive, confirming he saionariy of periodically mean-revering cycles. Table Summary saisics of daily logarihmic reurns itraxx STOXX600 VSTOXX 50 Euro Swap Mean (%) Median (%) Maximum (%) Minimum (%) Sd. Dev. (%) Skewness Kurosis Jarque-Bera Tes * * * * ADF Tes * * * * * denoe significanly a 5% significance level. Figure. The itraxx Europe 5-year index and is deerminans, normalized o sar a itraxx Index Soxx 600 Index Vsoxx Index Euro Swap Rae 0 Aug-04 Feb-05 Aug-05 Feb-06 Aug-06 Feb-07 Aug-07 Feb-08 Aug-08 Feb-09 Aug-09 Bysröm (005, 006), and Alexander and Kaeck (008) poin ou ha he itraxx Europe CDS index exhibis significan auocorrelaion in is previous day s 8
9 changes, resuling in he inefficiency in he European 5-year CDS marke. According o he resuls of he Ljung Box es, Q(0) and Q(30) are and respecively, supporing earlier empirical sudies. In order o deal wih he auocorrelaion problem, he effec of he lagged reurns on previous day s itraxx CDS spread will be included in he nex secion. As seen in Figure, before 6 July 007 he itraxx CDS index demonsraes sable downward rend, and displays posiive correlaion wih he VSTOXX 50 index and negaive correlaion wih he Euro swap rae and he STOXX 600 index. Afer 6 July 007, all key marke variables and he itraxx CDS index flucuaed dramaically. I's worh menioning ha he Euro swap rae seems no o be significanly negaively correlaed o he itraxx index afer 6 July Linear Regression Analysis In his secion, we use he following linear regression (Equaion (3)) o analyze he dependence beween he daily log reurns of he itraxx CDS spreads and daily log reurns of he explanaory variables. ΔCDS = θ + θ ΔS + θ ΔV + θ ΔCDS + θ Δr + ε, (3) The regression will be esed in hree sages: he whole period, he pre-crisis period from Augus o July 5 007, and he crisis period beween July and January 8, 00. Le Δ CDS denoe he logarihmic reurns of he itraxx CDS spreads, Δ V denoe logarihmic reurns of he VSTOXX 50 index, Δ r denoe he logarihmic reurns of he -year Euro swap rae, and Δ S denoe he logarihmic reurns of he STOXX 600 index. The error erm, ε, are i.i.d. random errors wih zero mean and uni variance, and will be assumed o be normally, symmeric suden s and skewed suden s disribued respecively. The regression resuls are given in Table. All he explanaory variables are saisically significan a he 5% level in he main and wo sub-period regressions excep for he Euro swap rae during he crisis period. Bysröm (005, 006) and Alexander and Kaeck (008) discover significan predicive abiliy for lagged daily itraxx spread changes by using previous day s itraxx spreads, he resuls in Table suppor his in ha he European CDS marke exhibis significan posiive firs-order auocorrelaion. However, he impac of he posiive firs-order auocorrelaion in he crisis period is no as sensiive as in he pre-crisis period. The flucuaion of he itraxx CDS index has he negaive correlaion wih he lagged reurns in he STOXX 600 index and he posiive correlaion wih he lagged 9
10 reurns in VSTOXX 50 index, which is consisen wih previous invesigaions. The flucuaion of he itraxx CDS index is more sensiive o lagged reurns in he STOXX 600 and he VSTOXX 50 indices during he crisis period. The Euro swap rae has a significan effec on he itraxx CDS spreads during he pre-crisis period only. Alexander and Kaeck (008) indicae ha he risk-free rae has no saisically significan impac on he itraxx CDS spreads during he urbulen period, consisen wih our finding in he crisis period. We also use he -year Euribor rae as he proxy of he risk-free ineres rae and he resuls appear similar o hose displayed in Table. However, he values of R for hree esing periods are no as good as using he Euro swap rae. For his reason, we do no provide he resuls of using he -year Euribor rae in he sudy. Table Regressions wih all explanaory variables Whole Period Pre-crisis Period Crisis Period θ (0.3834) (.0945) ( ) θ (-3.930) (-4.65) ( ) θ (4.038) (3.437) (4.0849) θ Adjused (7.60) (9.364) (3.9387) θ ( ) (-4.336) (-.653) R R Each column repors he esimaes of he regression by Eq. (3), wih -saisics below in brackes. Comparing he wo sub-periods, he marke facors have a sronger effec during he crisis period han in he pre-crisis period. The degree of explanaion, R, can be used o measure how well he regression esimaes he ime series. In he crisis period, he itraxx CDS spreads were more volaile and R is much higher han ha in he pre-crisis period, which may indicae ha hese heoreical deerminans have sronger explanaory power in he period of high volailiy. Using he proxy of firm value suggesed by Alexander and Kaeck (008) in Equaion (3), he values of R are around 3% for he whole period and 36% for he crisis period. The main difference is ha Alexander and Kaeck (008) generae an equally weighed sock porfolio comprised of mos of he underlying eniies from he itraxx 5-year CDS Europe 0
11 index as he proxy firm value. However, he itraxx CDS index only covers 5 invesmen grade European companies, which may no reflec in enirey he European economic siuaion. On he conrary, he STOXX 600 index can represen he performance of he Euro zone equiy marke, which may explain he daily flucuaion of he itraxx CDS index beer. 4.4 Residual Analysis The AR()-GARCH(,) model wih he skewed suden s marginal disribuion is used o esimae he behaviour of he regression residuals insead of he sandard AR-GARCH models. In order o assess he pracical relevance of his disribuion, he comparison among he skewed suden s disribuion, he normal and he symmery suden s disribuions are aken ino accoun. In addiion, he Ljung Box Q-Tes, he ARCH-LM es, and he Pearson goodness-of-fi (GOF) es are used o address esimaion risk. The Ljung Box Q-Tes for squared sandardized residuals deecs any remaining serial correlaion in he condiional variance equaion. If he condiional variance equaion is correcly specified, all Q-saisics of sandardized residuals should be insignifican wih no observable auocorrelaion. The ARCH-LM ess he null hypohesis ha here is no ARCH effec up o order q in he squared residuals. Moreover, we employ he Pearson goodness-of-fi es for sandardized residuals as a saisical diagnosic in order o es he null hypohesis of he disribuion of cerain ime series is consisen wih a paricular heoreical disribuion. Table 3 