Information Spillover, Volatility and the Currency Markets for the Binary Choice Model

Omrane, Walid Ben; Hafner, Christian M. Article Information Spillover, Volatility and the Currency Markets for the Binary Choice Model International Econometric Review (IER) Provided in Cooperation with: Econometric Research Association (ERA), Ankara Suggested Citation: Omrane, Walid Ben; Hafner, Christian M. (2009) : Information Spillover, Volatility and the Currency Markets for the Binary Choice Model, International Econometric Review (IER), ISSN 1308-8815, Econometric Research Association (ERA), Ankara, Vol. 1, Iss. 1, pp. 50-62 This Version is available at: https://hdl.handle.net/10419/238784 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by-nc-nd/4.0/ Omrane and Hafner-Information Spillover, Volatility and the Currency Markets 50 Information Spillover, Volatility and the Currency Markets Walid Ben Omrane and Christian M. Hafner  Brock University and Universite catholique de Louvain ABSTRACT We use an impulse response methodology to analyse the effects of U.S. macroeconomic news announcements on the volatilities of three major exchange rates (Euro, Pound Sterling and Yen). Our data consist of 5 minute returns on exchange rates as well as the times of news announcements. In the definition of impulse responses, we allow for different types of news, and consider two categories in the application: those considered positive or negative for the U.S. economy. Using a multivariate GARCH model with exogenous news effects, we find that the initial impact of positive news on the volatility of the Pound is higher than that of the Euro, whereas the persistence of shocks is highest for the Yen. For negative news, we find that an important part of the impact on the Yen and Pound is induced by volatility spillover from the Euro. Key words: Information, Volatility, Impulse Response Function, Foreign Exchange JEL Classifications: C32, C53, F31 1. INTRODUCTION The impact of news announcements on foreign exchange (FX) volatility has been studied in several papers, e.g. Degennaro and Shrieves (1997), Andersen and Bollerslev (1998), Cai, Cheung et al. (2001) and Bauwens et al. (2005). Each study has focused on the effect of some news announcements on volatility corresponding to the one of the most active currency markets (Euro/US Dollar (EUR/USD), Great Britain Pound/US Dollar (GBP/USD) and Japanese Yen/US Dollar (JPY/USD)). All find that some categories of public information, and more specifically their unexpected component, have a significant positive effect on FX volatility. Their methodology consists of implementing univariate ARCH-type or realized volatility models, considering news announcements through lagged dummies as exogenous variables. The above studies have, however, limited their investigation to the discrete shock of public information on one currency volatility without studying its persistency through time. Beine (2004) has analysed the effect of central bank interventions on multivariate volatilities and correlations, but to the best of our knowledge, no previous study has investigated the simultaneous effect of public news announcements taking into account the dependence between the currencies. Thus, the aim of this paper is twofold. Firstly, we analyze the impact  Walid Ben Omrane, Department of Finance, Operations, and Information Systems, Brock University, St. Catharines, Ontario, Canada, (e-mail: [email protected]), Christian M. Hafner, Corresponding author, Institut de statistique, Universite catholique de Louvain, Voie du Roman Pays 20, B-1348 Louvain-la-Neuve, Belgium, (e-mail: [email protected]). This text presents research results of the Belgian Program on Interuniversity Poles of Attraction initiated by the Belgian State, Prime Minister's Office, Science Policy Programming. Hafner acknowledges financial support by the Fonds Spéciaux de Recherche (FSR 05) of the Universite catholique de Louvain, Louvain-la-Neuve, Belgium. The scientific responsibility is assumed by the authors. International Econometric Review (IER) 51 of the most important news announcement, involving the US macro-economic figures, simultaneously on high frequency EUR/USD, GBP/USD and JPY/USD