This paper reviews previous and current research on the relation between price changes and trading volume in financial markets, and makes four contributions. First, two empirical relations are established: volume is positively related to the magnitude of the price change and, in equity markets, to the price change per se. Second, previous theoretical research on the price-volume relation is summarized and critiqued, and major insights are emphasized. Third, a simple model of the price-volume relation is proposed that is consistent with several seemingly unrelated or contradictory observations. And fourth, several directions for future research are identified.

https://www.jstor.org/stable/pdfplus/2330874.pdf

The Relation between Price Changes and Trading Volume: A Survey

This paper proposes a new statistical model for the analysis of data which arrive at irregular intervals. The model treats the time between events as a stochastic process and proposes a new class of point processes with dependent arrival rates. The conditional intensity is developed and compared with other self-exciting processes. Because the model focuses on the expected duration between events, it is called the autoregressive conditional duration (ACD) model. Asymptotic properties of the quasi maximum likelihood estimator are developed as a corollary to ARCH model results. Strong evidence is provided for duration clustering for the financial transaction data analyzed; both deterministic time-of-day effects and stochastic effects are important. The model is applied to the arrival times of trades and therefore is a model of transaction volume, and also to the arrival of other events such as price changes. Models for the volatility of prices are estimated with price-based durations, and examined from a market microstructure point of view.

Autoregressive conditional duration: a new model for irregularly spaced transaction data

New techniques for the analysis of stochastic volatility models in which the logarithm of conditional variance follows an autoregressive model are developed. A cyclic Metropolis algorithm is used to construct a Markov-chain simulation tool. Simulations from this Markov chain coverage in distribution to draws from the posterior distribution enabling exact finite-sample inference. The exact solution to the filtering/smoothing problem of inferring about the unobserved variance states is a by-product of our Markov-chain method. In addition, multistep-ahead predictive densities can be constructed that reflect both inherent model variability and parameter uncertainty. We illustrate our method by analyzing both daily and weekly data on stock returns and exchange rates. Sampling experiments are conducted to compare the performance of Bayes estimators to method of moments and quasi-maximum likelihood estimators proposed in the literature. In both parameter estimation and filtering, the Bayes estimators outperform ...

https://www.jstor.org/stable/info/1392199

Bayesian Analysis of Stochastic Volatility Models

This paper investigates the relationship between aggregate stock market trading volume and the serial correlation of daily stock returns. For both stock indexes and individual large stocks, the first-order daily return autocorrelation tends to decline with volume. The paper explains this phenomenon using a model in which risk-averse "market makers" accommodate buying or selling pressure from "liquidity" or "noninformational" traders. Changing expected stock returns reward market makers for playing this role. The model implies that a stock price decline on a high-volume day is more likely than a stock price decline on a low-volume day to be associated with an increase in the expected stock return.

/pdf/trading-volume-and-serial-correlation-in-stock-returns-37e99m1079.pdf

Trading Volume and Serial Correlation in Stock Returns

Financial market volatility is an important input for investment, option pricing, and financial market regulation. The emphasis of this review article is on forecasting instead of modelling; it compares the volatility forecasting findings in 93 papers published and written in the last two decades. Provided in this paper as well are volatility definitions, insights into problematic issues of forecast evaluation, data frequency, extreme values and the measurement of "actual" volatility. We compare volatility forecasting performance of two main approaches; historical volatility models and volatility implied from options. Forecasting results are compared across different asset classes and geographical regions.

/pdf/forecasting-volatility-in-financial-markets-a-review-4c8zo5z26d.pdf

Forecasting Volatility in Financial Markets: A Review

This paper concerns the relationship between the variability of the daily price change and the daily volume of trading on the speculative markets. Our work extends the theory of speculative markets in two ways. First, we derive from economic theory the joint probability distribution of the price change and the trading volume over any interval of time within the trading day. And second, we determine how this joint distribution changes as more traders enter (or exit from) the market. The model's parameters are estimated by FIML using daily data from the 90-day T-bills futures market. The results of the estimation can reconcile a conflict between the price variability-volume relationship for this market and the relationship obtained by previous investigators for other speculative markets. THIS PAPER CONCERNS the relationship between the variability of the daily price change and the volume of trading on speculative markets. Previous empirical studies [2, 3, 6, 12, 14, 16] of both futures and equity markets always find a positive association between price variability (as measured by the squared price change Ap2) and the trading volume.2 There are two explanations for the relationship. Clark's [2] explanation, which is secondary to his effort to explain why the probability distribution of the daily price change is leptokurtic, emphasizes randomness in the number of within-day transactions. In Clark's model the daily price change is the sum of a random number of within-day price changes. The variance of the daily price change is thus a random variable with a mean proportional to the mean number of daily transactions. Clark argues that the trading volume is related positively to the number of within-day transactions, and so the trading volume is related positively to the variability of the price change. The second explanation is due to Epps and Epps [6]. Their model examines the mechanics of within-day trading. The change in the market price on each within-day transaction or market clearing is the average of the changes in all of the traders' reservation prices. Epps and Epps assume there is a positive relationship between the extent to which traders disagree when they revise their reservation prices and the absolute value of the change in the market price. That is, an increase in the extent to which traders disagree is associated with a larger absolute price change. The price variability-volume relationship arises, then, because the volume of trading is positively related to the extent to which traders disagree when they revise their reservation prices.

/pdf/the-price-variability-volume-relationship-on-speculative-jr1ghxk23o.pdf

Mark Pitts

Papers

The price variability-volume relationship on speculative markets