shows he AR()-GARCH(,) esimaions and he ess resuls for he whole period. The AR()-GARCH(,) model can be adequae o capure he dynamics of he residual series of Equaion (3). All he ARCH-LM ess are highly saisically significan a he 5% level, meaning he heeroskedasiciy is removed. The resuls of he Ljung Box Q-saisic wih 30 lags es accep he null hypohesis of no auocorrelaion, meaning he AR()-GARCH (,) model is adequae o capure he condiional mean and he condiional variance. The esimaed numbers of degrees of freedom ν are saisically significan lying on 5.9 and 5.68, which indicae residual series of he whole period o be fa-ailed. The skewness parameer λ is posiively significanly differen from 0 a he 5% level, exhibiing he disribuions of residual series seem o be skewed. According o he Pearson goodness-of-fi saisics, he skewed suden s disribuion is more suiable o capure he volailiy clusering due o he insignifican Pearson goodness-of-fi saisics of he normally and he symmeric suden s disribued assumpions. Moreover, he Akaike informaion crieria (AIC) and he
12 log-likelihood values highligh he fac ha AR()-GARCH(,) wih skewed suden s marginal densiy funcion beer esimae he residual ime series han symmeric AR()-GARCH(,) model. Table 4 presens he Jarque-Bera and he Kolmogorov-Smirnov (KS) ess of he residual series for he whole period. The resuls show ha he residual is neiher normally disribued nor symmeric suden s disribued bu skewed suden s disribued, supporing he heory ha he AR()-GARCH(,) wih skewed suden s marginal densiy funcion is more suiable o capure he volailiy clusering feaure of he regression residual. Table 3 Esimaion resuls of AR()-GARCH(,) model for he whole period Normal Suden s Skewed Suden s Cons ( ) (59.75) ( ) ARCH () ( ) (4.834) ( ) GARCH () (4.980) (80.79) ( ) ν (6.9997) (9.6586) λ (5.53) AIC Log-Lik GOF(0) [0.0000] [0.0000] [0.0] ARCH-LM Tes [0.83] [0.588] [0.9769] Ljung Box Q-Tes [0.97] [0.9905] [0.989] Each column repors he esimaes of he model defined in secion., wih -saisics underneah in parenheses. The saisics of all ess are repored wih p-value underneah in brackes. AIC and Log-Lik are he Akaike Informaion crierion and Log-Likelihood value Table 4 Disribuion es of he residual series in he whole period Jarque-Bera Tes KS (Symmeric ) KS(Skewed ) Saisic p-value
13 As is ypical of AR-GARCH model esimaes, he sum of he coefficiens on he lagged squared error and lagged condiional variance for he whole period wih he skewed suden s marginal densiy funcion is very close o uniy (approximae ). This implies ha shocks o he condiional variance will be highly persisen. This can be demonsraed by considering he equaions for forecasing he sandardized regression residuals of he condiional variance using he AR()-GARCH(,) model based on skewed suden s disribuion. A large sum of hese coefficiens implies ha a large posiive or a large negaive change will lead o high fuure variance forecas for a proraced period. 4.5 Ou-of-Sample Forecas Evaluaion An ou-of-sample forecas evaluaion provides a powerful framework o evaluae he performances of compeing models. Many empirical sudies (e.g. Pagan and Schwer(990), Davis and Kuan(003), Alberg, Shali and Rosef(008), and so on) demonsrae ha he asymmeric assumpion of condiional variance provides a beer in-sample fi and beer ou-of-sample predicive power. In his secion, he whole daa se is divided ino an in-sample period from Augus 6, 004 o Sepember 008 and an ou-of-sample period from Sepember o January 8 00 for he forecasing evaluaion. Table 5 repors he ou-of-sample forecas evaluaion resuls using he saisical loss funcion from secion 3.. of his sudy ogeher wih various disribuions. All of he loss funcions clearly indicae ha he AR()-GARCH(,) model wih skewed suden s marginal densiy funcion performs bes for all of he four forecas horizons, and he second bes is based on he suden s disribuion. In order o examine if he forecas accuracy among he hree assumpions on disribuion are significanly differen, he DM es is adoped o check he saisical significance when all models are compared in pairwise. Table 6 presens he DM es resuls using he skewed suden s disribuion as he benchmark, and he comparison is carried ou wih regards o all he saisical loss funcions discussed in secion 3... As can be seen in Table 6, he skewed suden s disribuion significanly ouperforms he symmeric models a he 5% level. The signs of he DM saisics of he comparison beween he skewed suden s disribuion and he symmeric disribuions are always significanly posiive; indicaing he loss of he skewed suden s is significanly lower han ha of symmeric disribuions. In oher words, he AR()-GARCH(,) wih skewed suden s marginal densiy funcion provides a more accurae volailiy forecas, demonsraing he skewed suden s disribued assumpion of regression residual 3
14 ouperforms he symmeric disribued assumpion for he forecas evaluaion. Table 5 Ou-of-sample forecas evaluaion resuls for saisical loss funcions: -,5-,0- and 0-day forecas horizions Normal Suden's Skewed day MSE (%) MAE (%) LL (%) days MSE (%) MAE (%) LL (%) days MSE (%) MAE (%) LL (%) days MSE (%) MAE (%) LL (%) Table 6 Diebold-Mariano Tes MSE MAE LL Saisiic p-value Saisiic p-value Saisiic p-value day Normal v.s. Skewed Suden's v.s. Skewed days Normal v.s. Skewed Suden's v.s. Skewed days Normal v.s. Skewed Suden's v.s. Skewed days Normal v.s. Skewed Suden's v.s. Skewed
