Asset Price Dynamics, Volatility, and Prediction

Stephen J. Taylor is Professor of Finance at Lancaster University, England. He is the author of "Modelling Financial Time Series" and many influential articles about applications of financial econometrics.

• Preface xiii Chapter 1: Introduction 1 1.1 Asset Price Dynamics 1 1.2 Volatility 1 1.3 Prediction 2 1.4 Information 2 1.5 Contents 3 1.6 Software 5 1.7 Web Resources 6 PART I: Foundations 7 Chapter 2: Prices and Returns 9 2.1 Introduction 9 2.2 Two Examples of Price Series 9 2.3 Data-Collection Issues 10 2.4 Two Returns Series 13 2.5 Definitions of Returns 14 2.6 Further Examples of Time Series of Returns 19 Chapter 3: Stochastic Processes: Definitions and Examples 23 3.1 Introduction 23 3.2 Random Variables 24 3.3 Stationary Stochastic Processes 30 3.4 Uncorrelated Processes 33 3.5 ARMA Processes 36 3.6 Examples of ARMA 1 1 Specifications 44 3.7 ARIMA Processes 46 3.8 ARFIMA Processes 46 3.9 Linear Stochastic Processes 48 3.10 Continuous-Time Stochastic Processes 49 3.11 Notation for Random Variables and Observations 50 Chapter 4: Stylized Facts for Financial Returns 51 4.1 Introduction 51 4.2 Summary Statistics 52 4.3 Average Returns and Risk Premia 53 4.4 Standard Deviations 57 4.5 Calendar Effects 59 4.6 Skewness and Kurtosis 68 4.7 The Shape of the Returns Distribution 69 4.8 Probability Distributions for Returns 73 4.9 Autocorrelations of Returns 76 4.10 Autocorrelations of Transformed Returns 82 4.11 Nonlinearity of the Returns Process 92 4.12 Concluding Remarks 93 4.13 Appendix: Autocorrelation Caused by Day-of-the-Week Effects 94 4.14 Appendix: Autocorrelations of a Squared Linear Process 95 PART II: Conditional Expected Returns 97 Chapter 5: The Variance-Ratio Test of the Random Walk Hypothesis 99 5.1 Introduction 99 5.2 The Random Walk Hypothesis 100 5.3 Variance-Ratio Tests 102 5.4 An Example of Variance-Ratio Calculations 105 5.5 Selected Test Results 107 5.6 Sample Autocorrelation Theory 112 5.7 Random Walk Tests Using Rescaled Returns 115 5.8 Summary 120 Chapter 6: Further Tests of the Random Walk Hypothesis 121 6.1 Introduction 121 6.2 Test Methodology 122 6.3 Further Autocorrelation Tests 126 6.4 Spectral Tests 130 6.5 The Runs Test 133 6.6 Rescaled Range Tests 135 6.7 The BDS Test 136 6.8 Test Results for the Random Walk Hypothesis 138 6.9 The Size and Power of Random Walk Tests 144 6.10 Sources of Minor Dependence in Returns 148 6.11 Concluding Remarks 151 6.12 Appendix: the Correlation between Test Values for Two Correlated Series 153 6.13 Appendix: Autocorrelation Induced by Rescaling Returns 154 Chapter 7: Trading Rules and Market Efficiency 157 7.1 Introduction 157 7.2 Four Trading Rules 158 7.3 Measures of Return Predictability 163 7.4 Evidence about Equity Return Predictability 166 7.5 Evidence about the Predictability of Currency and Other Returns 168 7.6 An Example of Calculations for the Moving-Average Rule 172 7.7 Efficient Markets: Methodological Issues 175 7.8 Breakeven Costs for Trading Rules Applied to Equities 176 7.9 Trading Rule Performance for Futures Contracts 179 7.10 The Efficiency of Currency Markets 181 7.11 Theoretical Trading Profits for Autocorrelated Return Processes 184 7.12 Concluding Remarks 186 PART III: Volatility Processes 187 Chapter 8: An Introduction to Volatility 189 8.1 Definitions of Volatility 189 8.2 Explanations of Changes in Volatility 191 8.3 Volatility and Information Arrivals 193 8.4 Volatility and the Stylized Facts for Returns 195 8.5 Concluding Remarks 196 Chapter 9: ARCH Models: Definitions and Examples 197 9.1 Introduction 197 9.2 ARCH(1) 198 9.3 GARCH 1 1 199 9.4 An Exchange Rate Example of the GARCH 1 1 Model 205 9.5 A General ARCH Framework 212 9.6 Nonnormal Conditional Distributions 217 9.7 Asymmetric Volatility Models 220 9.8 Equity Examples of Asymmetric Volatility Models 222 9.9 Summary 233 Chapter 10: ARCH Models: Selection