# Asset Price Dynamics, Volatility, and Prediction

Stephen J. Taylor
Edition: STU - Student edition
Pages: 544
https://www.jstor.org/stable/j.ctt7t66m

1. Front Matter
(pp. i-vi)
(pp. vii-xii)
3. Preface
(pp. xiii-xviii)
4. 1 Introduction
(pp. 1-6)

Asset prices move as time progresses: they are dynamic. It is certainly very difficult to provide a correct prediction of future price changes. Nevertheless, we can make statements about the probability distributions that govern future prices. Asset price dynamics are statements that contain enough detail to specify the probability distributions of future prices. We seek statements that are empirically credible, that can explain the historical prices that we have already seen.

Investors and fund managers who understand the dynamic behavior of asset prices are more likely to have realistic expectations about future prices and the risks to which they are...

5. I Foundations
• 2 Prices and Returns
(pp. 9-22)

Methods for creating time series of market prices and returns to investors are described and illustrated in this chapter.

Any empirical investigation of the behavior of asset prices through time requires price data. Some questions to be answered are, Where will we find our data?, How many years of data do we want to analyze?, and How many prices for each year do we wish to obtain? Advice on these topics and other data-collection issues is provided in Section 2.3, after first presenting two representative examples of price series in Section 2.2.

Almost all empirical research analyzes returns to investors...

• 3 Stochastic Processes: Definitions and Examples
(pp. 23-50)

Prices and returns are modeled throughout this book by time-ordered sequences of random variables, called stochastic processes. This chapter reviews their definitions and properties. A key property is the level of correlation between variables measured at different times. We cover processes that exhibit a variety of correlation patterns, including several processes that possess no correlation across variables.

A time series of returns is a single sample that arises from competitive trading at a market. We are interested in probability models that can explain the data that we see and that can then be used to make predictions. These probability models...

• 4 Stylized Facts for Financial Returns
(pp. 51-96)

Several statistical properties of daily returns are documented and discussed in this chapter, before testing hypotheses and estimating time-series models in later chapters. These properties are presented for the means, variances, distributions, and autocorrelations of returns by referring to empirical evidence obtained from many datasets, including the twenty time series introduced in Chapter 2. This chapter ends by emphasizing that linear stochastic processes cannot explain all the empirical properties of returns.

General properties that are expected to be present in any set of returns are called stylized facts. There are three important properties that are found in almost all sets...

6. II Conditional Expected Returns
• 5 The Variance-Ratio Test of the Random Walk Hypothesis
(pp. 99-120)

Comparisons between the variances of one-period and multi-period returns are used to test the random walk hypothesis in this chapter. This variance-ratio test is straightforward and often powerful for detecting departures from randomness. Several empirical examples are discussed, as well as theoretical properties of the test statistic. These properties depend on results about the distributions of sample autocorrelations.

Chapters 5–7 cover tests about the conditionalfirstmoment properties of returns. These tests answer several questions, including, Are returns unpredictable? and Are markets weak-form efficient? Some readers may want to assume the answers are “yes” and to focus on understanding...

• 6 Further Tests of the Random Walk Hypothesis
(pp. 121-156)

Several test statistics are defined and evaluated for twenty time series of daily returns in this chapter. Significant, positive dependence is found in a majority of the series, and almost no dependence in the remaining series. The results are consistent with substantial variation in the power of the tests to detect the small dependence present in some of the series.

A variety of random walk tests have been motivated by particular alternatives to randomness. These alternatives include trends in prices, mean-reversion in prices, cyclical patterns, long-range dependence, and chaotic dynamics. This chapter covers several test statistics and compares their results...

• 7 Trading Rules and Market Efficiency
(pp. 157-186)

Trend-following trading rules have the potential to exploit any positive autocorrelation in the stochastic process that generates returns. Four of these rules are evaluated in this chapter. There have been long periods in the past when trading rules would have provided valuable information about future prices. However, their value has not been demonstrated in recent years.

Trading rules are numerical methods that use a time series of prices to decide the quantity of an asset owned by a market participant. This chapter considers the information that can be obtained from trading rules. Both the paradigm of efficient markets and the...

7. III Volatility Processes
• 8 An Introduction to Volatility
(pp. 189-196)

Asset price volatility is central to the following seven chapters, in which we cover volatility measurement and modeling, continuous-time processes, option pricing formulae, and volatility forecasting. This short introductory chapter commences with definitions of volatility and continues with a general discussion of explanations for volatility changes. It is then shown that volatility changes explain the major stylized facts for time series of asset returns.