volatilities. The idea is to assess the instantaneous impact of news related to the dollar on currencies quoted against USD. Secondly, we infer the persistence of the estimated news effects through an impulse response analysis. Since its introduction by Sims (1980), impulse response analysis has evolved into an important tool for analyzing the dynamics of macroeconomic and financial systems . It has been mainly designed for the conditional mean of linear systems, e.g. VARMA models, but recently interest has focused on generalizations to nonlinear systems and, in particular, to the volatility in conditionally heteroskedastic models. For example, Gallant et al. (1993) define conditional moment profiles in nonlinear models, Koop et al. (1996) propose a general simulation-based approach to nonlinear impulse response analysis, Lin (1997) proposes a particular approach to volatility impulse response analysis as a special case of Gallant et al. (1993), and Hafner and Herwartz (2006) use the notion of independence to identify endogenous news or innovations to the system. These approaches analyze the effect of endogenous news, i.e. news events that are not explicitly observed but have to be estimated within the econometric system, on volatility. In practice one may have observations of news events, for example those appearing on Reuters screens etc., which can be considered as exogenous to the variables of interest. In those cases one can use that information to estimate the impact of particular types of news on volatility. In this paper we use an impulse response methodology to analyze the effect of exogenous news on volatility in a multivariate system. We allow for different types of news to take into account different effects on exchange rates as documented by Cheung and Chinn (2001). In the empirical application we distinguish between positive and negative announcements for the U.S. economy. Our results suggest that in the very short term, positive macroeconomic news announcements in the US increase the GBP/USD volatility stronger than that of EUR/USD, whereas the JPY/USD volatility is only mildly affected. On the other hand, in the longer term (more than two hours), the effect of a shock on JPY/USD volatility is relatively more important than that of GBP/USD and EUR/USD. In other words, positive shocks are more persistent in JPY/USD volatility than they are in the two other rates. For negative news, on the other hand, the volatility of EUR/USD is affected the most, both in the short term and long term. Using a decomposition of the news effects in one FX rate according to volatility spillover from other FX rates, we find that more than 60 percent of the long run impact of positive news can be attributed to an instantaneous shock in JPY/USD, while the long run impact of negative news is dominated by the EUR/USD rate. The EUR/USD rate also has an important impact on the cumulated effect of both cross-rates in the case of negative news. The remainder of the paper is organised as follows. Section 2 introduces the impulse response methodology and Section 3 provides the empirical application to the exchange rates. Section 4 concludes. 2. METHODOLOGY Consider a system of returns to exchange rates Rt = (r1t,…, rNt). We use the following model ttt R   (2.1) ttt zH 21   (2.2) Omrane and Hafner-Information Spillover, Volatility and the Currency Markets 52 The vector μt is a function of past returns and therefore the mean of returns conditional on the past. Likewise, the N × N matrix Ht is a function of past returns and therefore the conditional variance-covariance matrix of returns. The error term zt is identically and independently distributed (i.i.d.) with mean zero and variance-covariance the identity matrix. For Ht we specify a constant conditional correlation (CCC) model as proposed by Bollerslev (1990). Thus, Ht = StRSt, where R is a constant correlation matrix and St is a diagonal matrix containing the conditional standard deviations on the diagonal. We specify these as an extension of the univariate GARCH model to the multivariate case as in Jeantheau (1998) and Ling and McAleer (2003):     L lltlttt DBhAh 1 11  (2.3) where1 ht = dg(Ht) is the N × 1 vector containing the