IIHIHIW'I'“
`
`"WH‘W'H
`
`An Introduction to
`High»FrequenC
`
`Finance —
`
`wiwfi‘mfla
`
`km,ijuWQQhFi
`1..*5?”51%?iii-5'
`
`' awkw—
`
`OANDA - EXHIBIT 2011
`
`OANDA - EXHIBIT 2011
`
`

`

`AN INTRODUCTION
`
`TO
`
`HIGH-FREQUENCY
`
`FINANCE
`
`

`

`
`
`AN INTRODUCTION
`
`TO
`
`HIGH-FREQUENCY
`
`FINANCE
`
`Michel M. Dacorogna
`Zurich Re, Switzerland
`
`Ramazan Gengay
`Universiiy of Windsor; Canada
`Olsen & Associates, Switzerland
`
`Ulrich A. Miiller
`
`Olsen & Assodates. Switzerland
`
`Richard B. Olsen
`
`Gisen d‘: Associates. Switzerland
`
`Olivier V. Pictet
`
`Dynamic Asset Management, Switzeriand
`
`ACADEMIC PRESS
`
`An Imprint offlsevier
`
`San Diego
`
`San Francisco New York Boston London
`
`Sydney Tokyo
`
`

`

`Cover Images © 200! Photo-Disc, Inc.
`
`This book is printed on acidwfree paper.
`
`Copyright© 2001 by ACADEMIC PRESS
`
`All Rights Reserved.
`No part of this publication may be reproduced or transmitied in an}!r form or by an}.r
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`Academic Piess
`An Imprint ofEIswicr
`525 B Street, Suite 1901}, San Diego. California 92lfllv4495, USA
`httpdfwwwacademicpresscom
`
`Academic Press
`84 Theobalds Road. London WCIK ERR. UK
`httptflwwwocadcmicpresscom
`
`Library of Congress Catalog Card Number: 2001083173
`
`ISBN—l 3: 9'?8~O-I2-2?9671-S
`ISBN-10: 0-12-27967l-3
`
`PRINTED IN THE UNITED STATES OF AMERICA
`
`070309IOHEB98
`
`

`

`To our parents and families
`
`

`

`This Page Intentionally Left Blank
`
`

`

`CONTENTS
`
`LIST OF FIGURES
`
`xv
`
`LIST OF TABLES
`
`xix
`
`PREFACE
`
`xxi
`
`ACKNOWLEDGMENTS xxiii
`
`INTRODUCTION
`
`I.I
`LI
`[.3
`L4
`|.5
`
`Markets: The Source of High-Frequency Data
`Methodology of High-Frequency Research
`Data Frequency and Market Information
`New Levels of Significance
`Interrelating Different Time Scales
`
`COOL-”MW
`
`vii
`
`

`

`viii
`
`2.!
`
`2.2
`
`2.3
`
`2.4
`
`2.5
`
`2.6
`2.1
`
`CONTENTS
`
`2
`
`MARKETS AND DATA
`
`General Remarks on Markets and Data Types
`2. I. I
`Spot Markets
`2. I.2 Futures Markets
`
`2. L3 Option Markets
`Foreign Exchange Markets
`2.2.I
`Structure of the Foreign Exchange Spot Market
`2.2.2 Synthetic Cross Rates
`2.2.3 Multiple Contributor Effects
`Over-the-Counter Interest Rate Markets
`
`Spot Interest Rates
`2.3.I
`2.3.2 Foreign Exchange Forward Rates
`Interest Rate Futo res
`
`2.4.l General Description of Interest Rate Futures
`2.4.2 Implied Forward Interest Rates and Yield Curves
`Bond Futures Markets
`2.5.l Bonds and Bond Futures
`2.5.2 Rollover Schemes
`
`Commodity Futures
`Equity Markets
`
`3
`
`TIME SERIES OF INTEREST
`
`Time Series and Operators
`Variables in Homogeneous Time Series
`3.2. |
`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
`
`3.3
`
`3.2.8 Overlapping Returns
`Convolution Operators
`3.3.l 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.? 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
`
`41
`45
`46
`46
`47
`51
`53
`54
`56
`53
`59
`59
`6 l
`
`

