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`Dacorogna
`Gencay
`Muller
`Olsen
`Pictet
`
`Michel
`Ramazan
`Ulrich
`Richard
`Olivier
`
`M.
`
`A
`B.
`V.
`
`Zurich, Switzerland
`Windsor, Ontario, Canada
`Zurich, Switzerland
`Zurich, Switzerland
`Zurich, Switzerland
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`TITLE OF THE INVENTION (280 characters max)
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`High-Frequency Finance Methods
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`F74
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`NY2 -1177882.1
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`GAIN CAPITAL - EXHIBIT 1003
`
`0001
`
`

`

`AN INTRODUCTION
`TO
`HIGH-FREQUENCY
`FINANCE
`
`1.•
`
`Michel M. Dacorogna
`Zurich Re, Switzerland
`
`Ramazan Gencay
`University of Windsor, Canada
`Olsen & Associates, Switzerland
`
`Ulrich A. Muller
`Olsen & Associates, Switzerland
`
`Richard B. Olsen
`Olsen & Associates, Switzerland
`
`Olivier V. Pictet
`Dynamic Asset Management, Switzerland
`
`0002
`
`

`

`CONTENTS
`
`LIST OF FIGURES xv
`
`LIST OF TABLES xix
`
`PREFACE xxi
`
`ACKNOWLEDGMENTS xxiii
`
`1
`INTRODUCTION
`1.1 Markets: The Source of High-Frequency Data
`1.2 Methodology of High-Frequency Research
`1.3 Data Frequency and Market Information
`1.4 New Levels of Significance
`1.5 Interrelating Different Time Scales
`
`1
`2
`3
`6
`8
`
`vii
`
`0003
`
`

`

`viii
`
`CONTENTS
`
`2
`MARKETS AND DATA
`2.1 General Remarks on Markets and Data Types
`2.1.1 Spot Markets
`2.1.2 Futures Markets
`2.1.3 Option Markets
`2.2 Foreign Exchange Markets
`2.2.1 Structure of the Foreign Exchange Spot Market
`2.2.2 Synthetic Cross Rates
`2.2.3 Multiple Contributor Effects
`2.3 Over-the-Counter Interest Rate Markets
`2.3.1 Spot Interest Rates
`2.3.2 Foreign Exchange Forward Rates
`Interest Rate Futures
`2.4.1 General Description of Interest Rate Futures
`2.4.2 Implied Forward Interest Rates and Yield Curves
`2.5 Bond Futures Markets
`2.5.1 Bonds and Bond Futures
`2.5.2 Rollover Schemes
`2.6 Commodity Futures
`2.7 Equity Markets
`
`2.4
`
`3
`TIME SERIES OF INTEREST
`3.1 Time Series and Operators
`3.2 Variables in Homogeneous Time Series
`3.2.1 Interpolation
`3.2.2 Price
`3.2.3 Return
`3.2.4 Realized Volatility
`3.2.5 Bid-Ask Spread
`3.2.6 Tick Frequency
`3.2.7 Other Variables
`3.2.8 Overlapping Returns
`3.3 Convolution Operators
`3.3.1 Notation Used for Time Series Operators
`3.3.2 Linear Operator and Kernels
`3.3.3 Build-Up Time Interval
`3.3.4 Homogeneous Operators and Robustness
`3.3.5 Exponential Moving Average (EMA)
`3.3.6 The Iterated EMA Operator
`3.3.7 Moving Average (MA)
`
`10
`11
`12
`13
`13
`15
`19
`19
`20
`21
`22
`23
`23
`25
`28
`28
`29
`31
`32
`
`34
`37
`37
`38
`40
`41
`45
`46
`46
`47
`51
`53
`54
`56
`58
`59
`59
`61
`
`0004
`
`