Volatility is a measure of price variability over some period of time. It typically describes the standard deviation of returns, in a particular context that depends on the definition used. Alternatively, we can say that volatility...

• 9 ARCH Models: Definitions and Examples
(pp. 197-234)

Examples of models for the conditional variances of returns are described and estimated in this chapter. These models are easy to estimate from a time series of returns and provide insights into the movement of volatility through time. The models belong within a general class of ARCH models that is also defined.

ARCH stands forautoregressive conditional heteroskedasticity. Changes in the scale of a variable give us the wordheteroskedastic. A scale parameter is a standard deviation or a variance and the variable of interest here is the return from an asset. The variance of a return,conditionalon the...

• 10 ARCH Models: Selection and Likelihood Methods
(pp. 235-266)

Several additional ARCH models are described in this chapter. Methods for selecting a model from the many possibilities are given, including hypothesis tests that use maximum likelihood estimates and their standard errors.

There seem to be few limits to the complexity that can be built into an ARCH model. The simple examples described in Chapter 9 suffice for many purposes. There are, however, applications that require more complicated structures, as does the search for more accurate descriptions of observed returns. The exponential GARCH model of Nelson (1991) is another asymmetric volatility model. It is described in Section 10.2, where we...

• 11 Stochastic Volatility Models
(pp. 267-302)

Stochastic processes for volatility and hence returns are defined and investigated in this chapter. These models have a simple structure and can explain the major stylized facts for asset returns. Their parameters can be estimated in many ways, although the most efficient methods are rather complicated.

Volatility changes are so frequent that it is appropriate to model volatility by a random variable. We now do this in a discrete-time framework, although it is also instructive to consider continuous-time models when pricing options as we will see later in Chapter 14. Volatility cannot be observed directly from discrete-time returns data because...

8. IV High-Frequency Methods
• 12 High-Frequency Data and Models
(pp. 305-350)

Prices recorded several times each hour generate large datasets. Several properties and applications of these high-frequency datasets are described in this chapter, for both equity and foreign exchange markets. Special attention is given to the more precise volatility estimates obtained from high-frequency return data.

High-frequency is the adjective used to indicate that prices are recorded more often than daily. The more prices a day, the higher is the frequency of the observations. Complete datasets contain all prices and/or quotes, for which Engle (2000) uses the phrase ultra-high frequency. Most research, however, employs regularly sampled data and the most common frequency...

9. V Inferences from Option Prices
• 13 Continuous-Time Stochastic Processes
(pp. 353-368)

Diffusion and jump processes that are defined for a continuous range of times are described in this chapter and used to construct a variety of processes for prices and their stochastic volatility. These processes are of particular importance when option prices are considered in later chapters.

The stochastic processes that describe prices in the previous chapters only provide probability distributions for asset prices at discrete moments in time, typically once every day or once every five minutes. Processes defined for a continuous range of times are also interesting. They are important when pricing option contracts, whose prices can help us...

• 14 Option Pricing Formulae
(pp. 369-396)

This chapter reviews the determination of rational option prices for a variety of stochastic processes for the underlying asset price. These option prices often depend on a volatility risk premium. The chapter also covers the inverse problem of using observed asset and option prices to obtain implied levels of future volatility.

Option prices are a source of valuable information about the distributions of future asset prices. This motivates our interest in option pricing formulae, which are needed to extract and interpret predictive information from the market prices of options. This chapter includes several pricing formulae for European options, all of...

• 15 Forecasting Volatility
(pp. 397-422)

Several methods for forecasting volatility are reviewed in this chapter. Forecasts derived from option prices and intraday asset prices are of particular interest—they incorporate more volatility information than the history of daily asset prices and they provide superior predictions.

Forecasts of volatility are important when assessing and managing the risks of portfolios that may include derivative securities. A remarkable variety of methods have been used and the conclusions obtained often appear to be contradictory. This variety reflects the fact that volatility is inherently unobservable, so that forecasts must be made of related observable quantities. It also reflects the increasing...

• 16 Density Prediction for Asset Prices
(pp. 423-466)

Probability densities for future asset prices can often be obtained from previous asset prices and/or the prices of options. This chapter describes many of the methods that have been proposed and provides numerical examples of one-month-ahead predictive densities.

A volatility forecast is a number that provides some information about the distribution of an asset price in the future. A far more challenging forecasting problem is to use market information to produce a predictive density for the future asset price. A realistic density will have a shape that is more general than provided by the lognormal family. In particular, a satisfactory...

10. Symbols
(pp. 467-472)
11. References
(pp. 473-502)
12. Author Index
(pp. 503-512)
13. Subject Index
(pp. 513-525)