`

`CONTENTS
`
`3.3.3 Moving Norm, Variance, and Standard Deviation
`3 .33 Differential
`
`3.3.I0 Derivative and y-Derivative
`3.3.I I Volatility
`3.3.I 2 Standardized Time Series, Moving Skewness, and Kurtosis
`3.3.! 3 Moving Correlation
`3.3. l4 Windowed Fourier Transform
`
`3.4
`
`Microscopic Operators
`3.4.! 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. l
`4.2
`
`introduction: Using a Filter to Clean the Data
`Data and Data Errors
`
`4.2. | Time Series of Ticks
`
`4.2.2 Data Error Types
`General Overview of the Filter
`
`4‘3
`
`4.3.l The Functionality of the Filter
`4.3.2 Overview of the Filtering Algorithm and Its Structure
`
`Basic Filtering Elements and Operations
`4.4. | 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
`The Scalar Filtering Window
`4.5.l 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 Disn‘tissing 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
`
`The Full-Quote Filtering Window
`4.6.I Quote Splitting Depending on the Instrument Type
`4.6.2 The Basic Validity Test
`4.6.3 Transforming the Filtered Variable
`Univariate Filtering
`
`4.4
`
`4.5
`
`4.6
`
`4.?
`
`82
`
`84
`84
`35
`86
`86
`
`88
`88
`
`89
`91
`93
`
`98
`[00
`103
`104
`104
`106
`107
`108
`108
`
`109
`110
`110
`112
`113
`
`

`

`CONTENTS
`
`4.1.1 The Results of Univariate Filtering
`4.7.2 Filtering in Historical and Real-Time Modes
`4.7.3 Choosing the Filter Parameters
`Special Filter Elements
`4.8.I Multivariate Filtering: Filtering Sparse Data
`Behavior and Effects of the Data Filter
`
`4.8
`
`4.9
`
`5
`
`BASIC STYLIZED FACTS
`
`5.1
`5.2
`
`Introduction
`Price Formation Process
`
`5.2.I Negative First-Order Autocon'elation of Returns
`5.2.2 Discreteness of Quoted Spreads
`5.2.3 Short-Term Triangular Arbitrage
`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
`
`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
`
`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
`Autocorrelatiort and Seasonality
`5.6.! 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
`
`Introduction
`
`A Model of Market Activity
`6.2.1
`Seasonal Patterns of the Volatility and Presence of Markets
`
`5.3
`
`5.4
`
`5.6
`
`6.1
`6.2
`
`114
`
`115
`116
`
`116
`116
`118
`
`121
`
`123
`123
`125
`12?
`
`127
`127
`
`129
`129
`132
`132
`
`135
`144
`147
`
`147'
`151
`154
`158
`160
`
`161
`163
`
`167
`169
`170
`
`174
`
`I75
`175
`
`