15 5. Conclusion This sudy invesigaes he linear relaionship beween heoreical deerminans and he itraxx Europe CDS index. The heoreical deerminans of he itraxx CDS index have a significan impac on he itraxx CDS marke, excep for -year Euro Swap rae, which has no saisically significan effec on he itraxx CDS marke in he crisis period. This finding indicaes ha he risk-free rae yield curve has no saisically significan effec on he itraxx CDS marke in he period of high volailiy. Moreover, all he explanaory variables in his sudy have higher explanaory power han previous empirical sudies due o a beer proxy of firm s value suggesed in his sudy. Furhermore, financial ime series are known o be condiionally heeroskedasic, fa-ailed, and ofen skewed. To accommodae for his we furher relaxed he assumpion of ime series of regression residuals from symmeric disribuions o an asymmeric disribuion. Our resuls show ha volailiy clusering feaures in he itraxx CDS marke can no be fully capured by using he sandard AR()-GARCH(,) model. The AR()-GARCH(,) model wih he skewed suden s marginal densiy funcion is much more suiable o capure mean-revering condiionally heeroscedasic process for innovaions. In addiion, he sums of he coefficiens on he lagged squared error and lagged condiional variance are very close o uniy, indicaing a large posiive or a large negaive change will lead o high fuure variance forecas for a proraced period. Ou-of-sample forecasing comparison is carried ou by comprising -day, 5-day, 0-day and 0-day ahead volailiy forecass. The saisical loss funcions demonsrae ha AR()-GARCH(,) model wih skewed suden s marginal densiy funcion ouperforms he sandard AR()-GARCH(,) models in forecasing volailiy for all four forecas horizons. The Diebold-Mariano is applied o furher examine wheher he differences in he performances among hree disribued assumpions are significan, and he resuls show ha he AR()-GARCH (,) model based on he skewed suden s disribued assumpion significanly ouperforms oher wo compeing models. Overall, he inclusion of AR()-GARCH(,) effecs wih fa-ailedness and skewness provides no only a beer in-sample fi bu also more accurae ou-of-sample forecass. 5
16 References Alexander, C., Kaeck, A., (008), Regimes Dependen Deerminans of Credi Defaul Swap Spreads, Journal of Banking & Finance, Vol. 3, pp Alberg, D., Shali, H., Rosef, R., (008), Esimaing Sock Marke Volailiy Using Asymmeric GARCH Models, Applied Financial Economics, Vol. 8, pp Benker, C., (004), Explaining Credi Defaul Swap Premia, Journal of Fuures Markes, Vol. 4, pp Black, F., Cox J. C., (976), Valuing Corporae Securiies: Some Effecs of Bond Indenure Provisions, Journal of Finance, Vol. 3, pp Black, F., Scholes, M., (973), The Pricing of Opions and Corporae Liabiliies, Journal of Poliical Economy, Vol. 8, pp Bollerslev, T., (986), Generalized Auoregressive Condiional Heeroscedasiciy, Journal of Economerics, Vol. 3, pp Bysröm, H., (005), Credi Defaul Swaps and Equiy Prices: The itraxx CDS Index Marke, Working Papers, Lund Universiy, Deparmen of Economics. Bysröm, H., (006), CrediGrades and he itraxx CDS Index Marke. Financial Analyss Journal, Vol.6, pp Collin-Dufresne, P., Goldsein, R.S., Marin, J.S., (00), The Deerminans of Credi Spread Changes, Journal of Finance, Vol.56, pp Davis, N., Kuan, M., (003), Inflaion and Oupu as Predicors of Sock Reurns and Volailiy: Inernaional Evidence, Applied Financial Economics, Vol.3, pp Diebold, F., Mariano, R., (995), Comparing Predicive Accuracy. Journal of Business and Economic Saisics, Vol.3, pp Duffie, D., (999), Credi Swap Valuaion, Financial Analys Journal, Vol.55, pp Engle, R., (98), Auoregressive Condiional Heeroscedasiciy wih Esimaes of Variance of Unied Kingdom Inflaion, Economerica Vol. 50, pp Ericsson, J., Jacobs, K., Oviedo-Helfenberger, R., (009), The Deerminans of Credi Defaul Swap Premia, Journal of Financial and Quaniaive Analysis, Vo.44, pp Geske, R., (977), The Valuaion of Corporae Liabiliies as Compound Opions, Journal of Financial and Quaniaive Analysis, Vol.5, pp Hansen, B., (994), Auoregressive Condiional Densiy Esimaion, Inernaional Economic Review, Vol. 35, pp Houweling, P., Vors, T., (005), Pricing Defaul Swaps: Empirical Evidence, Journal of Inernaional Money and Finance, Vol. 4, pp
17 Leland, H., Tof, K., (996), Opimal Capial Srucure, Endogenous Bankrupcy, and he Term Srucure of Credi Spreads, Journal of Finance, Vol.5, pp Longsaff, F.A., Mihal, S., Neis, E., (005), Corporae Yield Spreads: Defaul Risk or Liquidiy? New Evidence from he Credi Defaul Swap Marke, Journal of Finance, Vol.60, pp Meron, R. C., (974), On he Pricing of Corporae Deb: The Risk Srucure of Ineres Raes, Journal of Finance, Vol. 9, pp Pagan, R., Schwer, W., (990), Alernaive Models for Condiional Sock Volailiy, Journal of Economerics, Vol.45, pp Zhou C., (00), The Term Srucure of Credi Spreads wih Jump Risk, Journal of Banking & Finance, Vol.5, pp Zhang, B., Zhou, H., Zhu, H., (006), Explaining Credi Defaul Swap Spreads wih he Equiy Volailiy and Jump Risks of Individual Firms, Working Paper, BIS. 7
On the Impact of Inflation and Exchange Rate on Conditional Stock Market Volatility: A Re-Assessment
MPRA Munich Personal RePEc Archive On he Impac of Inflaion and Exchange Rae on Condiional Sock Marke Volailiy: A Re-Assessmen OlaOluwa S Yaya and Olanrewaju I Shiu Deparmen of Saisics, Universiy of Ibadan,
More informationVOLATILITY CLUSTERING, NEW HEAVY-TAILED DISTRIBUTION AND THE STOCK MARKET RETURNS IN SOUTH KOREA
64 VOLATILITY CLUSTERING, NEW HEAVY-TAILED DISTRIBUTION AND THE STOCK MARKET RETURNS IN SOUTH KOREA Yoon Hong, PhD, Research Fellow Deparmen of Economics Hanyang Universiy, Souh Korea Ji-chul Lee, PhD,
More informationNon-Stationary Processes: Part IV. ARCH(m) (Autoregressive Conditional Heteroskedasticity) Models
Alber-Ludwigs Universiy Freiburg Deparmen of Economics Time Series Analysis, Summer 29 Dr. Sevap Kesel Non-Saionary Processes: Par IV ARCH(m) (Auoregressive Condiional Heeroskedasiciy) Models Saionary
More informationComparison of back-testing results for various VaR estimation methods. Aleš Kresta, ICSP 2013, Bergamo 8 th July, 2013
Comparison of back-esing resuls for various VaR esimaion mehods, ICSP 3, Bergamo 8 h July, 3 THE MOTIVATION AND GOAL In order o esimae he risk of financial invesmens, i is crucial for all he models o esimae
More informationThe Relationship between Money Demand and Interest Rates: An Empirical Investigation in Sri Lanka
The Relaionship beween Money Demand and Ineres Raes: An Empirical Invesigaion in Sri Lanka R. C. P. Padmasiri 1 and O. G. Dayarana Banda 2 1 Economic Research Uni, Deparmen of Expor Agriculure 2 Deparmen
More informationFORECASTING WITH A LINEX LOSS: A MONTE CARLO STUDY
Proceedings of he 9h WSEAS Inernaional Conference on Applied Mahemaics, Isanbul, Turkey, May 7-9, 006 (pp63-67) FORECASTING WITH A LINEX LOSS: A MONTE CARLO STUDY Yasemin Ulu Deparmen of Economics American
More information1 Purpose of the paper
Moneary Economics 2 F.C. Bagliano - Sepember 2017 Noes on: F.X. Diebold and C. Li, Forecasing he erm srucure of governmen bond yields, Journal of Economerics, 2006 1 Purpose of he paper The paper presens