`

`CONTENTS
`
`3.3.8 Moving Norm, Variance, and Standard Deviation
`3.3.9 Differential
`3.3.10 Derivative and y-Derivative
`3.3.11 Volatility
`3.3.12 Standardized Time Series, Moving Skewness, and Kurtosis
`3.3.13 Moving Correlation
`3.3.14 Windowed Fourier Transform
`3.4 Microscopic Operators
`3.4.1 Backward Shift and Time Translation Operators
`3.4.2 Regular Time Series Operator
`3.4.3 Microscopic Return, Difference, and Derivative
`3.4.4 Microscopic Volatility
`3.4.5 Tick Frequency and Activity
`
`4
`ADAPTIVE DATA CLEANING
`4.1 Introduction: Using a Filter to Clean the Data
`4.2 Data and Data Errors
`4.2.1 Time Series of Ticks
`4.2.2 Data Error Types
`4.3 General Overview of the Filter
`4.3.1 The Functionality of the Filter
`4.3.2 Overview of the Filtering Algorithm and Its Structure
`4.4 Basic Filtering Elements and Operations
`4.4.1 Credibility and Trust Capital
`4.4.2 Filtering of Single Scalar Quotes: The Level Filter
`4.4.3 Pair Filtering: The Credibility of Returns
`4.4.4 Computing the Expected Volatility
`4.4.5 Pair Filtering: Comparing Quote Origins
`4.4.6 A Time Scale for Filtering
`4.5 The Scalar Filtering Window
`4.5.1 Entering a New Quote in the Scalar Filtering Window
`4.5.2 The Trust Capital of a New Scalar Quote
`4.5.3 Updating the Scalar Window
`4.5.4 Dismissing Quotes from the Scalar Window
`4.5.5 Updating the Statistics with Credible Scalar Quotes
`4.5.6 A Second Scalar Window for Old Valid Quotes
`4.6 The Full-Quote Filtering Window
`4.6.1 Quote Splitting Depending on the Instrument Type
`4.6.2 The Basic Validity Test
`4.6.3 Transforming the Filtered Variable
`4.7 Univariate Filtering
`
`IX
`
`63
`64
`66
`68
`71
`71
`74
`76
`77
`77
`78
`79
`79
`
`82
`84
`84
`85
`86
`86
`88
`88
`89
`91
`93
`96
`98
`100
`103
`104
`104
`106
`107
`108
`108
`109
`110
`110
`112
`113
`
`0005
`
`

`

`X
`
`CONTENTS
`
`4.7.1 The Results of Univariate Filtering
`4.7.2 Filtering in Historical and Real-Time Modes
`4.7.3 Choosing the Filter Parameters
`4.8 Special Filter Elements
`4.8.1 Multivariate Filtering: Filtering Sparse Data
`4.9 Behavior and Effects of the Data Filter
`
`5
`BASIC STYLIZED FACTS
`
`5.1 Introduction
`5.2 Price Formation Process
`5.2.1 Negative First-Order Autocorrelation of Returns
`5.2.2 Discreteness of Quoted Spreads
`5.2.3 Short-Term Triangular Arbitrage
`5.3 Institutional Structure and Exogeneous Impacts
`5.3.1 Institutional Framework
`5.3.2 Positive Impact of Official Interventions
`5.3.3 Mixed Effect of News
`5.4 Distributional Properties of Returns
`5.4.1 Finite Variance, Symmetry and Decreasing Fat-Tailedness
`5.4.2 The Tail Index of Return Distributions
`5.4.3 Extreme Risks in Financial Markets
`5.5 Scaling Laws
`5.5.1 Empirical Evidence
`5.5.2 Distributions and Scaling Laws
`5.5.3 A Simple Model of the Market Maker Bias
`5.5.4 Limitations of the Scaling Laws
`5.6 Autocorrelation and Seasonality
`5.6.1 Autocorrelations of Returns and Volatility
`5.6.2 Seasonal Volatility: Across Markets for OTC Instruments
`5.6.3 Seasonal Volatility: U-Shaped for Exchange Traded
`Instruments
`5.6.4 Deterministic Volatility in Eurofutures Contracts
`5.6.5 Bid-Ask Spreads
`
`6
`MODELING SEASONAL VOLATILITY
`6.1 Introduction
`6.2 A Model of Market Activity
`6.2.1 Seasonal Patterns of the Volatility and Presence of Markets
`
`114
`115
`116
`116
`116
`118
`
`121
`123
`123
`125
`127
`127
`127
`129
`129
`132
`132
`135
`144
`147
`147
`151
`154
`158
`160
`161
`163
`
`167
`169
`170
`
`174
`175
`175
`
`0006
`
`