`

`CONTENTS
`
`6.2.2 Modeling the Volatility Patterns with an Alternative Time
`Scale and an Activity Variable
`8.2.3 Market Activity and Scaling Law
`6.2.4 Geographical Components of Market Activity
`6.2.5 A Model of lntraweek Market Activity
`
`6.2.6 Interpretation of the Activity Modeling Results
`A New Business Time Scale (fi-Scale)
`6.3.I Definition of the d—Seale
`
`6.3.2 Adjustments of the d-Scale Definition
`6.3.3 A Ratio Test for the d-Scale Quality
`Filtering lntraday Seasonalities with Wavelets
`
`7
`
`REALIZED VOLATILITY DYNAMICS
`Introduction
`
`The Bias of Realized Volatility and Its Correction
`Conditional Heteroskedasticity
`1.3.I Autocorrelation of Volatility in iii-Time
`7.3.2 Short and Long Memory
`The Heterogeneous Market Hypothesis
`1.4.! Volatilities of Different Time Resolutions
`
`7.4.2 Asymmetric Lead-Lag Correlation of Volatilities
`7.4.3 Conditional Predictability
`
`8
`
`VOLATI LITY PROCESSES
`
`Introduction
`
`Intraday Volatility and GARCH Models
`8.2.!
`Parameter Estimation of GARCH Models
`
`3.2.2 Temporal Aggregation of GARCH Models
`8.2.3 Estimates of GARC l-l( 1. l) for Various Frequencies
`Modeling Heterogeneous Volatilities
`8.3.! The HARCl-l Model
`
`8.3.2 HARCH and Market Components
`8.3.3 Generalization of the Process Equation
`8.3-4 EMA—HARCI-I Model
`
`8.3.5 Estimating HARCH and EMA-HARCH Models
`8.3.6 HARCH in Interest Rate Modeling
`Forecasting Short-Term Volatility
`8.4.I A Framework to Measure the Forecasting Performance
`8.4.2 Performance of ARCH-Type Models
`
`6.3
`
`6.4
`
`7.1
`7.2
`7.3
`
`7.4
`
`8.1
`8.2
`
`8.3
`
`8.4
`
`xi
`
`176
`177
`178
`I79
`I83
`188
`188
`189
`192
`193
`
`197
`198
`204
`204
`
`207
`209
`210
`211
`215
`
`219
`221
`222
`224
`226
`23 l
`231
`234
`237
`237
`239
`242
`
`243
`243
`246
`
`

`

`
`
`xii
`
`CONTENTS
`
`9
`
`FORECASTING RISK AND RETURN
`
`Introduction to Forecasting
`9. I
`9.2 Forecasting Volatility for Value—at—Risk
`9.2.! Three Simple Volatility Forecasting Models
`9.2.2 Choosing the Best Volatility Forecasting Model
`9.3 Forecasting Returns over Multiple Time Horizons
`9.3. |
`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. | Appropriate Measures of Forecast Accuracy
`9.4.2 Empirical Results for the Multid-lon'zon Model
`9.4.] Forecast Effectiveness in Intraday Horizons
`
`CORRELATION AND MULTIVARIATE RISK
`Introduction
`
`I 0. I
`
`I0
`
`"1.2 Estimating the Dependence of Financial Time Series
`"1.3 Covolatiiity Weighting
`I0.3.|
`Formulation of an Adjusted Correlation Measure
`I0.3.2 Monte Carlo and Empirical Tests
`I0.4 Stability of Return Correlations
`l0.4.I Correlation Variations over Time
`
`“3.4.2 The Exponential Memory of Return Correlations
`“)5 Correlation Behavior at High Data Frequencies
`I 0.6 Conclusions
`
`I i. I
`
`Introduction
`
`TRADING MODELS
`
`I l.2 Real-Time Trading Strategies
`I I .2.I The Trading Model and Its Data-Processing Environment
`I I .2.2 Simulated Trader
`I L3 Risk Sensitive Performance Measures
`
`X63": A Symmetric Effective Returns Measure
`I I .3. |
`1 I 3.2 Ref: An Asymmetric Effective Returns Measure
`I L4 Trading Model Algorithms
`
`248
`250
`250
`254
`255
`255
`256
`256
`257
`259
`26 I
`262
`263
`264
`
`268
`269
`270
`272
`274
`277
`278
`282
`287
`293
`
`295
`
`297
`299
`
`303
`304
`305
`307
`309
`
`