diagonal elements of Ht, ηt = )',,( 22 1Ntt   and Dlt are dummy variables that take the value 1 if there were news of type l at time t, and zero otherwise. We assume that the arrival of news of any type is independent of the past, such that Dlt is independent of Dl’s for all s ≠ t and all l’. There are L types of news, for example originating in different markets or indicating good or bad news. Parameters of the model (2.3) are the (N × N) matrices A and B and the (N × 1) vectors ω, γ1,…,γL . This model has the advantage of being sufficiently flexible such that volatility spillover between the exchange rates can be taken into account with non-zero off-diagonal elements in A or B. On the other hand, it is very easy to estimate since univariate GARCH estimation tools can be used by adding lagged cross-returns as observed variables in the volatility equation. We now define the volatility impulse response function of exogenous shocks of type l at time horizon k as ]0,|[]1,|[   lttktlttktkl DhEDhEV (2.4) where t is the information set at time t. By direct calculation we obtain V1l = γl, V2l =(A+B)γl, …, Vkl = (A+B)k–1γl. If the process is covariance stationary, then all eigenvalues of A+B are smaller than one in modulus and Vkl tends to zero as k → ∞, that is, the impact of shocks on volatility will eventually die out. Rather than calculating the news effect at a given time horizon k, one may be interested in the accumulated effect after k periods, ΣN i=1Vil. Given the form of Vkl, this accumulated effect converges to (IN –A – B)–1 as k → ∞, where IN is the identity matrix of dimension N. For inference on Vkl we first refer to results of Jeantheau (1998) and Ling and McAleer (2003) on the consistency and asymptotic normality, respectively, of quasi maximum likelihood (QML) parameter estimators. Under regularity conditions, they show that  L n) ˆ (  ),0( ˆ  N , where θ is the vector containing all model parameters and n is the number of observations. Analytical formulae for the asymptotic covariance matrix  ˆ  are provided by Hafner and Herwartz (2008). For Vkl denote an estimator based on QML parameter estimators by kl V ˆ . We can then use the delta method to show that 1 The operator dg stacks the diagonal of a matrix into a column vector. International Econometric Review (IER) 53 ) ' ,0() ˆ (ˆ          klkl L klkl VV NVVn (2.5) where ∂Vkl/∂θ′ is evaluated at the true parameter values. Analytical expressions are given by ∂Vkl/∂ω′ = 0, ∂Vkl/∂γ′ l = (A+B)k–1, ∂Vkl/∂γ′ r = 0, r ≠ l             k i iki Nl klkl BABAI B V A V 1 )()()( )(vec)(vec  and where  is the Kronecker product operator. These results can be used to construct pointwise confidence bands for the estimated volatility impulse response functions. One may further be interested in the proportion of the total effect of type l news in one exchange rate that is explained by volatility spillover from some other rate. Let us define the relative type l news spillover effect from the j-th to the i-th exchange rate at time horizon k as    lrirk N r ljijk ijkl    ,1 , , i,j = 1,…,N (2.6) where Гk = (A+B)k–1, Гk,ij is the ij-element of Гk and γlr is the r-th element of γl. The denominator of (2.6) is just the i-th component of Vkl and thus gives the total effect for the i-th exchange rate after k periods for news of type l. The numerator of (2.6), Гk,ijγlj, is the contribution of the j-th exchange rate to this total effect. If the instantaneous news effect in the j-th exchange rate is not zero (γlj ≠ 0) and there is volatility spillover (A and/or B are not diagonal), then this contribution will not be zero for k > 1. The ratio δijkl now gives the relative contribution of individual exchange rates' instantaneous news effects to the total news effects of other exchange rates in subsequent periods due to volatility spillover. Note that δijkl converges to the same proportion, δjl say, for k → ∞ irrespective of i. This is due to the fact that Гk/||Гk|| converges to a rank one matrix, see e.g. Friedland (2004), which implies that limk→∞ Гk,ij/ΣN r=1 Гk,ir is the same for all i. Thus, for very long horizons the contributions of the j-th exchange rate news effect to that of the i-th exchange rates is the same irrespective of i and