More informationExtreme Risk Value and Dependence Structure of the China Securities Index 300
MPRA Munich Personal RePEc Archive Exreme Risk Value and Dependence Srucure of he China Securiies Index 300 Terence Tai Leung Chong and Yue Ding and Tianxiao Pang The Chinese Universiy of Hong Kong, The
More informationA Note on Missing Data Effects on the Hausman (1978) Simultaneity Test:
A Noe on Missing Daa Effecs on he Hausman (978) Simulaneiy Tes: Some Mone Carlo Resuls. Dikaios Tserkezos and Konsaninos P. Tsagarakis Deparmen of Economics, Universiy of Cree, Universiy Campus, 7400,
More informationFinancial Econometrics Jeffrey R. Russell Midterm Winter 2011
Name Financial Economerics Jeffrey R. Russell Miderm Winer 2011 You have 2 hours o complee he exam. Use can use a calculaor. Try o fi all your work in he space provided. If you find you need more space
More informationModelling Volatility Using High, Low, Open and Closing Prices: Evidence from Four S&P Indices
Inernaional Research Journal of Finance and Economics ISSN 1450-2887 Issue 28 (2009) EuroJournals Publishing, Inc. 2009 hp://www.eurojournals.com/finance.hm Modelling Volailiy Using High, Low, Open and
More informationModeling Volatility of Exchange Rate of Chinese Yuan against US Dollar Based on GARCH Models
013 Sixh Inernaional Conference on Business Inelligence and Financial Engineering Modeling Volailiy of Exchange Rae of Chinese Yuan agains US Dollar Based on GARCH Models Marggie Ma DBA Program Ciy Universiy
More informationAre CDS spreads predictable? An analysis of linear and non-linear forecasting models
Are CDS spreads predicable? An analysis of linear and non-linear forecasing models Davide Avino and Ogonna Nneji* ICMA Cenre, Universiy of Reading, Henley School of Business, PO Box 242 RG6 6BA, UK Curren
More informationVaR and Low Interest Rates
VaR and Low Ineres Raes Presened a he Sevenh Monreal Indusrial Problem Solving Workshop By Louis Doray (U de M) Frédéric Edoukou (U de M) Rim Labdi (HEC Monréal) Zichun Ye (UBC) 20 May 2016 P r e s e n
More informationEstimating Earnings Trend Using Unobserved Components Framework
Esimaing Earnings Trend Using Unobserved Componens Framework Arabinda Basisha and Alexander Kurov College of Business and Economics, Wes Virginia Universiy December 008 Absrac Regressions using valuaion
More informationHedging Performance of Indonesia Exchange Rate
Hedging Performance of Indonesia Exchange Rae By: Eneng Nur Hasanah Fakulas Ekonomi dan Bisnis-Manajemen, Universias Islam Bandung (Unisba) E-mail: enengnurhasanah@gmail.com ABSTRACT The flucuaion of exchange
More informationPortfolio Risk of Chinese Stock Market Measured by VaR Method
Vol.53 (ICM 014), pp.6166 hp://dx.doi.org/10.1457/asl.014.53.54 Porfolio Risk of Chinese Sock Marke Measured by VaR Mehod Wu Yudong School of Basic Science,Harbin Universiy of Commerce,Harbin Email:wuyudong@aliyun.com
More informationFinancial Markets And Empirical Regularities An Introduction to Financial Econometrics
Financial Markes And Empirical Regulariies An Inroducion o Financial Economerics SAMSI Workshop 11/18/05 Mike Aguilar UNC a Chapel Hill www.unc.edu/~maguilar 1 Ouline I. Hisorical Perspecive on Asse Prices
More informationForecasting Financial Time Series
1 Inroducion Forecasing Financial Time Series Peer Princ 1, Sára Bisová 2, Adam Borovička 3 Absrac. Densiy forecas is an esimae of he probabiliy disribuion of he possible fuure values of a random variable.
More informationGARCH Model With Fat-Tailed Distributions and Bitcoin Exchange Rate Returns
Journal of Accouning, Business and Finance Research ISSN: 5-3830 Vol., No., pp. 7-75 DOI: 0.0448/00..7.75 GARCH Model Wih Fa-Tailed Disribuions and Bicoin Exchange Rae Reurns Ruiping Liu Zhichao Shao Guodong
More informationA NOTE ON BUSINESS CYCLE NON-LINEARITY IN U.S. CONSUMPTION 247
Journal of Applied Economics, Vol. VI, No. 2 (Nov 2003), 247-253 A NOTE ON BUSINESS CYCLE NON-LINEARITY IN U.S. CONSUMPTION 247 A NOTE ON BUSINESS CYCLE NON-LINEARITY IN U.S. CONSUMPTION STEVEN COOK *
More informationDecision Science Letters
Decision Science Leers (3) 9 4 Conens liss available a GrowingScience Decision Science Leers homepage: www.growingscience.com/dsl Esimaing he risk-reurn radeoff in MENA Sock Markes Salim Lahmiri * ESCA
More informationDYNAMIC ECONOMETRIC MODELS Vol. 7 Nicolaus Copernicus University Toruń Krzysztof Jajuga Wrocław University of Economics
DYNAMIC ECONOMETRIC MODELS Vol. 7 Nicolaus Copernicus Universiy Toruń 2006 Krzyszof Jajuga Wrocław Universiy of Economics Ineres Rae Modeling and Tools of Financial Economerics 1. Financial Economerics
More informationAsymmetry and Leverage in Stochastic Volatility Models: An Exposition
Asymmery and Leverage in Sochasic Volailiy Models: An xposiion Asai, M. a and M. McAleer b a Faculy of conomics, Soka Universiy, Japan b School of conomics and Commerce, Universiy of Wesern Ausralia Keywords:
More informationCh. 10 Measuring FX Exposure. Is Exchange Rate Risk Relevant? MNCs Take on FX Risk
Ch. 10 Measuring FX Exposure Topics Exchange Rae Risk: Relevan? Types of Exposure Transacion Exposure Economic Exposure Translaion Exposure Is Exchange Rae Risk Relevan?? Purchasing Power Pariy: Exchange
More informationThe Expiration-Day Effect of Derivatives Trading: Evidence from the Taiwanese Stock Market
Journal of Applied Finance & Banking, vol. 5, no. 4, 2015, 53-60 ISSN: 1792-6580 (prin version), 1792-6599 (online) Scienpress Ld, 2015 The Expiraion-Day Effec of Derivaives Trading: Evidence from he Taiwanese
More informationUCLA Department of Economics Fall PhD. Qualifying Exam in Macroeconomic Theory
UCLA Deparmen of Economics Fall 2016 PhD. Qualifying Exam in Macroeconomic Theory Insrucions: This exam consiss of hree pars, and you are o complee each par. Answer each par in a separae bluebook. All
More informationDynamic Analysis on the Volatility of China Stock Market Based on CSI 300: A Financial Security Perspective
Inernaional Journal of Securiy and Is Applicaions Vol., No. 3 (07), pp.9-38 hp://dx.doi.org/0.457/ijsia.07..3.03 Dynamic Analysis on he Volailiy of China Sock Marke Based on CSI 300: A Financial Securiy
More informationMacroeconomics II A dynamic approach to short run economic fluctuations. The DAD/DAS model.