and Likelihood Methods 235 10.1 Introduction 235 10.2 Asymmetric Volatility: Further Specifications and Evidence 235 10.3 Long Memory ARCH Models 242 10.4 Likelihood Methods 245 10.5 Results from Hypothesis Tests 251 10.6 Model Building 256 10.7 Further Volatility Specifications 261 10.8 Concluding Remarks 264 10.9 Appendix: Formulae for the Score Vector 265 Chapter 11: Stochastic Volatility Models 267 11.1 Introduction 267 11.2 Motivation and Definitions 268 11.3 Moments of Independent SV Processes 270 11.4 Markov Chain Models for Volatility 271 11.5 The Standard Stochastic Volatility Model 278 11.6 Parameter Estimation for the Standard SV Model 283 11.7 An Example of SV Model Estimation for Exchange Rates 288 11.8 Independent SV Models with Heavy Tails 291 11.9 Asymmetric Stochastic Volatility Models 293 11.10 Long Memory SV Models 297 11.11 Multivariate Stochastic Volatility Models 298 11.12 ARCH versus SV 299 11.13 Concluding Remarks 301 11.14 Appendix: Filtering Equations 301 PART IV: High-Frequency Methods 303 Chapter 12: High-Frequency Data and Models 305 12.1 Introduction 305 12.2 High-Frequency Prices 306 12.3 One Day of High-Frequency Price Data 309 12.4 Stylized Facts for Intraday Returns 310 12.5 Intraday Volatility Patterns 316 12.6 Discrete-Time Intraday Volatility Models 321 12.7 Trading Rules and Intraday Prices 325 12.8 Realized Volatility: Theoretical Results 327 12.9 Realized Volatility: Empirical Results 332 12.10 Price Discovery 342 12.11 Durations 343 12.12 Extreme Price Changes 344 12.13 Daily High and Low Prices 346 12.14 Concluding Remarks 348 12.15 Appendix: Formulae for the Variance of the Realized Volatility Estimator 349 PART V: Inferences from Option Prices 351 Chapter 13: Continuous-Time Stochastic Processes 353 13.1 Introduction 353 13.2 The Wiener Process 354 13.3 Diffusion Processes 355 13.4 Bivariate Diffusion Processes 359 13.5 Jump Processes 361 13.6 Jump-Diffusion Processes 363 13.7 Appendix: a Construction of the Wiener Process 366 Chapter 14: Option Pricing Formulae 369 14.1 Introduction 369 14.2 Definitions, Notation, and Assumptions 370 14.3 Black-Scholes and Related Formulae 372 14.4 Implied Volatility 378 14.5 Option Prices when Volatility Is Stochastic 383 14.6 Closed-Form Stochastic Volatility Option Prices 388 14.7 Option Prices for ARCH Processes 391 14.8 Summary 394 14.9 Appendix: Heston's Option Pricing Formula 395 Chapter 15: Forecasting Volatility 397 15.1 Introduction 397 15.2 Forecasting Methodology 398 15.3 Two Measures of Forecast Accuracy 401 15.4 Historical Volatility Forecasts 403 15.5 Forecasts from Implied Volatilities 407 15.6 ARCH Forecasts that Incorporate Implied Volatilities 410 15.7 High-Frequency Forecasting Results 414 15.8 Concluding Remarks 420 Chapter 16: Density Prediction for Asset Prices 423 16.1 Introduction 423 16.2 Simulated Real-World Densities 424 16.3 Risk-Neutral Density Concepts and Definitions 428 16.4 Estimation of Implied Risk-Neutral Densities 431 16.5 Parametric Risk-Neutral Densities 435 16.6 Risk-Neutral Densities from Implied Volatility Functions 446 16.7 Nonparametric RND Methods 448 16.8 Towards Recommendations 450 16.9 From Risk-Neutral to Real-World Densities 451 16.10 An Excel Spreadsheet for Density Estimation 458 16.11 Risk Aversion and Rational RNDs 461 16.12 Tail Density Estimates 464 16.13 Concluding Remarks 465 Symbols 467 References 473 Author Index 503 Subject Index 513

Winner of the 2005 BestBook Award, Riskbook.com "This book provides thorough, well-presented and concise coverage of asset price dynamics and manages to combine new developments, established issues, theory and application in a practical and refreshing manner. It is well illustrated with time series graphs and tables and has a good balance between theoretical concepts and their practical applications with a mathematical treatment that is not too specialized."--Anthony F. Gyles, RSS