`

`CONTENTS
`
`ILS
`
`11.6
`
`IIJr
`II.II
`
`I I .4.I An Example of a Trading Model
`I I.4.2 Model Design with Genetic Programming
`Optimization and Testing Procedures
`I I .5.I Robust Optimization with Genetic Algorithms
`I I .5.2 Testing Procedures
`Statistical Study of a Trading Model
`I I .6.I Heterogeneous Real-Time Trading Strategies
`I I .6.2 Price-Generation Processes and Trading Models
`Trading Model Portfolios
`Currency Risk Hedging
`I I.8.l The Hedging Ratio and the “Neutral Point”
`II.8.2 RiskfReturn of an Overlay with Static and Dynamic
`Positions
`
`I |.8.3 Dynamic Hedging with Exposure Constraints
`I I 3.4 Concluding Remarks
`
`I2
`
`TOWARD A THEORY
`
`OF HETEROGENEOUS MARKETS
`Definition of Efficient Markets
`
`Dynamic Markets and Relativistic Effects
`Impact of the New Technology
`Zero-Sum Game or Perpetuum Mobile?
`Discussion of the Conventional Definition
`
`An Improved Definition of “Efficient Markets"
`
`I2.l
`I22
`I13
`I14
`I25
`I2.6
`
`BIBLIOGRAPHY 356
`
`INDEX 376
`
`310
`31 l
`3 l "I
`317'
`32 I
`323
`323
`
`328
`338
`340
`343
`
`344
`345
`346
`
`349
`350
`352
`353
`354
`354
`
`

`

`This Page Intentionally Left Blank
`
`

`

`LIST OF FIGURES
`
`
`
`I.l
`
`LI
`L3
`
`3.!
`
`3.1
`
`3.3
`3.4
`
`3.5
`
`3.6
`3.7
`
`3.8
`
`3.9
`3.10
`
`3.”
`
`3J2
`3.13
`
`3.”
`
`3J5
`3J6
`
`3J7
`
`4.I
`
`Size and data frequency of different samples
`Models versus time Scale
`
`Volatility with daily versun high-Frequency data
`
`Types of time series operators
`
`Interpolation methods
`Overlapping time intervals
`
`One week of USD—CHF prices
`
`Moving average (MA) kernel
`MA kernel on a logarithmic scale
`Schematic differential kernel
`
`Kernel of a differential operator
`Decay of a differential kernel
`Differential and return
`
`Distribution of derivative operator
`Annualized volatility as a moving norm
`
`Moving moments of returns
`
`Kernel of a windowed Fourier operator
`Normed windowed Fourier Iransfonn
`
`Microscopic volatility
`
`Tick activity
`
`Flowchart of a data-cleaning filter
`
`Utah-
`
`had
`
`36
`
`4B
`
`53
`61
`
`62
`
`65
`
`67
`
`68
`71
`
`72
`
`75
`
`77
`79
`
`80
`
`S7
`
`