Macroeconomics II A dynamic approach o shor run economic flucuaions. The DAD/DAS model. Par 2. The demand side of he model he dynamic aggregae demand (DAD) Inflaion and dynamics in he shor run So far,
More informationConditional Heavy Tails, Volatility Clustering and Asset Prices of the Precious Metal
Condiional Heavy Tails, Volailiy Clusering and Asse Prices of he Precious Meal Wei Ma, Keqi Ding, Yumin Dong, and Li Wang DOI: 10.6007/IJARBSS/v7-i7/3131 URL: hp://dx.doi.org/10.6007/ijarbss/v7-i7/3131
More informationFINAL EXAM EC26102: MONEY, BANKING AND FINANCIAL MARKETS MAY 11, 2004
FINAL EXAM EC26102: MONEY, BANKING AND FINANCIAL MARKETS MAY 11, 2004 This exam has 50 quesions on 14 pages. Before you begin, please check o make sure ha your copy has all 50 quesions and all 14 pages.
More informationOn the Relationship between Time-Varying Price dynamics of the Underlying. Stocks: Deregulation Effect on the Issuance of Third-Party Put Warrant
On he Relaionship beween Time-Varying Price dynamics of he Underlying Socks: Deregulaion Effec on he Issuance of Third-Pary Pu Warran Yi-Chen Wang * Deparmen of Financial Operaions, Naional Kaohsiung Firs
More informationStock Market Behaviour Around Profit Warning Announcements
Sock Marke Behaviour Around Profi Warning Announcemens Henryk Gurgul Conen 1. Moivaion 2. Review of exising evidence 3. Main conjecures 4. Daa and preliminary resuls 5. GARCH relaed mehodology 6. Empirical
More informationIMPACTS OF FINANCIAL DERIVATIVES MARKET ON OIL PRICE VOLATILITY. Istemi Berk Department of Economics Izmir University of Economics
IMPACTS OF FINANCIAL DERIVATIVES MARKET ON OIL PRICE VOLATILITY Isemi Berk Deparmen of Economics Izmir Universiy of Economics OUTLINE MOTIVATION CRUDE OIL MARKET FUNDAMENTALS LITERATURE & CONTRIBUTION
More informationINSTITUTE OF ACTUARIES OF INDIA
INSIUE OF ACUARIES OF INDIA EAMINAIONS 23 rd May 2011 Subjec S6 Finance and Invesmen B ime allowed: hree hours (9.45* 13.00 Hrs) oal Marks: 100 INSRUCIONS O HE CANDIDAES 1. Please read he insrucions on
More informationModels of Default Risk
Models of Defaul Risk Models of Defaul Risk 1/29 Inroducion We consider wo general approaches o modelling defaul risk, a risk characerizing almos all xed-income securiies. The srucural approach was developed
More informationSubdivided Research on the Inflation-hedging Ability of Residential Property: A Case of Hong Kong
Subdivided Research on he -hedging Abiliy of Residenial Propery: A Case of Hong Kong Guohua Huang 1, Haili Tu 2, Boyu Liu 3,* 1 Economics and Managemen School of Wuhan Universiy,Economics and Managemen
More informationFinal Exam Answers Exchange Rate Economics
Kiel Insiu für Welwirhschaf Advanced Sudies in Inernaional Economic Policy Research Spring 2005 Menzie D. Chinn Final Exam Answers Exchange Rae Economics This exam is 1 ½ hours long. Answer all quesions.