given by δjl. A similar analysis of relative contributions can be performed with the accumulated volatility impulse responses, i.e. ΣN i=1 Vil. In an analogous way, we can define the accumulated relative news spillover effect from the j-th to the i-th exchange rate after k periods as         lrirm N r k m ljijm k m ijkl   ,11 ,1 , i,j = 1,…,N (2.7) The coefficient Δijkl represents the proportion of the total accumulated type l news effect of exchange rate i that can be attributed to the accumulated news effect of exchange rate j. Unlike the relative contribution at a given horizon k, the relative contribution of the accumulated volatility impulse responses converges as k → ∞ to a proportion that depends on i. 3. DATA AND EMPIRICAL RESULTS The database (provided by Olsen and Associates) consists of five-minute quotes for the EUR/USD, GBP/USD, and JPY/USD over the period ranging from May 15 to November 14, 2001 i.e. 6 months. These currency quotes are market makers' quotes and not transaction prices, as would be preferable. Since Danielsson and Payne (2002) showed that the statistical properties of five-minute US dollar/Deutsche Mark quotes are similar to those of transaction quotes, and transaction quotes are not widely available, we have resorted to using five minute Omrane and Hafner-Information Spillover, Volatility and the Currency Markets 54 quotes. The database also contains the date, the time-of-day stamped to the five minutes in Greenwich mean time (GMT), and the mid-quotes. The return at time t is computed as the difference between the logarithms of the mid-quotes2 at times t and t – 1, multiplied by 100 to get percentage returns. Because of scarce trading activity during the week-end, we excluded all returns computed between Friday 22h05 and Sunday 24h. In addition, we took into account the daylight saving time and we excluded the first return of each Monday to avoid possible biases due to the lack of activity during the week-end. The total number of returns is 37,653. The final data transformation consists of adjusting the returns for the intradaily seasonality component of volatility The seasonally adjusted returns are obtained by dividing each return by the standard deviation of all returns belonging to the corresponding intra-day five minute interval. An average value of volatility is computed and attributed to the endpoint of every 5 minute interval. The time series of these values constitutes an intradaily 'seasonal index' of volatility. This can be done by considering all days of the week as similar (an overall index), or by computing a specific index for each day of the week3. In the appendix we explain the details of the procedure we adopted to compute these indices and to adjust the returns. For example, the return of May 16, 2001, 9h05, is divided by the standard deviation of those returns over the whole sample that are recorded at 9h05. By construction, the average volatility for all adjusted series is one. Furthermore, our news announcements database includes the news headlines related to US macro-economic figures that were released on the Reuters news-alert screens over the May 15 to November 14, 2001 period. These events are time stamped to the minute and are a key feature of our news announcements analysis. A total of 142 news events are identified in our sample period. As in Bauwens et al. (2005), we classify the news into two categories, i.e. news that are considered positive or negative for the U.S. economy. Thus, we define two news dummy variables D1t and D2t corresponding to positive or negative news, respectively. To distinguish positive from negative news, we consider the difference between expected and realized values: if the realization is larger than the expectation and is a figure which corresponds to economic growth, the news is classified as positive; if the actual figure implies instead higher-than-expected inflation or a slowdown of the economy, it is regarded as negative. The expected values are given on Reuters screens a few days before the news announcements. Note that by assessing the effects of news announcements on the deseasonalized volatility, we consider only the unexpected components of news, see Bauwens et