`

`LIST OF FIGURES
`
`4.2
`
`5. I
`
`5.2
`
`5.3
`
`5.4
`
`5.5
`
`5.6
`
`5.7
`
`5.8
`
`5.9
`
`5. IO
`
`5.“
`
`SJ!
`
`5. I 3
`5.I4
`
`5. I 5
`6.1
`
`6.2
`6.3
`
`6.4
`
`6.5
`
`6.6
`
`6.7
`
`6.8
`6.9
`
`Schematic scalar filtering window
`Short-term autocorrelation of returns
`
`Comparison between quoted and transaction spreads
`Scaling law exponent as a function of time
`
`Seasonality in the interest rates
`
`Intraday distribution of 15-min mean changes of absolute returns
`Cumulative distributions of 10-min, 1-day, and 1-week USD-JPY
`returns
`
`Order statistics for Student-r distribution
`
`Scaling law for USD-JPY and GBP-USD
`Wavelet variance at different scales
`
`Autocorrelations of hourlyr returns. absolute returns, and squared
`returns
`
`Autocorrelation as a function of the power of the absolute returns
`Hourly intraday and intraweek distribution of absolute return.
`spread and the tick frequency
`
`Intraday analysis of Eurofutures
`
`Deterministic volatility of Eurofutures
`
`Cumulative distributions of spreads
`
`The USD-DEM intraweek activity pattern
`
`Activity functions of geographical market components
`
`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
`
`The o-time versus physical time for USU-DEM
`Hourly returns of USD—DEM in physical and o—time
`
`Seasonality and wavelet filtering
`Autocorrelations of the 5-min absolute returns for USD-DEM and
`USDJPY
`
`6.l0
`
`Autocorrelations of the 5-min filtered absolute returns for
`USD-DEM and USD-JPY
`
`1. I
`
`7.2
`
`7.3
`7.4
`
`7.5
`
`7.6
`7.7
`
`1.8
`
`Interaction of trader groups
`
`The bias of realized volatility
`
`The residual bias of bias-corrected realized volatility
`Autocorrelation function of USD-DEM in physical-time
`Autocorrelation function of USU-DEM in tit-time
`
`USD~DEM autocorrelations from daily data
`Coarse and fine volatilities
`
`Asymmetric lagged correlation for USD-DEM
`
`[03
`
`123
`125
`
`128
`
`129
`
`130
`
`136
`
`139
`
`149
`
`160
`
`161
`
`162
`
`165
`
`163
`
`169
`
`172
`
`178
`
`182
`
`185
`
`186
`
`188
`
`190
`191
`
`194
`
`195
`
`195
`
`199
`
`201
`
`203
`205
`
`206
`
`208
`
`2 1 2
`2 l4
`
`

`

`
`LIST OF FIGURES
`
`xvii
`
`7.9
`1.")
`
`II I
`
`8.|
`8.2
`
`8.3
`
`3.4
`
`3.5
`9.]
`
`9.2
`I0.|
`
`I0.2
`I0.3
`
`I0.4
`[0.5
`
`[0.6
`[0.7
`
`I03
`
`[0.9
`
`I0.10
`
`I0.||
`I0.|2
`
`ll.l
`”.2
`
`”.3
`”.4
`”.5
`
`Asymmetric lagged correlation for Euromark IR futures
`
`Asymmetry of lagged correlation
`Conditional autocorrelation of returns
`
`Estimated and theoretical GARCH coefficients in business time
`Estimated and theoretical GARCH coefficients in fi—time
`
`GARCH estimates on a moving sample
`
`Moment conditions for a HARCHQ) process
`
`Impacts of market components for HARCH processes
`Standard RiskMetrics volatility at different daytimcs
`
`Momentum indicator for forecasting
`Autocorrelation of absolute returns for USD-DEM
`
`Linear correlation coefficients for USDIDEMJNLG
`Linear correlation coefficients for USDI'DEMIGBP
`
`Linear correlation coefficients for USDIDEMIITL
`Linear correlation coefficients for DJIAIAMEX
`
`Linear correlation coefficients for USD 3-6MJDEM 3-6M
`
`Linear correlation coefficients for DEM 3—6MlDEM 9-12M
`Autocorrelations of correlation coefficients
`
`Exponential decay of the autocorrelation of correlation
`coefficients
`
`Correlation coefficients as a function of return time interval
`
`Correlation versus logarithmic return time interval
`Correlation stabiiization intervals versus data frequencies
`
`Data flow within a real-time trading model
`Crossover operator
`
`Syntactic restrictions for basic arithmetic operators
`Total return of a portfolio of 10 0&A trading models
`Set of feasible portfolios with currency hedging
`
`216
`
`2 l 7
`2] 8
`
`226
`227
`
`230
`
`234
`241
`
`252
`258
`277
`
`280
`
`281
`
`282
`283
`
`284
`
`235
`286
`
`287
`
`289
`290
`
`292
`
`298
`
`3 13
`3 1 4
`34 1
`342
`
`