`

`CONTENTS
`
`6.2.2 Modeling the Volatility Patterns with an Alternative Time
`Scale and an Activity Variable
`6.2.3 Market Activity and Scaling Law
`6.2.4 Geographical Components of Market Activity
`6.2.5 A Model of Intraweek Market Activity
`6.2.6 Interpretation of the Activity Modeling Results
`6.3 A New Business Time Scale (0-Scale)
`6.3.1 Definition of the 19—Scale
`6.3.2 Adjustments of the 1,-Scale Definition
`6.3.3 A Ratio Test for the 2,-Scale Quality
`6.4 Filtering Intraday Seasonalities with Wavelets
`
`7
`REALIZED VOLATILITY DYNAMICS
`7.1 Introduction
`7.2 The Bias of Realized Volatility and Its Correction
`7.3 Conditional Heteroskedasticity
`7.3.1 Autocorrelation of Volatility in 6-Time
`7.3.2 Short and Long Memory
`7.4 The Heterogeneous Market Hypothesis
`7.4.1 Volatilities of Different Time Resolutions
`7.4.2 Asymmetric Lead-Lag Correlation of Volatilities
`7.4.3 Conditional Predictability
`
`8
`VOLATILITY PROCESSES
`
`8.1 Introduction
`8.2 Intraday Volatility and GARCH Models
`8.2.1 Parameter Estimation of GARCH Models
`8.2.2 Temporal Aggregation of GARCH Models
`8.2.3 Estimates of GARCH(1,1) for Various Frequencies
`8.3 Modeling Heterogeneous Volatilities
`8.3.1 The HARCH Model
`8.3.2 HARCH and Market Components
`8.3.3 Generalization of the Process Equation
`8.3.4 EMA-HARCH Model
`8.3.5 Estimating HARCH and EMA-HARCH Models
`8.3.6 HARCH in Interest Rate Modeling
`8.4 Forecasting Short-Term Volatility
`8.4.1 A Framework to Measure the Forecasting Performance
`8.4.2 Performance of ARCH-Type Models
`
`xi
`
`176
`177
`178
`179
`183
`188
`188
`189
`192
`193
`
`197
`198
`204
`204
`207
`209
`210
`211
`215
`
`219
`221
`222
`224
`226
`231
`231
`234
`237
`237
`239
`242
`243
`243
`246
`
`0007
`
`

`

`xi i
`
`CONTENTS
`
`9
`FORECASTING RISK AND RETURN
`Introduction to Forecasting
`9.1
`9.2 Forecasting Volatility for Value-at-Risk
`9.2.1 Three Simple Volatility Forecasting Models
`9.2.2 Choosing the Best Volatility Forecasting Model
`9.3 Forecasting Returns over Multiple Time Horizons
`9.3.1 Intrinsic Time
`9.3.2 Model Structure
`9.3.3 A Linear Combination of Nonlinear Indicators
`9.3.4 Moving Averages, Momenta, and Indicators
`9.3.5 Continuous Coefficient Update
`9.4 Measuring Forecast Quality
`9.4.1 Appropriate Measures of Forecast Accuracy
`9.4.2 Empirical Results for the Multi-Horizon Model
`9.4.3 Forecast Effectiveness in Intraday Horizons
`
`10
`CORRELATION AND MULTIVARIATE RISK
`10.1 Introduction
`10.2 Estimating the Dependence of Financial Time Series
`10.3 Covolatility Weighting
`10.3.1 Formulation of an Adjusted Correlation Measure
`10.3.2 Monte Carlo and Empirical Tests
`10.4 Stability of Return Correlations
`10.4.1 Correlation Variations over Time
`10.4.2 The Exponential Memory of Return Correlations
`10.5 Correlation Behavior at High Data Frequencies
`10.6 Conclusions
`
`11
`TRADING MODELS
`
`11.1 Introduction
`11.2 Real-Time Trading Strategies
`11.2.1 The Trading Model and Its Data-Processing Environment
`11.2.2 Simulated Trader
`11.3 Risk Sensitive Performance Measures
`11.3.1 Xeff: A Symmetric Effective Returns Measure
`11.3.2 Reif: An Asymmetric Effective Returns Measure
`11.4 Trading Model Algorithms
`
`248
`250
`250
`254
`255
`255
`256
`256
`257
`259
`261
`262
`263
`264
`
`268
`269
`270
`272
`274
`277
`278
`282
`287
`293
`
`295
`297
`299
`303
`304
`305
`307
`309
`
`0008
`
`

