Asset Price Dynamics, Volatility, and Prediction

This hardback book is a 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. The book is organized into five parts each with up to four chapters. The introduction covers useful definitions, information that is relevant to assessing asset values, relevant software, including the popular and easy-to-use EXCEL, and Web resources. Most chapters end with a combination of a summary, concluding remarks and further reading. The remainder of the book contains a listing of the symbols, Greek and Roman letters, mathematical notations and acronyms that are used, a comprehensive list of references and the author and subject index. Part I covers foundations and an array of housekeeping issues. Chapter 2, ‘Prices and returns’, covers further definitions, examples and data collection issues and the time series of asset returns. Chapter 3, ‘Stochastic processes’, looks at definitions and examples, random variables, stationarity, the autoregressive integrated moving average family of processes and linear and continuous time processes. Chapter 4, ‘Stylized facts for financial returns’, extends key housekeeping issues by focusing on summary statistics, measurement, calendar effects, distribution issues, autocorrelations and non-linearity. The author provides a thorough coverage of important issues that acts as the foundation for a good understanding of the intrinsic dynamics of asset prices. Part II, on conditional expected returns, contains three chapters which focus on tests of the random-walk hypothesis, trading rules and market efficiency. Chapter 5 focuses on the variance ratio test and provides a practical and reusable example in EXCEL along with the results for some assets for daily, weekly, monthly and annual returns as well as more details on autocorrelation theory with results for various assets. Chapter 6 covers further tests of the random-walk hypothesis and compares them with the variance ratio test. These alternative tests are designed to identify other causal factors than randomness in determining asset prices such as price trends, cyclical patterns and mean reversion. Chapter 7, ‘Trading rules and market efficiency’, focuses on the information that trading rules contain about future asset price returns. Four such rules are evaluated, namely the short and long run moving average and channel, filter and statistical autoregressive moving average. There is a practical and reusable example of the moving average rule in EXCEL and the remainder of the chapter considers methodologies for assessing market efficiency. The four chapters in part III, on volatility processes, form the core of the book, in that they are central to the topics that are covered in parts IV and V. Chapter 8 serves as an introduction to the concept of volatility, with definitions, explanations of why volatility changes, the effect of the arrival of information on volatility and a classification of volatility-stylized facts for asset returns. Chapter 9 considers autoregressive conditional heteroscedasticity (ARCH) models in detail, covering key definitions and providing several very useful practical and reusable examples of the different class of models for exchange rates in EXCEL. Chapter 10 considers ARCH models in further detail, particularly exponential generalized (EGARCH) models, GJR and others by addressing issues that are associated with model selection and methods of estimation. There is an extension that addresses issues that are associated with models that have long memories and the introduction of the concept of fractional integration from the autoregressive fractional integrated moving average ARFIMA(1,d,1) class of models to EGARCH giving the FIEGARCH(1,d,1) class. There are examples of the application of these models and the main findings, tests for normality, the unit root in volatility, best practice when building such models and practical implementation with examples for exchange rate and equity. Chapter 11, ‘Stochastic volatility models’, extends the concepts that are discussed in Chapter 10 addressing volatility as a discrete stochastic process. Stochastic volatility is defined as a stochastic process, and after good background information a standard stochastic volatility model is discussed and then estimated in EXCEL for exchange rates. The chapter goes on to discuss long memory in stochastic volatility models and multivariate forms of such models and compares them with ARCH models before giving concluding remarks. Part IV, on high frequency methods, has one chapter that is dedicated to high frequency data and models. It is somewhat specialized in that it covers issues around large data sets that result from sampling multiple times within the hour such as half-hourly, quarter-hourly, and every 5 minutes to realtime. Such data sets are common in equities, exchange rate and energy markets and provide some advantages but with intrinsic challenges. The chapter starts with an introduction that focuses on the pros and cons such as improved accuracy, difficulties in modelling market behaviour, data sampling, the effect of the arrival of information, intrinsic dynamic behaviour, large data sets management and the costs of acquiring such data. It then moves on to discuss key issues such as the stylized facts for intraday returns, intraday volatility and discrete structures, trading rules, realized volatility and extreme events. Part V, on inference from option pricing, contains Chapters 13–16 with Chapter 13 setting the focus on continuous time processes which extends the dynamic processes that are outlined in Chapter 12, on the one hand, and sets the foundation for later option pricing and volatility analysis, on the other. Chapter 13 really serves as an introduction to continuous time processes and outlines the key processes such as Brownian motion, diffusion and jumps in a manner that is not too mathematically taxing. Chapter 14 is concerned entirely with the pricing of options for asset prices that have different stochastic volatility. It starts with an introduction and then moves to cover definitions, notation and assumptions; a discussion of the Black–Scholes pricing formula, implied volatility, the properties of option prices when volatility is stochastic and option prices for processes that can be modelled by using ARCH. There is an example in EXCEL of the general Black–Scholes price formula which can be reused to carry out sensitivity and simulation analysis. Chapter 15 covers volatility forecasting as an integral part of asset risk portfolio management through the gathering of information about the future dynamic path of the portfolio. The chapter starts by identifying that there are numerous forecasting methodologies with varying and at times contradictory results that stem from volatility being unobserved. It then moves on to look at these methodologies, historical volatility forecasts, forecasts from implied volatility and ARCH and high frequency forecasts. Chapter 16 covers density prediction for asset prices and here the focus is to forecast the distribution of future asset prices, not just information about the price distribution based on the forecast of volatility. The chapter makes it clear that this is not an easy forecasting exercise and that there are several methods that can be employed. It also stresses that such densities have several applications in assessing market sentiment and option pricing. Real world densities are simulated from ARCH models of historical asset prices and risk neutral densities from option prices. There is a discussion on how to simulate real world densities by using ARCH, an overview of the concepts and definitions of risk neutral densities, estimation of implied risk neutral densities highlighting the lack of insight into the true specification of risk neutral density, risk neutral densities from implied volatility and the relationship between risk neutral and real world densities. The chapter ends with a practical and reusable example of how to calculate the risk neutral and real world density estimation in EXCEL. I recommend this book to a large audience, including data and quantitative analysts with an interest in asset price dynamics, modelling and forecasting, and financial analysts who are interested in modelling and forecasting volatility and option pricing. Asset risk analysts and risk managers who are interested in using advanced methods and techniques in modelling and managing asset prices, academic and industry researchers seeking to extend and apply their existing knowledge in the area, teachers, advanced graduates and undergraduates will all benefit from the various practical and reusable examples of models and calculations that are carried out in EXCEL. Importantly, throughout the book one does not need to be very well versed in the mathematics of stochastic processes, volatility and option pricing to follow the material and to be able to understand and apply the calculations and examples.