`

`This Page Intentionally Left Blank
`
`

`

`LIST OF TABLES
`
`2. I
`
`2.2
`
`4. I
`
`4.2
`
`4.3
`
`4.4
`
`4.5
`4.6
`
`5. I
`
`5.2
`
`5.3
`5.4
`
`5.5
`
`5.6
`
`5.7
`
`5.8
`
`5.9
`
`5.10
`5.l |
`
`5.”
`
`The traditional FXFX page of Reuters
`FX data frequency
`
`Data cleaning filter structure
`
`Credibility addition
`
`Trust capital as a function of price move size and time interval
`Active periods of the three generic markets
`
`Data cleaning filter parameters
`Data cleaning rejection rates
`Moments of return distributions for FK rates
`
`Moments of retum distributions for FX cross rates
`Tail index of FX returns
`
`Tail index of FX cross rates
`
`Tail index of spot interest rates
`
`Estimated tail index for different data frequencies and sample
`Sizes
`
`Extreme risks in the FX market
`
`Drift exponents for FX rates
`
`Drift exponents for Eurofutures
`Timezone conversion table
`
`Average number of ticks versus dayr of the week
`Average volatility versus day of the week
`
`xix
`
`16
`18
`
`89
`
`96
`101
`
`11?
`
`1:9
`
`B3
`
`134
`
`140
`141
`
`143
`
`144
`
`146
`
`150
`151
`
`163
`
`164
`166
`
`

`

`XX
`
`5. | 3
`
`5. I 4
`6. I
`
`6.2
`
`6.3
`7. I
`
`8. I
`8.2
`
`8.3
`
`8.4
`
`8.5
`
`3.6
`9.l
`
`9.2
`
`9.3
`
`9.4
`
`I0.l
`I0.2
`
`"1.3
`
`"3.4
`"3.5
`I LI
`”.2
`
`”.3
`
`”.4
`”.5
`“.6
`”.1
`
`[LB
`
`”.9
`
`LIST OF TABLES
`
`Correlation coefficients between activity measures
`
`Average spreads versus day of the week
`
`Definition of the three generic markets
`The 19-time parameter estimates for the three generic markets
`The volatility ratio for the quality of the n~scale
`Difference between lagged correlations
`Results of a GARCH( l ,1) estimation in business time
`Results of a GARCH( 1,1) estimation in anime
`
`Market components of a HARCH process
`HARCH coefficients for USD- DEM
`
`Results of the EMA-HARCH for the LIFFE Three-Month
`Euromark
`
`Volatility forecasting performance for USD-DEM
`The sampling periods of the forecast study
`
`Forecast quality for 10 FX rates against the USD
`Forecast quality for 10 FX cross rates
`
`Significance of the forecast quality for 20 FX rates
`Correlations from Monte Carlo simulations
`
`Data sampling for correlation as function of time
`Mean values, variances, maxima and minima of correlation
`Estimation results of the autocorrelation of correlation
`
`Correlation results characterizing the Epps effect
`Market time constraints
`
`Trading model results versus tree complexity
`Performance comparison between models
`Performance comparison between markets
`
`The best Xa}? as a function of opening hours
`p-value Comparisons
`Random walk Simulations for USD-DEM
`
`GARCH( 1,1 } parameter estimates
`GARCHU ,l) simulations for USD-DEM
`
`I I. I 0 AR(4)-GARCH(I,1) parameter estimates
`
`l L! | AR(4)-GARCH(I,1) simulations for USD-DEM
`
`I I. I 2 Portfolio performance of 0&A trading models
`
`16?
`171
`
`l 30
`184
`192
`
`213
`228
`
`229
`236
`
`240
`
`242
`
`246
`264
`
`265
`266
`
`26?
`
`275
`278
`
`279
`
`283
`291
`
`299
`3 16
`324
`325
`
`326
`33 l
`
`332
`
`334
`
`335
`
`33?
`338
`
`340
`
`

`

`PREFACE
`
`
`
`This book presents a unified view ofhigh-frequencytime 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
`
`