`

`CONTENTS
`
`11.4.1 An Example of a Trading Model
`11.4.2 Model Design with Genetic Programming
`11.5 Optimization and Testing Procedures
`11.5.1 Robust Optimization with Genetic Algorithms
`11.5.2 Testing Procedures
`11.6 Statistical Study of a Trading Model
`11.6.1 Heterogeneous Real-Time Trading Strategies
`11.6.2 Price-Generation Processes and Trading Models
`11.7 Trading Model Portfolios
`11.8 Currency Risk Hedging
`11.8.1 The Hedging Ratio and the "Neutral Point"
`11.8.2 Risk/Return of an Overlay with Static and Dynamic
`Positions
`11.8.3 Dynamic Hedging with Exposure Constraints
`11.8.4 Concluding Remarks
`
`12
`TOWARD A THEORY
`OF HETEROGENEOUS MARKETS
`12.1 Definition of Efficient Markets
`12.2 Dynamic Markets and Relativistic Effects
`12.3 Impact of the New Technology
`12.4 Zero-Sum Game or Perpetuum Mobile?
`12.5 Discussion of the Conventional Definition
`12.6 An Improved Definition of "Efficient Markets"
`
`XIii
`
`310
`311
`317
`317
`321
`323
`323
`328
`338
`340
`343
`
`344
`345
`346
`
`349
`350
`352
`353
`354
`354
`
`BIBLIOGRAPHY 356
`
`INDEX 376
`
`0009
`
`

`

`LIST OF FIGURES
`
`Size and data frequency of different samples
`1.1
`1.2 Models versus time scale
`1.3 Volatility with daily versus high-frequency data
`3.1
`Types of time series operators
`3.2
`Interpolation methods
`3.3 Overlapping time intervals
`3.4 One week of USD-CHF prices
`3.5 Moving average (MA) kernel
`3.6 MA kernel on a logarithmic scale
`Schematic differential kernel
`3.7
`3.8 Kernel of a differential operator
`3.9 Decay of a differential kernel
`3.10 Differential and return
`3.11 Distribution of derivative operator
`3.12 Annualized volatility as a moving norm
`3.13 Moving moments of returns
`3.14 Kernel of a windowed Fourier operator
`3.15 Normed windowed Fourier transform
`3.16 Microscopic volatility
`3.17 Tick activity
`4.1
`Flowchart of a data-cleaning filter
`
`xv
`
`4
`5
`7
`36
`38
`48
`53
`61
`62
`64
`65
`66
`67
`68
`71
`72
`75
`77
`79
`80
`87
`
`0010
`
`

`

`XVi
`
`LIST OF FIGURES
`
`Schematic scalar filtering window
`4.2
`5.1
`Short-term autocorrelation of returns
`5.2 Comparison between quoted and transaction spreads
`Scaling law exponent as a function of time
`5.3
`5.4
`Seasonality in the interest rates
`Intraday distribution of 15-min mean changes of absolute returns
`5.5
`5.6 Cumulative distributions of 10-min, 1-day, and 1-week USD-JPY
`returns
`5.7 Order statistics for Student-t distribution
`Scaling law for USD-JPY and GBP-USD
`5.8
`5.9 Wavelet variance at different scales
`5.10 Autocorrelations of hourly returns, absolute returns, and squared
`returns
`5.11 Autocorrelation as a function of the power of the absolute returns
`5.12 Hourly intraday and intraweek distribution of absolute return,
`spread and the tick frequency
`5.13
`Intraday analysis of Eurofutures
`5.14 Deterministic volatility of Eurofutures
`5.15 Cumulative distributions of spreads
`6.1 The USD-DEM intraweek activity pattern
`6.2 Activity functions of geographical market components
`6.3 Histograms of the average hourly activity for USD-JPY and
`USD-CHF
`The activity model for USD-JPY and USD-CHF
`Comparison of tick activity and volatility for different data
`sources
`6.6
`The .a-time versus physical time for USD-DEM
`6.7 Hourly returns of USD-DEM in physical and i9-time
`6.8
`Seasonality and wavelet filtering
`6.9 Autocorrelations of the 5-min absolute returns for USD-DEM and
`USD-JPY
`6.10 Autocorrelations of the 5-min filtered absolute returns for
`USD-DEM and USD-JPY
`7.1
`Interaction of trader groups
`7.2
`The bias of realized volatility
`7.3
`The residual bias of bias-corrected realized volatility
`7.4 Autocorrelation function of USD-DEM in physical-time
`7.5 Autocorrelation function of USD-DEM in '0-time
`7.6 USD-DEM autocorrelations from daily data
`7.7
`Coarse and fine volatilities
`7.8 Asymmetric lagged correlation for USD-DEM
`
`6.4
`6.5
`
`103
`123
`125
`128
`129
`130
`
`136
`139
`149
`160
`
`161
`162
`
`165
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`169
`172
`178
`182
`
`185
`186
`
`188
`190
`191
`194
`
`195
`
`195
`199
`201
`203
`205
`206
`208
`212
`214
`
`0011
`
`