More informationMeasuring and Forecasting the Daily Variance Based on High-Frequency Intraday and Electronic Data
Measuring and Forecasing he Daily Variance Based on High-Frequency Inraday and Elecronic Daa Faemeh Behzadnejad Supervisor: Benoi Perron Absrac For he 4-hr foreign exchange marke, Andersen and Bollerslev
More informationUncovered interest parity and policy behavior: new evidence
Economics Leers 69 (000) 81 87 www.elsevier.com/ locae/ econbase Uncovered ineres pariy and policy behavior: new evidence Michael Chrisensen* The Aarhus School of Business, Fuglesangs Alle 4, DK-810 Aarhus
More informationOnline Appendix to: Implementing Supply Routing Optimization in a Make-To-Order Manufacturing Network
Online Appendix o: Implemening Supply Rouing Opimizaion in a Make-To-Order Manufacuring Nework A.1. Forecas Accuracy Sudy. July 29, 2008 Assuming a single locaion and par for now, his sudy can be described
More informationPaper ID : Paper title: How the features of candlestick encourage the performance of volatility forecast? Evidence from the stock markets
Paper ID : 10362 Paper ile: How he feaures of candlesick encourage he performance of volailiy forecas? Evidence from he sock markes Jung-Bin Su Deparmen of Finance, China Universiy of Science and Technology,
More informationAn Analysis About Market Efficiency in International Petroleum Markets: Evidence from Three Oil Commodities
An Analysis Abou Marke Efficiency in Inernaional Peroleum Markes: Evidence from Three Oil Commodiies Wang Shuping, Li Jianping, and Zhang Shulin The College of Economics and Business Adminisraion, Norh
More informationEmpirical analysis on China money multiplier
Aug. 2009, Volume 8, No.8 (Serial No.74) Chinese Business Review, ISSN 1537-1506, USA Empirical analysis on China money muliplier SHANG Hua-juan (Financial School, Shanghai Universiy of Finance and Economics,
More informationR e. Y R, X R, u e, and. Use the attached excel spreadsheets to
HW # Saisical Financial Modeling ( P Theodossiou) 1 The following are annual reurns for US finance socks (F) and he S&P500 socks index (M) Year Reurn Finance Socks Reurn S&P500 Year Reurn Finance Socks
More informationForecasting Malaysian Gold Using. a Hybrid of ARIMA and GJR-GARCH Models
Applied Mahemaical Sciences, Vol. 9, 15, no. 3, 1491-151 HIKARI Ld, www.m-hikari.com hp://dx.doi.org/1.1988/ams.15.514 Forecasing Malaysian Gold Using a Hybrid of ARIMA and GJR-GARCH Models Maizah Hura
More informationEstimating the Dynamics of Weak Efficiency on the Prague Stock Exchange Using the Kalman Filter *
JEL Classificaion: C, D53, G4 Keywords: GARCH, Kalman filer, maringale, weak-efficiency Esimaing he Dynamics of Weak Efficiency on he Prague Sock Exchange Using he Kalman Filer * Ví POŠTA Universiy of
More informationPredictive Ability of Three Different Estimates of Cay to Excess Stock Returns A Comparative Study for South Africa and USA
European Research Sudies, Volume XVII, Issue (1), 2014 pp. 3-18 Predicive Abiliy of Three Differen Esimaes of Cay o Excess Sock Reurns A Comparaive Sudy for Souh Africa and USA Noha Emara 1 Absrac: The
More informationESTIMATING STOCK MARKET VOLATILITY USING ASYMMETRIC GARCH MODELS. Dima Alberg, Haim Shalit and Rami Yosef. Discussion Paper No
ESTIMATING STOCK MARKET VOLATILITY USING ASYMMETRIC GARCH MODELS Dima Alberg, Haim Shali and Rami Yosef Discussion Paper No. 06-0 Sepember 006 Monaser Cener for Economic Research Ben-Gurion Universiy of
More information2. Quantity and price measures in macroeconomic statistics 2.1. Long-run deflation? As typical price indexes, Figure 2-1 depicts the GDP deflator,
1 2. Quaniy and price measures in macroeconomic saisics 2.1. Long-run deflaion? As ypical price indexes, Figure 2-1 depics he GD deflaor, he Consumer rice ndex (C), and he Corporae Goods rice ndex (CG)
More informationOption trading for optimizing volatility forecasting
Journal of Saisical and Economeric Mehods, vol.6, no.3, 7, 65-77 ISSN: 79-66 (prin), 79-6939 (online) Scienpress Ld, 7 Opion rading for opimizing volailiy forecasing Vasilios Sogiakas Absrac This paper
More informationThe Mathematics Of Stock Option Valuation - Part Four Deriving The Black-Scholes Model Via Partial Differential Equations
The Mahemaics Of Sock Opion Valuaion - Par Four Deriving The Black-Scholes Model Via Parial Differenial Equaions Gary Schurman, MBE, CFA Ocober 1 In Par One we explained why valuing a call opion as a sand-alone
More informationThe Empirical Study about Introduction of Stock Index Futures on the Volatility of Spot Market
ibusiness, 013, 5, 113-117 hp://dx.doi.org/10.436/ib.013.53b04 Published Online Sepember 013 (hp://www.scirp.org/journal/ib) 113 The Empirical Sudy abou Inroducion of Sock Index Fuures on he Volailiy of
More informationINSTITUTE OF ACTUARIES OF INDIA
INSTITUTE OF ACTUARIES OF INDIA EXAMINATIONS 05 h November 007 Subjec CT8 Financial Economics Time allowed: Three Hours (14.30 17.30 Hrs) Toal Marks: 100 INSTRUCTIONS TO THE CANDIDATES 1) Do no wrie your
More informationParametric Forecasting of Value at Risk Using Heavy Tailed Distribution
Parameric Forecasing of Value a Risk Using Heavy Tailed Disribuion Josip Arnerić Universiy of Spli, Faculy of Economics, Croaia Elza Jurun Universiy of Spli, Faculy of Economics Spli, Croaia Snježana Pivac
More informationThe role of the SGT Density with Conditional Volatility, Skewness and Kurtosis in the Estimation of VaR: A Case of the Stock Exchange of Thailand
Available online a www.sciencedirec.com Procedia - Social and Behavioral Sciences 4 ( ) 736 74 The Inernaional (Spring) Conference on Asia Pacific Business Innovaion and Technology Managemen, Paaya, Thailand
More informationLinkages and Performance Comparison among Eastern Europe Stock Markets
Easern Europe Sock Marke hp://dx.doi.org/10.14195/2183-203x_39_4 Linkages and Performance Comparison among Easern Europe Sock Markes Faculdade de Economia da Universidade de Coimbra and GEMF absrac This
More informationPricing formula for power quanto options with each type of payoffs at maturity
Global Journal of Pure and Applied Mahemaics. ISSN 0973-1768 Volume 13, Number 9 (017, pp. 6695 670 Research India Publicaions hp://www.ripublicaion.com/gjpam.hm Pricing formula for power uano opions wih
More informationAsymmetric Stochastic Volatility in Nordic Stock Markets
EconWorld017@Rome Proceedings 5-7 January, 017; Rome, Ialy Asymmeric Sochasic Volailiy in Nordic Sock Markes Aycan Hepsağ 1 Absrac The goal of his paper is o invesigae he asymmeric impac of innovaions
More informationJarrow-Lando-Turnbull model
Jarrow-Lando-urnbull model Characerisics Credi raing dynamics is represened by a Markov chain. Defaul is modelled as he firs ime a coninuous ime Markov chain wih K saes hiing he absorbing sae K defaul
More informationImportance of the macroeconomic variables for variance. prediction: A GARCH-MIDAS approach
Imporance of he macroeconomic variables for variance predicion: A GARCH-MIDAS approach Hossein Asgharian * : Deparmen of Economics, Lund Universiy Ai Jun Hou: Deparmen of Business and Economics, Souhern
More informationUncovered Interest Parity and Monetary Policy Freedom in Countries with the Highest Degree of Financial Openness
www.ccsene.org/ijef Inernaional Journal of Economics and Finance Vol. 3, No. 1; February 11 Uncovered Ineres Pariy and Moneary Policy Freedom in Counries wih he Highes Degree of Financial Openness Yuniaro
More informationHave bull and bear markets changed over time? Empirical evidence from the US-stock market
Journal of Finance and Invesmen Analysis, vol.1, no.1, 2012, 151-171 ISSN: 2241-0988 (prin version), 2241-0996 (online) Inernaional Scienific Press, 2012 Have bull and bear markes changed over ime? Empirical
More informationVolatility Spillovers between U.S. Home Price Tiers. Tiers during the Housing Bubble
Inroducion Daa The dynamic correlaion-coefficien model Volailiy Spillovers beween U.S. Home Price Tiers during he Housing Bubble Damian Damianov Deparmen of Economics and Finance The Universiy of Texas
More informationVolatility Spillovers between Stock Market Returns and Exchange Rate Changes: the New Zealand Case
Volailiy Spillovers beween Sock Marke eurns and Exchange ae Changes: he New Zealand Case Choi, D.F.S., V. Fang and T.Y. Fu Deparmen of Finance, Waikao Managemen School, Universiy of Waikao, Hamilon, New
More informationModeling Risk: VaR Methods for Long and Short Trading Positions. Stavros Degiannakis
Modeling Risk: VaR Mehods for Long and Shor Trading Posiions Savros Degiannakis Deparmen of Saisics, Ahens Universiy of Economics and Business, 76, Paision sree, Ahens GR-14 34, Greece Timoheos Angelidis
More informationThe Middle East Business and Economic Review, Vol.22, No.1 (March 2010)
The Middle Eas Business and Economic Review, Vol.22, No.1 (March 2010) CRUDE OIL PRICE: HOW TO ANTICIPATE ITS FUTURE TRAJECTORY? A specific phenomenon of volailiy clusering Isabelle Crisiani-d Ornano 1,
More informationInternational Review of Business Research Papers Vol. 4 No.3 June 2008 Pp Understanding Cross-Sectional Stock Returns: What Really Matters?
