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4 XVI LIST OF FIGURES 4.2 Schematic scalar filtering window 103 5.1 Short-term autocorrelation of returns 123 5.2 Comparison between quoted and transaction spreads 125 5.3 Scaling law exponent as a function of time 128 5.4 Seasonality in the interest rates 129 5.5 Intraday distribution of 15-min mean changes of absolute returns 130 5.6 Cumulative distributions of 10-min, 1-day, and 1-week USD-JPY returns 136 5.7 Order statistics for Student-r distribution 139 5.8 Scaling law for USD-JPY and GBP-USD 149 5.9 Wavelet variance at different scales 160 5.10 Autocorrelations of hourly returns, absolute returns, and squared returns 161 5.11 Autocorrelation as a function of the power of the absolute returns 162 5.12 Hourly intraday and intraweek distribution of absolute return, spread and the tick frequency 165 5.13 Intraday analysis of Eurofutures 168 5.14 Deterministic volatility of Eurofutures 169 5.15 Cumulative distributions of spreads 172 6.1 The USD-DEM intraweek activity pattern 178 6.2 Activity functions of geographical market components 182 6.3 Histograms of the average hourly activity for USD-JPY and USD-CHF 185 6.4 The activity model for USD-JPY and USD-CHF 186 6.5 Comparison of tick activity and volatility for different data sources 188 6.6 The #-time versus physical time for USD-DEM 190 6.7 Hourly returns of USD-DEM in physical and #-time 191 6.8 Seasonality and wavelet filtering 194 6.9 Autocorrelations of the 5-min absolute returns for USD-DEM and USD-JPY 195 6.10 Autocorrelations of the 5-min filtered absolute returns for USD-DEM and USD-JPY 195 7.1 Interaction of trader groups 199 7.2 The bias of realized volatility 201 7.3 The residual bias of bias-corrected realized volatility 203 7.4 Autocorrelation function of USD-DEM in physical-time 205 7.5 Autocorrelation function of USD-DEM in #-time 206 7.6 USD-DEM autocorrelations from daily data 208 7.7 Coarse and fine volatilities 212 7.8 Asymmetric lagged correlation for USD-DEM 214
7.9 Asymmetric lagged correlation for Euromark IR futures 216 7.10 Asymmetry of lagged correlation 217 7.11 Conditional autocorrelation of returns 218 8.1 Estimated and theoretical GARCH coefficients in business time 226 8.2 Estimated and theoretical GARCH coefficients in #-time 227 8.3 GARCH estimates on a moving sample 230 8.4 Moment conditions for a HARCH(2) process 234 8.5 Impacts of market components for HARCH processes 241 9.1 Standard RiskMetrics volatility at different daytimes 252 9.2 Momentum indicator for forecasting 258 10.1 Autocorrelation of absolute returns for USD-DEM 277 10.2 Linear correlation coefficients for USD/DEM/NLG 280 10.3 Linear correlation coefficients for USD/DEM/GBP 281 10.4 Linear correlation coefficients for USD/DEM/TTL 282 10.5 Linear correlation coefficients for DJIA/AMEX 283 10.6 Linear correlation coefficients for USD 3-6M/DEM 3-6M 284 10.7 Linear correlation coefficients for DEM 3-6M/DEM 9- 12M 285 10*.8 Autocorrelations of correlation coefficients 286 10.9 Exponential decay of the autocorrelation of correlation coefficients 287 10.10 Correlation coefficients as a function of return time interval 289 10.11 Correlation versus logarithmic return time interval 290 10.12 Correlation stabilization intervals versus data frequencies 292 11.1 Data flow within a real-time trading model 298 11.2 Crossover operator 313 11.3 Syntactic restrictions for basic arithmetic operators 314 11.4 Total return of a portfolio of 10 O&A trading models 341 11.5 Set of feasible portfolios with currency hedging 342
LIST OF TABLES 2.1 The traditional FXFX page of Reuters 16 2.2 FX data frequency 18 4.1 Data cleaning filter structure 89 4.2 Credibility addition 90 4.3 Trust capital as a function of price move size and time interval 96 4.4 Active periods of the three generic markets 101 4.5 Data cleaning filter parameters 117 4.6 Data cleaning rejection rates 119 5.1 Moments of return distributions for FX rates 133 5.2 Moments of return distributions for FX cross rates 134 5.3 Tail index of FX returns 140 5.4 Tail index of FX cross rates 141 5.5 Tail index of spot interest rates 143 5.6 Estimated tail index for different data frequencies and sample sizes 144 5.7 Extreme risks in the FX market 146 5.8 Drift exponents for FX rates 150 5.9 Drift exponents for Eurofutures 151 5.10 Timezone conversion table 163 5.11 Average number of ticks versus day of the week 164 5.12 Average volatility versus day of the week 166
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