`

`LIST OF FIGURES
`
`7.9 Asymmetric lagged correlation for Euromark IR futures
`7.10 Asymmetry of lagged correlation
`7.11 Conditional autocorrelation of returns
`8.1
`Estimated and theoretical GARCH coefficients in business time
`Estimated and theoretical GARCH coefficients in 1,-time
`8.2
`8.3 GARCH estimates on a moving sample
`8.4 Moment conditions for a HARCH(2) process
`8.5
`Impacts of market components for HARCH processes
`9.1
`Standard RiskMetrics volatility at different daytimes
`9.2 Momentum indicator for forecasting
`10.1 Autocorrelation of absolute returns for USD-DEM
`10.2 Linear correlation coefficients for USD/DEM/NLG
`10.3 Linear correlation coefficients for USD/DEM/GBP
`10.4 Linear correlation coefficients for USD/DEM/ITL
`10.5 Linear correlation coefficients for DJIA/AMEX
`10.6 Linear correlation coefficients for USD 3-6M/DEM 3-6M
`10.7 Linear correlation coefficients for DEM 3-6M/DEM 9-12M
`10.8 Autocorrelations of correlation coefficients
`10.9 Exponential decay of the autocorrelation of correlation
`coefficients
`10.10 Correlation coefficients as a function of return time interval
`10.11 Correlation versus logarithmic return time interval
`10.12 Correlation stabilization intervals versus data frequencies
`11.1 Data flow within a real-time trading model
`11.2 Crossover operator
`11.3 Syntactic restrictions for basic arithmetic operators
`11.4 Total return of a portfolio of 10 O&A trading models
`11.5 Set of feasible portfolios with currency hedging
`
`XVi i
`
`216
`217
`218
`226
`227
`230
`234
`241
`252
`258
`277
`280
`281
`282
`283
`284
`285
`286
`
`287
`289
`290
`292
`298
`313
`314
`341
`342
`
`0012
`
`

`

`LIST OF TABLES
`
`2.1
`The traditional FXFX page of Reuters
`FX data frequency
`2.2
`4.1 Data cleaning filter structure
`4.2
`Credibility addition
`4.3
`Trust capital as a function of price move size and time interval
`4.4 Active periods of the three generic markets
`4.5 Data cleaning filter parameters
`4.6 Data cleaning rejection rates
`5.1 Moments of return distributions for FX rates
`5.2 Moments of return distributions for FX cross rates
`5.3
`Tail index of FX returns
`5.4
`Tail index of FX cross rates
`5.5
`Tail index of spot interest rates
`Estimated tail index for different data frequencies and sample
`5.6
`sizes
`5.7
`Extreme risks in the FX market
`5.8 Drift exponents for FX rates
`5.9 Drift exponents for Eurofutures
`5.10 Timezone conversion table
`5.11 Average number of ticks versus day of the week
`5.12 Average volatility versus day of the week
`
`16
`18
`89
`90
`96
`101
`117
`119
`133
`134
`140
`141
`143
`
`144
`146
`150
`151
`163
`164
`166
`
`xix
`
`0013
`
`