Inernaional Review of Business Research Papers Vol. 4 No.3 June 2008 Pp.256-268 Undersanding Cross-Secional Sock Reurns: Wha Really Maers? Yong Wang We run a horse race among eigh proposed facors and eigh
More informationSTOCK MARKET EFFICIENCY IN NEPAL
40 Vol. Issue 5, May 0, ISSN 3 5780 ABSTRACT STOCK MARKET EFFICIENCY IN NEPAL JEETENDRA DANGOL* *Lecurer, Public Youh Campus, Tribhuvan Universiy, Nepal. The paper examines random-walk behaviour and weak-form
More information(1 + Nominal Yield) = (1 + Real Yield) (1 + Expected Inflation Rate) (1 + Inflation Risk Premium)
5. Inflaion-linked bonds Inflaion is an economic erm ha describes he general rise in prices of goods and services. As prices rise, a uni of money can buy less goods and services. Hence, inflaion is an
More informationAlexander L. Baranovski, Carsten von Lieres and André Wilch 18. May 2009/Eurobanking 2009
lexander L. Baranovski, Carsen von Lieres and ndré Wilch 8. May 2009/ Defaul inensiy model Pricing equaion for CDS conracs Defaul inensiy as soluion of a Volerra equaion of 2nd kind Comparison o common
More informationWatch out for the impact of Scottish independence opinion polls on UK s borrowing costs
Wach ou for he impac of Scoish independence opinion polls on UK s borrowing coss Cosas Milas (Universiy of Liverpool; email: cosas.milas@liverpool.ac.uk) and Tim Worrall (Universiy of Edinburgh; email:
More informationNON-LINEAR MODELING OF DAILY EXCHANGE RATE RETURNS, VOLATILITY, AND NEWS IN A SMALL DEVELOPING ECONOMY. José R. Sánchez-Fung Kingston University
NON-LINEAR MODELING OF DAILY EXCHANGE RATE RETURNS, VOLATILITY, AND NEWS IN A SMALL DEVELOPING ECONOMY José R. Sánchez-Fung Kingson Universiy Absrac This paper models daily reurns, volailiy, and news in
More informationEvaluating Risk Models with Likelihood Ratio Tests: Use with
Evaluaing Risk Models wih Likelihood Raio Tess: Use wih Care! Gabriela de Raaij and Burkhard Raunig *,** March, 2002 Please do no quoe wihou permission of he auhors Gabriela de Raaij Cenral Bank of Ausria
More informationCountry-Specific Idiosyncratic Risk and Global Equity Index Returns
Counry-Specific Idiosyncraic Risk and Global Equiy Index Reurns C. James Hueng and Ruey Yau Absrac: The idiosyncraic volailiy puzzle arises from he empirical evidence ha socks wih higher pas idiosyncraic
More informationThe Predictive Content of Futures Prices in Iran Gold Coin Market
American Inernaional Journal of Conemporary Research Vol. 7, No. 3, Sepember 017 The Predicive Conen of Fuures Prices in Iran Gold Coin Marke Ali Khabiri PhD in Financial Managemen Faculy of Managemen,
More informationModeling Risk for Long and Short Trading Positions
MPRA Munich Personal RePEc Archive Modeling Risk for Long and Shor Trading Posiions Timoheos Angelidis and Savros Degiannakis Deparmen of Banking and Financial Managemen, Universiy of Piraeus, Deparmen
More informationEVA NOPAT Capital charges ( = WACC * Invested Capital) = EVA [1 P] each
VBM Soluion skech SS 2012: Noe: This is a soluion skech, no a complee soluion. Disribuion of poins is no binding for he correcor. 1 EVA, free cash flow, and financial raios (45) 1.1 EVA wihou adjusmens
More informationSeasonal asymmetric persistence in volatility: an extension of GARCH models
Seasonal asymmeric persisence in volailiy: an exension of GARCH models Virginie TERRAZA CREA, universiy of Luxembourg Absrac In his paper, we sudy non-linear dynamics in he CAC 40 sock index. Our empirical
More informationPrinciples of Finance CONTENTS
Principles of Finance CONENS Value of Bonds and Equiy... 3 Feaures of bonds... 3 Characerisics... 3 Socks and he sock marke... 4 Definiions:... 4 Valuing equiies... 4 Ne reurn... 4 idend discoun model...
More informationPricing Vulnerable American Options. April 16, Peter Klein. and. Jun (James) Yang. Simon Fraser University. Burnaby, B.C. V5A 1S6.
