This book shows how current and recent market prices convey information about the probability distributions that govern future prices. Moving beyond purely theoretical models, Stephen Taylor applies methods supported by empirical research of equity and foreign exchange markets to show how daily and more frequent asset prices, and the prices of option contracts, can be used to construct and assess predictions about future prices, their volatility, and their probability distributions. Stephen Taylor provides a comprehensive introduction to the dynamic behavior of asset prices, relying on finance theory and statistical evidence. He uses stochastic processes to define mathematical models for price dynamics, but with less mathematics than in alternative texts. The key topics covered include random walk tests, trading rules, ARCH models, stochastic volatility models, high-frequency datasets, and the information that option prices imply about volatility and distributions. Asset Price Dynamics, Volatility, and Prediction is ideal for students of economics, finance, and mathematics who are studying financial econometrics, and will enable researchers to identify and apply appropriate models and methods. It will likewise be a valuable resource for quantitative analysts, fund managers, risk managers, and investors who seek realistic expectations about future asset prices and the risks to which they are exposed.
Intro Title Copyright Contents Preface 1 Introduction 1.1 Asset Price Dynamics 1.2 Volatility 1.3 Prediction 1.4 Information 1.5 Contents 1.6 Software 1.7 Web Resources I: Foundations 2 Prices and Returns 2.1 Introduction 2.2 Two Examples of Price Series 2.3 Data-Collection Issues 2.4 Two Returns Series 2.5 Definitions of Returns 2.6 Further Examples of Time Series of Returns 3 Stochastic Processes: Definitions and Examples 3.1 Introduction 3.2 Random Variables 3.3 Stationary Stochastic Processes 3.4 Uncorrelated Processes 3.5 ARMA Processes 3.6 Examples of ARMA(1, 1) Specifications 3.7 ARIMA Processes 3.8 ARFIMA Processes 3.9 Linear Stochastic Processes 3.10 Continuous-Time Stochastic Processes 3.11 Notation for Random Variables and Observations 4 Stylized Facts for Financial Returns 4.1 Introduction 4.2 Summary Statistics 4.3 Average Returns and Risk Premia 4.4 Standard Deviations 4.5 Calendar Effects 4.6 Skewness and Kurtosis 4.7 The Shape of the Returns Distribution 4.8 Probability Distributions for Returns 4.9 Autocorrelations of Returns 4.10 Autocorrelations of Transformed Returns 4.11 Nonlinearity of the Returns Process 4.12 Concluding Remarks 4.13 Appendix: Autocorrelation Caused by Day-of-the-Week Effects 4.14 Appendix: Autocorrelations of a Squared Linear Process II: Conditional Expected Returns 5 The Variance-Ratio Test of the Random Walk Hypothesis 5.1 Introduction 5.2 The Random Walk Hypothesis 5.3 Variance-Ratio Tests 5.4 An Example of Variance-Ratio Calculations 5.5 Selected Test Results 5.6 Sample Autocorrelation Theory 5.7 Random Walk Tests Using Rescaled Returns 5.8 Summary 6 Further Tests of the Random Walk Hypothesis 6.1 Introduction. 6.2 Test Methodology 6.3 Further Autocorrelation Tests 6.4 Spectral Tests 6.5 The Runs Test 6.6 Rescaled Range Tests 6.7 The BDS Test 6.8 Test Results for the Random Walk Hypothesis 6.9 The Size and Power of Random Walk Tests 6.10 Sources of Minor Dependence in Returns 6.11 Concluding Remarks 6.12 Appendix: the Correlation between Test Values for Two Correlated Series 6.13 Appendix: Autocorrelation Induced by Rescaling Returns 7 Trading Rules and Market Efficiency 7.1 Introduction 7.2 Four Trading Rules 7.3 Measures of Return Predictability 7.4 Evidence about Equity Return Predictability 7.5 Evidence about the Predictability of Currency and Other Returns 7.6 An Example of Calculations for the Moving-Average Rule 7.7 Efficient Markets: Methodological Issues 7.8 Breakeven Costs for Trading Rules Applied to Equities 7.9 