al. (2005). For the conditional mean μt in model (2.1) we specify an MA(2) model based on standard model selection criteria. To simplify the conditional variances in model (2.2) but still allow for volatility spillover, we let A be a full 3 × 3 parameter matrix but restrict B to be diagonal, thus containing only three parameters. We have tried additional lagged dummies in model (2.2), but none of them were significant. Thus, news events appear to be incorporated almost instantaneously (within five minutes) into exchange rate volatility. Our impulse response methodology permits us to analyse how these instantaneous effects are propagated through the system over time. 2 Where the mid-quote is the average of the bid and ask prices. 3 Since Bauwens et al. (2005) showed that each day of the week has its own seasonal profile, we have considered a specific index for each day of the week. International Econometric Review (IER) 55 EUR/USD (i=1) GBP/USD (i=2) JPY/USD (i=3) c0 0.0007 0.003 -0.003 (0.86) (0.45) (0.50) c1 -0.166 -0.137 -0.093 (0.00) (0.00) (0.00) c2 -0.026 -0.032 -0.024 (0.00) (0.00) (0.00) ωi 0.061 0.109 0.042 (0.00) (0.00) (0.00) Ai1 0.079 0.016 0.008 (0.00) (0.00) (0.00) Ai2 0.011 0.090 0.005 (0.00) (0.00) (0.00) Ai3 0.019 0.024 0.068 (0.00) (0.00) (0.00) Bii 0.826 0.756 0.875 (0.00) (0.00) (0.00) γ1i 0.215 0.316 0.107 (0.00) (0.00) (0.01) γ2i 0.201 0.096 0.013 (0.00) (0.22) (0.82) Table 3.1 Estimation results for equations (2.1) to (2.3). P-values are in parentheses. For the conditional mean equations, c0 is the intercept, c1 the MA(1) coefficient and c2 the MA(2) coefficient. The maximum eigenvalue of the matrix A+B is 0.949. The estimated constant conditional correlation between EUR/USD and GBP/USD is 0.3500, between EUR/USD and JPY/USD 0.1560 and between GBP/USD and JPY/USD 0.0922. The sample involves 37653 observations from May 15 to November 14, 2001. Estimation results of model (2.1)-(2.2) are given in Table 3.1. All first order MA coefficients are negative and highly significant, reflecting the bid-ask bounce effect. The diagonal elements of A tend to be higher than those off-diagonal, showing that the own lagged squared returns of an exchange rate have a higher impact on its volatility than those of other rates. However, there is significant spillover in volatilities, as all off-diagonal elements of A are significantly different from zero. Note that the estimator of B is substantially smaller than in typical GARCH estimates without exogenous news dummies, i.e. the estimated persistence is smaller. For example, for the full sample, the maximum eigenvalue of the matrix A + B is given by 0.949 as opposed to values typically much closer to one for GARCH (1,1) models applied to high-frequency FX rates. The reason is that some of the persistence is absorbed by the exogenous news. The estimated γ1 coefficients corresponding to positive news, which represents the instantaneous effect of positive news on volatility, is highest for GBP/USD (31.6 percent of average volatility), followed by EUR/USD (21.5 percent), and JPY/USD (10.7 percent). This is surprising as one would expect the highest effect in the largest and most liquid exchange Omrane and Hafner-Information Spillover, Volatility and the Currency Markets 56 rate, the EUR/USD. This latter is the largest FX market in terms of volume, liquidity and number of participants. Indeed, we see the largest instantaneous impact in the EUR/USD for negative news (γ2): 20.1 %, compared with 9.6 % of GBP/USD and 1.3 % for JPY/USD. There is an asymmetry of the amplitude of news effects on GBP/USD and JPY/USD volatility with respect to events of positive or negative news. k ∆t EUR/USD GBP/USD JPY/USD + − + − + − 1 5 min 0.2154 0.2014 0.3164 0.0958 0.1073 0.0131 (0.0569) (0.0689) (0.0713) (0.0538) (0.0504) (0.0422) 3 15 min 0.1766 0.1651 0.2271 0.0688 0.0954 0.0116 (0.0457) (0.0554) (0.0501) (0.0374) (0.0445) (0.0372) 6 30 min 0.1314 0.1229 0.1386 0.0419 0.0803 0.0098 (0.0331) (0.0467) (0.0296) (0.0216) (0.0371) (0.0310) 12 1 hour 0.0736 0.0688 0.0526 0.0159 0.0572 0.0070 (0.0181) (0.0215) (0.0110) (0.0077) (0.0262) (0.0217) 24 2 hours 0.0242 0.0226 0.0087 0.0027 0.0296 0.0036 (0.0068) (0.0071) (0.0035) (0.0028) (0.0138) (0.0111) 