`

`X X
`
`LIST OF TABLES
`
`5.13 Correlation coefficients between activity measures
`5.14 Average spreads versus day of the week
`6.1 Definition of the three generic markets
`6.2
`The 19-time parameter estimates for the three generic markets
`The volatility ratio for the quality of the 7 -scale
`6.3
`7.1 Difference between lagged correlations
`8.1 Results of a GARCH(1,1) estimation in business time
`8.2 Results of a GARCH(1,1) estimation in 79-time
`8.3 Market components of a HARCH process
`8.4 HARCH coefficients for USD-DEM
`8.5 Results of the EMA-HARCH for the LIFFE Three-Month
`Euromark
`8.6 Volatility forecasting performance for USD-DEM
`9.1
`The sampling periods of the forecast study
`9.2
`Forecast quality for 10 FX rates against the USD
`9.3
`Forecast quality for 10 FX cross rates
`9.4
`Significance of the forecast quality for 20 FX rates
`10.1 Correlations from Monte Carlo simulations
`10.2 Data sampling for correlation as function of time
`10.3 Mean values, variances, maxima and minima of correlation
`10.4 Estimation results of the autocorrelation of correlation
`10.5 Correlation results characterizing the Epps effect
`11.1 Market time constraints
`11.2 Trading model results versus tree complexity
`11.3 Performance comparison between models
`11.4 Performance comparison between markets
`11.5 The best Xeff as a function of opening hours
`11.6 p-value Comparisons
`11.7 Random walk Simulations for USD-DEM
`11.8 GARCH(1,1) parameter estimates
`11.9 GARCH(1,1) simulations for USD-DEM
`11.10 AR(4)-GARCH(1,1) parameter estimates
`11.11 AR(4)-GARCH(1,1) simulations for USD-DEM
`11.12 Portfolio performance of O&A trading models
`
`167
`171
`180
`184
`192
`213
`228
`229
`236
`240
`
`242
`246
`264
`265
`266
`267
`275
`278
`279
`288
`291
`299
`316
`324
`325
`326
`331
`332
`334
`335
`337
`338
`340
`
`1.4
`
`0014
`
`

`

`PREFACE
`
`T his book presents a unified view of high-frequency time series methods
`
`with a particular emphasis on foreign exchange markets as well as interest
`rate spot and futures markets. The scope of this book is also applicable
`to other markets, such as equity and commodity markets.
`As the archetype of financial markets, the foreign exchange market is the
`largest financial market worldwide. It involves dealers in different geographic loca-
`tions, time zones, and working hours who have different time horizons, home cur-
`rencies, information access, transaction costs, and other institutional constraints.
`The time horizons vary from intraday dealers, who close their positions every
`evening, to long-term investors and central banks. In this highly complex and
`heterogeneous market structure, the market participants are faced with different
`constraints and use different strategies to reach their financial goals, such as by
`maximizing their profits or maximizing their utility function after adjusting for
`market risk.
`This book provides a framework to the analysis, modeling, and inference of
`high-frequency financial time series. It begins with the elementary foundations
`and definitions needed for studying the fundamental properties of high-frequency
`financial time series. It extends into the adaptive data-cleaning issues, treatment
`of seasonal volatility, and modeling of intraday volatility. Fractal properties of the
`high-frequency financial time series are found and explored, and an intrinsic time
`is used to construct forecasting models. The book provides a detailed study of how
`the adopted framework can be effectively utilized to build econometric models of
`
`xxi
`
`0015
`
`

`

`XXii
`
`PREFACE
`
`the price-formation process. Going beyond the price-formation process, the book
`presents the techniques to construct real-time trading models for financial assets.
`It is designed for those who might be starting research in the area as well as for
`those who are interested in appreciating the statistical and econometric theory that
`underlies high-frequency financial time series modeling. The targeted audience
`includes finance professionals, including risk managers and research profession-
`als in the public and private sectors; those taking graduate courses in finance,
`economics, econometrics, statistics, and time series analysis; and advanced MBA
`students. Because the high-frequency finance field is relatively new and the lit-
`erature is scattered in a wide range of academic and nonacademic platforms, this
`book aims to provide a uniform treatment of the field and an easily accessible
`platform to high-frequency financial time series analysis — an exciting new field
`of research.
`With the development of this field, a huge new area of research has been
`initiated, where work has hardly started. This work could not be more fascinating,
`and a number of discoveries are waiting to be made. We expect research to increase
`in this field, as people start to understand how these insights can dramatically
`improve risk-adjusted performances in asset management, market making, and
`treasury functions and be the foundation for other applications, such as an early
`warning system of financial markets.
`
`Michel M. Dacorogna
`Ramazan Gengay
`Ulrich A. Muller
`Richard B. Olsen
`Olivier V Pictet
`
`0016
`
`