Trading Rule Performance for Futures Contracts 7.10 The Efficiency of Currency Markets 7.11 Theoretical Trading Profits for Autocorrelated Return Processes 7.12 Concluding Remarks III: Volatility Processes 8 An Introduction to Volatility 8.1 Definitions of Volatility 8.2 Explanations of Changes in Volatility 8.3 Volatility and Information Arrivals 8.4 Volatility and the Stylized Facts for Returns 8.5 Concluding Remarks 9 ARCH Models: Definitions and Examples 9.1 Introduction 9.2 ARCH(1) 9.3 GARCH(1, 1) 9.4 An Exchange Rate Example of the GARCH(1, 1) Model 9.5 A General ARCH Framework 9.6 Nonnormal Conditional Distributions 9.7 Asymmetric Volatility Models 9.8 Equity Examples of Asymmetric Volatility Models 9.9 Summary 10 ARCH Models: Selection and Likelihood Methods 10.1 Introduction 10.2 Asymmetric Volatility: Further Specifications and Evidence 10.3 Long Memory ARCH Models 10.4 Likelihood Methods. 10.5 Results from Hypothesis Tests 10.6 Model Building 10.7 Further Volatility Specifications 10.8 Concluding Remarks 10.9 Appendix: Formulae for the Score Vector 11 Stochastic Volatility Models 11.1 Introduction 11.2 Motivation and Definitions 11.3 Moments of Independent SV Processes 11.4 Markov Chain Models for Volatility 11.5 The Standard Stochastic Volatility Model 11.6 Parameter Estimation for the Standard SV Model 11.7 An Example of SV Model Estimation for Exchange Rates 11.8 Independent SV Models with Heavy Tails 11.9 Asymmetric Stochastic Volatility Models 11.10 Long Memory SV Models 11.11 Multivariate Stochastic Volatility Models 11.12 ARCH versus SV 11.13 Concluding Remarks 11.14 Appendix: Filtering Equations IV: High-Frequency Methods 12 High-Frequency Data and Models 12.1 Introduction 12.2 High-Frequency Prices 12.3 One Day of High-Frequency Price Data 12.4 Stylized Facts for Intraday Returns 12.5 Intraday Volatility Patterns 12.6 Discrete-Time Intraday Volatility Models 12.7 Trading Rules and Intraday Prices 12.8 Realized Volatility: Theoretical Results 12.9 Realized Volatility: Empirical Results 12.10 Price Discovery 12.11 Durations 12.12 Extreme Price Changes 12.13 Daily High and Low Prices 12.14 Concluding Remarks 12.15 Appendix: Formulae for the Variance of the Realized Volatility Estimator V: Inferences from Option Prices 13 Continuous-Time Stochastic Processes 13.1 Introduction 13.2 The Wiener Process 13.3 Diffusion Processes 13.4 Bivariate Diffusion Processes 13.5 Jump Processes 13.6 Jump-Diffusion Processes 13.7 Appendix: a Construction of the Wiener Process 14 Option Pricing Formulae 14.1 Introduction 14.2 Definitions, Notation, and Assumptions 14.3 Black-Scholes and Related Formulae. 14.4 Implied Volatility 14.5 Option Prices when Volatility Is Stochastic 14.6 Closed-Form Stochastic Volatility Option Prices 14.7 Option Prices for ARCH Processes 14.8 Summary 14.9 Appendix: Heston's Option Pricing Formula 15 Forecasting Volatility 15.1 Introduction 15.2 Forecasting Methodology 15.3 Two Measures of Forecast Accuracy 15.4 Historical Volatility Forecasts 15.5 Forecasts from Implied Volatilities 15.6 ARCH Forecasts that Incorporate Implied Volatilities 15.7 High-Frequency Forecasting Results 15.8 Concluding Remarks 16 Density Prediction for Asset Prices 16.1 Introduction 16.2 Simulated Real-World Densities 16.3 Risk-Neutral Density Concepts and Definitions 16.4 Estimation of Implied Risk-Neutral Densities 16.5 Parametric Risk-Neutral Densities 16.6 Risk-Neutral Densities from Implied Volatility Functions 16.7 Nonparametric RND Methods 16.8 Towards Recommendations 16.9 From Risk-Neutral to Real-World Densities 16.10 An Excel Spreadsheet for Density Estimation 16.11 Risk Aversion and Rational RNDs 16.12 Tail Density Estimates 16.13 Concluding Remarks Symbols References Author Index Subject Index.
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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2021. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.