72 6 hours 0.0006 0.0006 0.0002 5.19e–005 0.0023 0.0003 (0.0006) (0.0004) (0.0004) (0.0003) (0.0015) (0.0010) 144 12 hours 1.16e–005 1.09e–005 3.79e–006 1.14e–006 5.31e–005 6.47e–006 (2.27e–005) (1.31e–005) (1.62e–005) (8.89e–006) (6.06e–005) (3.18e–005) 288 24 hours 6.13e–008 5.73e–009 2.02e–009 6.10e–010 2.83e–008 3.44e–009 (2.66e–008) (1.28e–008) (1.79e–008) (8.56e–009) (6.23e–008) (2.96e–008) Table 3.2 Estimates of volatility impulse responses k V ˆ . Standard errors (in parentheses) are calculated using (2.5). The symbol (+) indicates positive news (l = 1) and (–) negative news (l = 2). In Table 3.2 we report estimates of volatility impulse responses k V ˆ and standard errors calculated using (2.5). These could be used to construct confidence bands for Vk. Until roughly six hours, estimated Vk are significantly different from zero for all three FX rates. Table 3.3 shows the relative contributions δijkl, defined by (2.6) as the contribution of exchange rate j to the volatility impulse response Vkl of the i-th exchange rate, divided by the corresponding total value of Vkl. As shown in Section 2, all proportions converge to the same distribution δjl. For positive news (l = 1), these proportions are given by 26 percent explained by the Euro, 13.7 percent by the Pound, and 60.3 percent by the Yen. Thus, more than sixty percent of the long run impact of positive news can be attributed to an instantaneous shock in JPY/USD and its persistence over time. For a fixed k of one hour, for example, 77 percent of the news effect on the Euro after one hour is attributed to the initial effect on the Euro, 12 percent are attributed to the Pound, and 11 percent to the Yen. For negative news (l = 2), the asymptotic proportions are given by 68 percent explained by the Euro, 12 percent by the Pound, and 20 percent by the Yen. Thus, more than two thirds of the long run impact of International Econometric Review (IER) 57 negative news can be attributed to an instantaneous shock in EUR/USD and its persistence over time. k ∆t EUR/USD GBP/USD JPY/USD (j=1) (j=2) (j=3) + − + − + − EUR/USD 1 5min 1.0000 1.0000 0.0000 0.0000 0.0000 0.0000 (i=1) 3 15min 0.9468 0.9861 0.0332 0.0112 0.0199 0.0027 6 30min 0.8787 0.9674 0.0712 0.0254 0.0501 0.0072 12 1hour 0.7699 0.9358 0.1181 0.0465 0.1120 0.0177 24 2hours 0.6090 0.8834 0.1524 0.0716 0.2385 0.0450 72 6hours 0.3093 0.7247 0.1424 0.1081 0.5483 0.1673 144 12hours 0.2612 0.6804 0.1372 0.1157 0.6016 0.2040 288 24hours 0.2598 0.6788 0.1370 0.1160 0.6032 0.2052 GBP/USD 1 5min 0.0000 0.0000 1.0000 1.0000 0.0000 0.0000 (i=2) 3 15min 0.0260 0.0772 0.9546 0.9153 0.0193 0.0075 6 30min 0.0678 0.1887 0.8784 0.7918 0.0538 0.0195 12 1hour 0.1538 0.3840 0.7060 0.5705 0.1402 0.0456 24 2hours 0.2794 0.6237 0.3863 0.2792 0.3342 0.0971 72 6hours 0.2753 0.6939 0.1400 0.1143 0.5846 0.1918 144 12hours 0.2602 0.6793 0.1371 0.1159 0.6026 0.2048 288 24hours 0.2598 0.6788 0.1370 0.1160 0.6032 0.2052 JPY/USD 1 5min 0.0000 0.0000 0.0000 0.0000 1.0000 1.0000 (i=3) 3 15min 0.0320 0.1953 0.0307 0.0606 0.9373 0.7442 6 30min 0.0706 0.3469 0.0626 0.0994 0.8668 0.5537 12 1hour 0.1261 0.4873 0.0980 0.1225 0.7759 0.3902 24 2hours 0.1898 0.5946 0.1239 0.1256 0.6863 0.2798 72 6hours 0.2536 0.6724 0.1363 0.1170 0.6100 0.2105 144 12hours 0.2596 0.6787 0.1370 0.1160 0.6034 0.2054 288 24hours 0.2598 0.6788 0.1370 0.1160 0.6032 0.2052 Table 3.3 Relative contributions δijkl, defined by (2.6) as the contribution of exchange rate j (in the columns) to the volatility impulse reponse Vkl of the i-th exchange rate, divided by the corresponding total value of Vkl. The symbol (+) indicates positive news (l = 1) and (–) negative news (l = 2). Table 3.4 shows the relative contributions Δijkl, defined by (2.7) as the contribution of exchange rate j to the cumulated volatility impulse response Σk m=1 Vml of the i-th exchange rate, divided by the corresponding total value of Σk m=1 Vml. For positive news (γ1), in all three cases, most of the cumulated effect is explained by the own initial effect. For example, for the Yen the cumulated effect after one day attributed to the Euro is only 13.8 percent of the total cumulated effect. For negative news, however, the EUR/USD rate has a substantial impact