`

`ACKNOWLEDGMENTS
`
`W e should start by acknowledging that 15 years ago, when our research
`
`team at Olsen & Associates (O&A) first began using the amazing
`magnifying glass provided by high-frequency data to see if we could
`uncover possible patterns in the financial markets, none of us anticipated just how
`expansive the effort would become.
`With the publication of this book originating from our work, sincere thanks are
`due to so many that we can only hope we have recognized most of the colleagues
`and friends who have advanced our work. Their help, their encouragement, their
`criticism, and their friendship have contributed to the style of teamwork we always
`favored.
`We begin with Matthias Schwarz, a biology student who computed the first
`scaling law working with us in the autumn of 1986. Our first academic visitor
`was Claude Morgenegg, coming from the University of Geneva, who taught our
`group of physicists the right language to use to reach the economists. Thanks
`also to Casper de Vries, who opened up for us the world of extreme value the-
`ory; Cindy L. Gauveau, who prepared forecasting models for foreign exchange
`rates and also brought the economic touch to our work; Rakhal Dave, for his
`explorations of the LeBaron effect; Marco Tomassini and Bastien Chopard, who
`brought to our attention the genetic algorithms; Mark Lundin and his correla-
`tion studies; Gennady Samorodnitsky and Paul Embrechts, who were able to
`prove the sufficiency of the stationarity condition of HARCH processes; Giuseppe
`Ballocchi, who led us into the research on interest rate futures; and Wolfgang
`
`0017
`
`

`

`XXiV
`
`ACKNOWLEDGMENTS
`
`Breymann, who has extended the g-time concept and developed the idea of a
`heterogeneous market in his cascade model. A particular thanks goes to Gilles
`Zumbach, who has contributed many graphs to this book. He continues the work,
`bringing it to new levels and uncovering many more properties with the powerful
`operator framework and the software tools in C++ that he has developed over the
`years.
`We also want to thank our colleagues who joined us at a later stage and have
`already reached out for other adventures: Lars Jaeger, Thomas Domenig, Peter
`Rice, and Hoss Hauksson. Our thanks extend also to Jurgen Olsen, whose wisdom
`and vast scientific culture has enlightened our seminars and whose road map for
`building a Richter scale for financial markets we implemented.
`One very important and enriching experience has been the visits of many
`students who spent time with us and brought along their enthusiasm and eager-
`ness to learn: Dominique Guillaume; Lukas Pulver; Petra Korndoerfer; Markus P.
`Herrchen; Jens Richelsen; Christian Jost; Jfirg S. Fiissler; Retus G. Sgier; Alexan-
`der Dimai; Jonathan Dawes; Jakob E. von Weizsdcker; Philipp Hartmann; Citalin
`Staried; Barbara Piccinato; Carl Hopman; Peter Rice, who later j oined our research
`team; Simone Deparis; Fulvio Corsi; and Paul Lynch. Without them, we would
`never have been able to explore so many different time series and to accomplish
`so many studies.
`Many of our academic friends around the world visited us and understood
`early on the interest in research on this type of data. They provided us with en-
`couragement to continue and the sense that we were working in the right direction.
`Hermann Garbers was the first to invite us to give a seminar at the University
`of Zurich, where we presented the scaling law in December 1988. From Benoit
`Mandelbrot in 1989 to Gennady Samorodnitsky just prior to the publication of this
`book, we have been fortunate to share time and work at O&A with some fine sci-
`entists: Tim Bollerslev, William Brock, Hans Bahlmann, Peter Biihlmann, Frank
`K. Diebold, Christian Dunis, Riidiger Frey, Helyette Geman, Charles Goodhart,
`Rudolf Kalman, Hans Rudolf Lerche, Bruce Mizrach, John Moody, Salih Neftci,
`Wolfgang Polasek, Remo Schnidrig, Albert N. Shiryaev, Gerhard Stahl, Massimo
`Tivegna, Murad Taqqu, Walter Wasserfallen, Andreas Weigend, and Diethelm
`Wiirtz. We would like to thank especially Charles Goodhart, whose support and
`insights led to the O&A "High-Frequency Data in Finance" conferences, but also
`Richard Baillie, Tim Bollerslev, Rob Engle, Joel Hasbrouck, Michael Melvin, and
`Maureen O'Hara. Gerhard Stahl has been a great partner in exploring new issues of
`risk management His scientific rigor was always refreshing in this field where ad
`hoc arguments often dominate. Michel Dacorogna would like to thank particularly
`Blake LeBaron for the many e-mail exchanges we have had over the years on our
`research. They were always stimulating and encouraged us to think deeper into the
`problems and find the connections with the traditional economic approach. Man-
`fred Harter and Mico Loretan have been always supportive of our work and have
`brought to us many ideas and opportunities for presenting it. Ramo Gencay would
`like to thank William Brock, Dee Dechert, Murray Frank, Blake LeBaron, and
`
`0018
`
`

