We undertake a comprehensive investigation of price and volume co-movement using daily New York Stock Exchange data from 1928 to 1987. We adjust the data to take into account well-known calendar effects and long-run trends. To describt tbe process, we use a seminonparametric estimate of the joint density of current price change and volume conditional on past price changes and volume. Four empirical regularities are found: 1) positive correlation between conditional volatility and volume, 2) large price movements are followed by high volume, 3) conditioning on lagged volume substantially attenuates the "leverage " effect, and 4) after conditioning on lagged volume, there is a positive risk/return relation.

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. This paper uses waveform dictionaries to decompose the signals contained within three foreign exchange rates using tick-by-tick observations obtained world wide. The three exchange rates examined are the Japanese Yen and the German Deutsche Mark against the U.S. dollar and the Deutsche Mark against the Yen. The data were provided by Olsen Associates. A waveform dictionary is a class of transforms that generalizes both windowed Fourier transforms and wavelets. Each wave form is parameterized by location, frequency, and scale. Such transforms can analyze signals that have highly localized structures in either time or frequency space as well as broad band structures; that is, waveforms can, in principle, detect everything from shocks represented by Dirac Delta functions, to "chirps", short bursts of energy within a narrow band of frequencies, to the presence of frequencies that occur sporadically, and finally to the presence of frequencies that hold over the entire observed period. Wave...

The volatility of a financial asset is the variance per unit time of the logarithm of the price of the asset. Volatility has a key role to play in the determination of risk and in the valuation of options and other derivative securities. The widespread Black-Scholes model for asset prices assumes constant volatility. The purpose of this chapter is to review the evidence for non-constant volatility and to consider the implications for option pricing of alternative random or stochastic volatility models. We concentrate on continuous time diffusion models for the volatility, but we also make comments about certain classes of discrete time models, such as ARV, ARCH and GARCH. 1 Volatility and the need for Stochastic Volatility models 1.1 Introduction A common approach in the modelling of financial assets is to assume that the proportional price changes of an asset form a Gaussian process with stationary independent increments. The celebrated (and ubiquitous) Black-Scholes option pricin...

This paper develops a subordinated stochastic process model for the asset price, where the directing process is identied as information. Motivated by recent empirical and theoretical work, we make use of the under-used market statistic of transaction count as a suitable proxy for the information ow. An option pricing formula is derived, and comparisons with stochastic volatility models are drawn. Both the asset price and the number of trades are used in parameter estimation. The underlying process is found to be fast mean reverting, and this is exploited to perform an asymptotic expansion. The implied volatility skew is then used to calibrate the model. 1 1 Introduction Derivative pricing depends crucially on the assumptions made concerning the distributional properties of the asset price. Without some model of the underlying price process, it is impossible to price a derivative. There are many variations on the lognormality assumption in the Black{Scholes model of option...

In this study, we demonstrate how price limits can a#ect a return series on limit-hitting days. Our identification of two e#ects -- a ceiling e#ect and a cooling or heating e#ect (C-H e#ect) is based on a resampling method suggested by Wei and Chiang (1999). We estimate the C-H e#ect by assuming that the return series will have a mixture normal density instead of a simple normal density. We apply our models to five randomly selected Taiwnese stocks as well as all the stocks that are continuously traded in our sample period. The simple normal density is soundly rejected and it would generally lead one to conclude that price limits can "cool o#" stock prices. On the other hand, if normal mixture density is used, one would generally conclude that price limits will have no e#ect on the variance of stock returns. Key Words: price limits, normal mixture # We thank Brad DeLong, Qi Li and John Quigley for useful comments. The remaining errors are ours.

This paper examines causality between the series of returns and transaction volumes in high frequency data. The dynamics of both series is restricted to transitions between a finite number of states. Depending on the state selection criteria, this approach approximates the dynamics of varying market regimes, or in a broader sense reflects the time varying heterogeneity of traders behavior. Our analysis is based on returns and volumes represented by Markov chains with constant or time varying transition probabilities. We derive methods to estimate the transition probabilities, the long run equilibrium probability, and the instantaneous speed of adjustments. The limiting transition probability approximates the average proportion of time spent by the processes in a given state whereas the adjustment speed reveals the frequency of stock market fluctuations between states. The univariate return series is examined to identify varying market regimes and determine the impact of stat...

DRAFT It is generally recognized that volatility in the prices of securities is due, in part, to traders continuously revising their preference sets in response to the arrival of unanticipated information. In particular, traders may update beliefs about the value of an asset in response to information on both market microstructure and the macro-economy. We argue that the microstructure characteristics of the Trinidad and Tobago Stock Exchange (TTSE) are consistent with serial correlation, volatility clustering, and nonlinearity in stock returns. The underlying behavioural patterns arise because informed traders may possess “long-lived ” information sets arising from poor dissemination and disclosure of market information. The paper has two objectives: (1) to investigate a price-volume relationship for stock returns, accounting for conditional heteroscedasticity and nonlinearity; and (2) to determine whether volume is a sufficient proxy for information flow. Our results show that simple linear autoregressive models of stock returns display significant nonlinearities, which can partly be explained by functional and variable misspecification in the functions describing the mean and variance of returns. In particular, we find that prices and volume are not sufficient statistics for the conditioning information set of traders because both volume and the real effective exchange rate are significant predictors for the distribution of stock returns.

In this paper we investigate whether macroeconomic variability can explain time variation in European stock market volatility. We ...nd that unlike the documented case of the U.S., in many cases, the time variation in stock market volatility is found to be signi...cantly aected by the past variability of either monetary or real macroecomic factors. Our ...ndings have important implications for capital and portfolio allocations. Classi...cation codes: G15, F41 Keywords: European stock markets, volatility, macroeconomic determinants, predictability Errunza is from the Faculty of Management, McGill University, Montreal, and Hogan is from Barclays Global Investors, San Francisco. The authors thank SSHRC for ...nancial support. Hogan also thanks FCAR for ...nacial support. We are grateful to an anonymous referee for many suggestions and the participants at the European Financial Management Conference for their helpful comments. 1 MACROECONOMIC DETERMINANTS OF EUROPEAN STOCK MARKE...

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