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Description of Asset Price Dynamics, Volatility, and Prediction

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.

Title Information

ISBN:

9780691115375

Pages:

544 pages

Format:

Hardback

Product Code:

22119

Publisher:

Princeton University Press

Published:

08/08/2005

Edition:

illustrated edition

Press and Industry Reviews

"I enjoyed reading this book, which offers a close to unique merging of detailed and careful empirics with the finance and time series theory associated with the study of asset pricing dynamics."
- Neil Shephard, Fellow, Nuffield College; Professor of Economics, Oxford University

"This well written text nicely balances new developments in various areas of theoretical and empirical finance, and it explains in a concise way how various models and methods are related."
- Philip Hans Franses, Professor of Applied Econometrics, Econometric Institute, Erasmus University, Rotterdam

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About Stephen J. Taylor

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.

Contents of Asset Price Dynamics, Volatility, and Prediction

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


PART 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


PART 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


PART 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


PART 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


PART 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