`

`ACKNOWLEDGMENTS
`
`XXV
`
`Thanasis Stengos for many exciting research conversations and Michael Charette,
`Ron Meng and Tibor Toronyi for research support. Ulrich Muller would like
`to thank Gunter Schwarz for his contribution to our understanding of portfolio
`theory.
`It is also clear that without the help and the dedication of our software team we
`would not have been able to access a database of such quantity and quality, cover-
`ing more than 14 years of tick-by-tick prices. From Rob J. Nagler to Kris Meissner
`through J. Robert Ward, William H. Kelly, Daniel P. Smith, Martin Lichtin, Devon
`Bowen, and Michael Stumm, we learned the subtleties of object-oriented program-
`ming and have enjoyed their constant support in our efforts to make sense of all that
`we were seeing. Paul Breslaw has been so helpful with the data and improving our
`English. Our thanks go also to our friends from the operation group who kept alive
`our system, especially Jorge Mota, Jeff Courtade, and Gary Swofford. Whenever
`we had a problem with bulbs going out of function or air conditioning not working
`(especially when it was needed most), Filippo Guglielmo would always be here to
`solve it.
`The trading model developments would not have been so interesting, nor
`so close to reality, without the contribution of our help desk: Pius Dall'Acqua,
`Stephan Schlatter, and last, but not least, Bernard Hechinger and his deep knowl-
`edge of the microstructure of financial markets. His interest in our models has
`brought us to rethink many aspects of their strategies and implement some of his
`ideas. In terms of market knowledge, we especially want to thank Dean LeBaron,
`whose vast experience and enthusiasm for new developments is a source of in-
`spiration and encouragement. Our customers also brought many ideas to us,
`especially in the group who participated in the development of the interest rate
`project: Michael Brockmann, Dieter Heitkamp, Luciano Steve, and Giuseppe
`Ciliberto. We always enjoyed the exchanges with the practitioners who under-
`stood the need for a scientific approach to the markets. Another example of
`this fertile interaction was with Monique Donders, Tjark Tjin, and Marcel Ver-
`nooy during our project of building a currency overlay product based on trad-
`ing models. Special thanks go also to Daniel Huber, who opened up so many
`doors for us.
`There is no question that we benefited greatly from the structure and orga-
`nization provided by our different administrative assistants over the years. Karin
`Jost, Rosemarie Arnold-Becker, and Melanie Kaslin all brought a strong sense of
`service and dedication that made our teamwork possible.
`The process of writing a book with many authors is complex and demanding
`but also very rewarding because it gave us the occasion to discuss, deepen our
`understanding of the matters and interact with interesting people. In this pro-
`cess, Scott Bentley's (the senior editor of Academic Press) help and feedback have
`been important for keeping the level of motivation high and for the success of this
`project. The care of Amy Hendrickson for many BTEX formatting problems of a
`book of more than 400 pages and containing so many figures was essential for the
`resulting appearance of this book.
`
`0019
`
`

`

`XXV1
`
`ACKNOWLEDGMENTS
`
`Before closing this page of gratitude, we do not want to forget Dina Weid-
`mann and Elisa Guglielmo, who cooked so many fine dishes with the Italian touch
`and make O&A's famous "Friday family lunches" a genuine gourmet experience.
`Faced with mountains of data to unravel, this lovely tradition warmed the soul.
`Grazie.
`
`Michel M. Dacorogna
`Ramazan Gencay
`Ulrich A. Muller
`Richard B. Olsen
`Olivier V. Pictet
`
`0020
`
`

`

`1
`
`INTRODUCTION
`
`1.1 MARKETS: THE SOURCE OF HIGH-FREQUENCY DATA
`
`A famous climber, when asked why he was willing to put his life in danger to climb
`dangerous summits, answered: "Because they are there." We would be tempted
`to give the same answer when people ask us why we take so much pain in dealing
`with high-frequency data. The reason is simple: financial markets are the source
`of high-frequency data. The original form of market prices is tick-by-tick data:
`each "tick" is one logical unit of information, like a quote or a transaction price
`(see Section 2.1). By nature these data are irregularly spaced in time. Liquid
`markets generate hundreds or thousands of ticks per business day. Data vendors
`like Reuters transmit more than 275,000 prices per day for foreign exchange spot
`rates alone.
`Thus high-frequency data should be the primary object of research for those
`who are interested in understanding financial markets. Especially so, because
`practitioners determine their trading decisions by observing high-frequency or
`tick-by-tick data. Yet most of the studies published in th