Pricing ulnerable American Opions April 16, 2007 Peer Klein and Jun (James) Yang imon Fraser Universiy Burnaby, B.C. 5A 16 pklein@sfu.ca (604) 268-7922 Pricing ulnerable American Opions Absrac We exend
More informationResearch & Reviews: Journal of Statistics and Mathematical Sciences
Research & Reviews: Journal of Saisics and Mahemaical Sciences Forecas and Backesing of VAR Models in Crude Oil Marke Yue-Xian Li *, Jin-Guo Lian 2 and Hong-Kun Zhang 2 Deparmen of Mahemaics and Saisics,
More informationPricing FX Target Redemption Forward under. Regime Switching Model
In. J. Conemp. Mah. Sciences, Vol. 8, 2013, no. 20, 987-991 HIKARI Ld, www.m-hikari.com hp://dx.doi.org/10.12988/ijcms.2013.311123 Pricing FX Targe Redempion Forward under Regime Swiching Model Ho-Seok
More informationCapital Market Volatility In India An Econometric Analysis
The Empirical Economics Leers, 8(5): (May 2009) ISSN 1681 8997 Capial Marke Volailiy In India An Economeric Analysis P K Mishra Siksha o Anusandhan Universiy, Bhubaneswar, Orissa, India Email: ier_pkm@yahoo.co.in
More informationThis specification describes the models that are used to forecast
PCE and CPI Inflaion Differenials: Convering Inflaion Forecass Model Specificaion By Craig S. Hakkio This specificaion describes he models ha are used o forecas he inflaion differenial. The 14 forecass
More informationFOREIGN INSTITUTIONAL INVESTOR S IMPACT ON STOCK PRICES IN INDIA
FOREIGN INSTITUTIONAL INVESTOR S IMPACT ON STOCK PRICES IN INDIA ANAND BANSAL Punjabi Universiy Guru Kashi Campus Damdama Sahib-530, Punjab Phone: +994736733; Fax: +9655099. Email: preemillie@yahoo.com
More informationGuglielmo Maria Caporale Brunel; University. Abstract
Herding behaviour in exreme marke condiions: he case of he Ahens Sock Exchange Guglielmo Maria Caporale Brunel; Universiy Foini Economou Universiy of Piraeus Nikolaos Philippas Universiy of Piraeus Absrac
More informationOptimal Early Exercise of Vulnerable American Options
Opimal Early Exercise of Vulnerable American Opions March 15, 2008 This paper is preliminary and incomplee. Opimal Early Exercise of Vulnerable American Opions Absrac We analyze he effec of credi risk
More informationPortfolio investments accounted for the largest outflow of SEK 77.5 billion in the financial account, which gave a net outflow of SEK billion.
BALANCE OF PAYMENTS DATE: 27-11-27 PUBLISHER: Saisics Sweden Balance of Paymens and Financial Markes (BFM) Maria Falk +46 8 6 94 72, maria.falk@scb.se Camilla Bergeling +46 8 6 942 6, camilla.bergeling@scb.se
More informationAvailable online at ScienceDirect
Available online a www.sciencedirec.com ScienceDirec Procedia Economics and Finance 8 ( 04 658 663 s Inernaional Conference 'Economic Scienific Research - Theoreical, Empirical and Pracical Approaches',
More informationMarket and Information Economics
Marke and Informaion Economics Preliminary Examinaion Deparmen of Agriculural Economics Texas A&M Universiy May 2015 Insrucions: This examinaion consiss of six quesions. You mus answer he firs quesion
More informationRelationship between Implied and Realized Volatility of S&P CNX Nifty Index in India. Siba Prasada Panda 1. Niranjan Swain 2. D.K.
Relaionship beween Implied and Realized Volailiy of S&P CNX Nify Index in India Siba Prasada Panda 1 Niranjan Swain 2 D.K. Malhora 3 Absrac Measures of volailiy implied in opion prices are widely believed
More informationMultivariate Volatility and Spillover Effects in Financial Markets
Mulivariae Volailiy and Spillover Effecs in Financial Markes Bernardo Veiga and Michael McAleer School of Economics and Commerce, Universiy of Wesern Ausralia (Bernardo@suden.ecel.uwa.edu.au, Michael.McAleer@uwa.edu.au)
More informationDocumentation: Philadelphia Fed's Real-Time Data Set for Macroeconomists First-, Second-, and Third-Release Values
Documenaion: Philadelphia Fed's Real-Time Daa Se for Macroeconomiss Firs-, Second-, and Third-Release Values Las Updaed: December 16, 2013 1. Inroducion We documen our compuaional mehods for consrucing
More informationBank of Japan Review. Performance of Core Indicators of Japan s Consumer Price Index. November Introduction 2015-E-7
Bank of Japan Review 5-E-7 Performance of Core Indicaors of Japan s Consumer Price Index Moneary Affairs Deparmen Shigenori Shirasuka November 5 The Bank of Japan (BOJ), in conducing moneary policy, employs
More informationIdiosyncratic Volatility and Cross-section of Stock Returns: Evidences from India
Asian Journal of Finance & Accouning Idiosyncraic Volailiy and Cross-secion of Sock Reurns: Evidences from India Prashan Sharma Assisan Professor and Area Chair (Finance and Accouns) Jaipuria Insiue of
More informationReturn-Volume Dynamics of Individual Stocks: Evidence from an Emerging Market
Reurn-Volume Dynamics of Individual Socks: Evidence from an Emerging Marke Cein Ciner College of Business Adminisraion Norheasern Universiy 413 Hayden Hall Boson, MA 02214 Tel: 617-373 4775 E-mail: c.ciner@neu.edu
More informationCapital Strength and Bank Profitability
Capial Srengh and Bank Profiabiliy Seok Weon Lee 1 Asian Social Science; Vol. 11, No. 10; 2015 ISSN 1911-2017 E-ISSN 1911-2025 Published by Canadian Cener of Science and Educaion 1 Division of Inernaional
More informationModelling the Effects of Trading Volume on Stock Return Volatility Using Conditional Heteroskedastic Models
Journal of Finance and Economics, 018, Vol. 6, No. 5, 193-00 Available online a hp://pubs.sciepub.com/jfe/6/5/5 Science and Educaion Publishing DOI:10.1691/jfe-6-5-5 Modelling he Effecs of Trading Volume
More informationValuing Real Options on Oil & Gas Exploration & Production Projects
Valuing Real Opions on Oil & Gas Exploraion & Producion Projecs March 2, 2006 Hideaka (Hugh) Nakaoka Former CIO & CCO of Iochu Oil Exploraion Co., Ld. Universiy of Tsukuba 1 Overview 1. Inroducion 2. Wha
More information