Modeling and forecasting exchange rate volatility in time-frequency domain

This paper proposes an enhanced approach to modeling and forecasting volatility using high frequency data. Using a forecasting model based on Realized GARCH with multiple time-frequency decomposed realized volatility measures, we study the influence of different timescales on volatility forecasts. The decomposition of volatility into several timescales approximates the behaviour of traders at corresponding investment horizons. The proposed methodology is moreover able to account for impact of jumps due to a recently proposed jump wavelet two scale realized volatility estimator. We propose a realized Jump-GARCH models estimated in two versions using maximum likelihood as well as observation-driven estimation framework of generalized autoregressive score. We compare forecasts using several popular realized volatility measures on foreign exchange rate futures data covering the recent financial crisis. Our results indicate that disentangling jump variation from the integrated variation is important for forecasting performance. An interesting insight into the volatility process is also provided by its multiscale decomposition. We find that most of the information for future volatility comes from high frequency part of the spectra representing very short investment horizons. Our newly proposed models outperform statistically the popular as well conventional models in both one-day and multi-period-ahead forecasting

Do Reuters spreads reflect currencies' differences in global trading activity?

A new estimate of the long-run impact of trading activity on bid-ask spreads in the foreign exchange markets is realized with a short panel containing around-the-clock Reuters quotes and global transaction volumes. Individual and time effects are accounted for in an unbalanced random effects model. In accordance with liquidity effect explanations the volume parameter is found to have a negative sign, although not at a high level of significance. The volatility parameter is positive and strongly significant. While the structural parameters of the model appear to be stable over time, the residuals are groupwise heteroscedastic. The higher standard error in 1992 might reflect the dynamic developments in the world forex market since 1989. Reuters quoting (tick) frequency is also tested as a measure of trading activity in spread estimations. The results turn out to be very similar to those with trading volumes, in particular when an instrumental variable estimator is employed to account for measurement errors or possible endogeneity problems

Realized wavelet-based estimation of integrated variance and jumps in the presence of noise

We introduce wavelet-based methodology for estimation of realized variance allowing its measurement in the time-frequency domain. Using smooth wavelets and Maximum Overlap Discrete Wavelet Transform, we allow for the decomposition of the realized variance into several investment horizons and jumps. Basing our estimator in the two-scale realized variance framework, we are able to utilize all available data and get feasible estimator in the presence of microstructure noise as well. The estimator is tested in a large numerical study of the finite sample performance and is compared to other popular realized variation estimators. We use different simulation settings with changing noise as well as jump level in different price processes including long memory fractional stochastic volatility model. The results reveal that our wavelet-based estimator is able to estimate and forecast the realized measures with the greatest precision. Our timefrequency estimators not only produce feasible estimates, but also decompose the realized variation into arbitrarily chosen investment horizons. We apply it to study the volatility of forex futures during the recent crisis at several investment horizons and obtain the results which provide us with better understanding of the volatility dynamics

Varying the VaR for Unconditional and Conditional Environments,

Accurate forecasting of risk is the key to successful risk management techniques. Using the largest stock index futures from twelve European bourses, this paper presents VaR measures based on their unconditional and conditional distributions for single and multi-period settings. These measures underpinned by extreme value theory are statistically robust explicitly allowing for fat-tailed densities. Conditional tail estimates are obtained by adjusting the unconditional extreme value procedure with GARCH filtered returns. The conditional modelling results in iid returns allowing for the use of a simple and efficient multi-period extreme value scaling law. The paper examines the properties of these distinct conditional and unconditional trading models. The paper finds that the biases inherent in unconditional single and multi-period estimates assuming normality extend to the conditional setting.

Varying the VaR for Unconditional and Conditional Environments

Accurate forecasting of risk is the key to successful risk management techniques. Using the largest stock index futures from twelve European bourses, this paper presents VaR measures based on their unconditional and conditional distributions for single and multi-period settings. These measures underpinned by extreme value theory are statistically robust explicitly allowing for fat-tailed densities. Conditional tail estimates are obtained by adjusting the unconditional extreme value procedure with GARCH filtered returns. The conditional modelling results in iid returns allowing for the use of a simple and efficient multi-period extreme value scaling law. The paper examines the properties of these distinct conditional and unconditional trading models. The paper finds that the biases inherent in unconditional single and multi-period estimates assuming normality extend to the conditional setting.extreme value theory; GARCH filter; conditional risk

Volatility Dynamics in Foreign Exchange Rates: Further Evidence from the Malaysian Ringgit and Singapore Dollar

Singapore dollar are analyzed in this paper. Our approach can simultaneously capture the empirical regularities of persistent and asymmetric effects in volatility and timevarying correlations of financial time series. Consistent with the results of Tse and Tsui (1997), there is only some weak support for asymmetric volatility in the case of the Malaysian ringgit when the two currencies are measured against the US dollar. However, there is strong evidence that depreciation shocks have a greater impact on future volatility levels compared with appreciation shocks of the same magnitude when both currencies measured against the yen. Moreover, evidence of time-varying correlation is highly significant when both currencies are measured against the yen. Regardless of the choice of the numeraire currency and the volatility models, shocks to exchange rate volatility are found to be significantly persistent.Constant correlations; Exchange rate volatility; Fractional integration; Long memory; Bivariate asymmetric GARCH; Varying correlations

Volatility Transmission in Emerging European Foreign Exchange Markets

This paper studies the dynamics of volatility transmission between Central European currencies and euro/dollar foreign exchange using model-free estimates of daily exchange rate volatility based on intraday data. We formulate a flexible yet parsimonious parametric model in which the daily realized volatility of a given exchange rate depends both on its own lags as well as on the lagged realized volatilities of the other exchange rates. We find evidence of statistically significant intra-regional volatility spillovers among the Central European foreign exchange markets. With the exception of the Czech currency, we find no significant spillovers running from euro/dollar to the Central European foreign exchange markets. To measure the overall magnitude and evolution of volatility transmission over time, we construct a dynamic version of the Diebold-Yilmaz volatility spillover index, and show that volatility spillovers tend to increase in periods characterized by market uncertainty.foreign exchange markets, volatility, spillovers, intraday data, nonlinear dynamics

Tail Behaviour of the Euro

This paper empirically analyses risk in the Euro relative to other currencies. Comparisons are made between a sub period encompassing the final transitional stage to full monetary union with a sub period prior to this. Stability in the face of speculative attack is examined using Extreme Value Theory to obtain estimates of tail exchange rate changes. The findings are encouraging. The Euro’s common risk measures do not deviate substantially from other currencies. Also, the Euro is stable in the face of speculative pressure. For example, the findings consistently show the Euro being less risky than the Yen, and having similar inherent risk to the Deutsche Mark, the currency that it is essentially replacing.

Tail Behaviour of the Euro

This paper empirically analyses risk in the Euro relative to other currencies. Comparisons are made between a sub period encompassing the final transitional stage to full monetary union with a sub period prior to this. Stability in the face of speculative attack is examined using Extreme Value Theory to obtain estimates of tail exchange rate changes. The findings are encouraging. The Euro’s common risk measures do not deviate substantially from other currencies. Also, the Euro is stable in the face of speculative pressure. For example, the findings consistently show the Euro being less risky than the Yen, and having similar inherent risk to the Deutsche Mark, the currency that it is essentially replacing.Extreme Value Theory; Tail Behaviour; GARCH; The Euro