`

`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. Dacomgna
`
`Ramon Genpay
`
`Ulrich A. Mt'iiier
`
`Richard B. Olsen
`
`Olivier V. Pieter
`
`

`

`ACKNOWLEDGMENTS
`
`
`
`e should start by acknowledging that 15 years ago, when our research
`
`Wteam at Olsen & Associates (0&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 as 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 [986. 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; Rakhai 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
`
`xxiii
`
`

`

`XXiV
`
`ACKNOWLEDGMENTS
`
`
`
`Breyrnann, who has extended the ii-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 whojoined us at a later stage and have
`already reached out for other adventures: Lars Jaeger, Thomas Domenig, Peter
`Rice. and Hess Hauksson. Our thanks extend also to Jorgen 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 Komdoerfer; Markus P.
`Herrchen; Jens Richelsen; Christian Jost; Jiirg S. Ffissler; Retus G. Sgi er; Alexan-
`der Dimai; Jonathan Dawes; Jakob E. von Weizsa'cker; Philipp Hartmann; Ct‘itiilin
`Starica; Barbara Piccinato; Carl Hopman; Peter Rice, who laterjoined our research
`team; Simone Depan's; 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 Gathers 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 0&A with some fine sci-
`entists: Tim Bollerslev, William Brock. Hans Bl'ihlmann, Peter Biihlmann, Frank
`
`K. Diebold. Christian Dunis, Rudiger Frey. Hélyette 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 Wasserfailen, Andreas Weigend, and Diethelm
`Wiirtz. We would like to thank especially Charles Goodhan, whose suppon and
`insights led to the 0&A “High-Frequency Data in Finance" conferences, but also
`Richard Baillie, Tim Bollerslev, Rob Engle, Joel Hasbrouck, Michael Melvin, and
`Maureen O'Hara. Gerhard Stab] has been a great partner in exploring new is-
`sues 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. Manfred Harter and Mice 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,
`
`

`

`
`ACKNOWLEDGMENTS
`
`XXV
`
`Blake LeBaron, and Thanasis Stengos for many exciting research conversations,
`and Michael Charette, Ron Meng and Tiber Toronyi for research support. Ulrich
`Muller would like to thank Gunter Schwarz for his contribution to our understand-
`
`ing 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 Meissaer
`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 Mote, 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 LeB aron,
`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
`.lost, 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 ’5 (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 ETEX formatting problems of a
`book of more than 400 pages and containing so many figures was essential for the
`resulting appearance of this book.
`
`

`

`xxvi
`
`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 0&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. Daeomgna
`Ramazan Geneay
`Ulrich A. Miiller
`Richard B. Olsen
`Olivier V. Pictet
`
`

`

`
`
`INTRODUCTION
`
`l.| 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-frequencyr 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 the financial literature
`deal with low-frequency, regularly spaced data. There are two main reasons for
`this. First, it is still rather costly and time-consuming to collect. collate. store.
`retrieve, and manipulate high-frequency data. That is why most of the available
`
`

`

`
`
`2
`
`CHAPTER 1
`
`INTRODUCTION
`
`financial data are at daily or lower frequency. The second reason is somehow
`more subtle but still quite important: most of the statistical apparatus has been
`developed and thought for homogeneous (i.e., equally spaced in time) time series.
`There is little work done to adapt the methods to data that arrive at random time
`intervals. Unfortunately in finance, regularly spaced data are not original data but
`artifacts derived from the original market prices. Nowadays with the development
`of computer technology, data availability is becoming less and less of a problem.
`For instance, most of the exchanges and especially those that trade electronically
`would gladly provide tick-by-tick data to interested parties. Data vendors have
`themselves improved their data structures and provide their users with tools to
`collect data for over-the-counter (01‘C) markets. Slowly, high-frequency data are
`becoming a fantastic experimental bench for understanding market microstructure
`and