No abstract

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 describe the process, we use a seminonparametric estimate of the joint density of current price change and volume conditional on past price changes and volume. Six empirical regularities are found: 1) highly persistent price volatility, 2) positive correlation between current price change and volume, 3) a peaked, thick-tailed conditional price change density, 4) large price movements are followed by high volume, 5) conditioning on lagged volume substantially attenuates the "leverage" effect, and 6) after conditioning on lagged volume, there is a positive risk/return relation. The first three findings are generally corroborative of those of previous studies. The last three findings are original to this paper.

Nous examinons un ensemble de diffusions avec volatilité stochastique et de sauts afin de modéliser la distribution des rendements d'actifs boursiers. Puisque certains modèles sont nonemboîtés, nous utilisons la méthode EMM afin d'étudier et de comparer le comportement des différents modèles. This paper evaluates the role of various volatility specifications, such as multiple stochastic volatility (SV) factors and jump components, in appropriate modeling of equity return distributions. We use estimation technology that facilitates non-nested model comparisons and use a long data set which provides rich information about the conditional and unconditional distribution of returns. We consider two broad families of models: (1) the multifactor loglinear family, and (2) the affine-jump family. Both classes of models have attracted much attention in the derivatives and econometrics literatures. There are various trade-offs in considering such diverse specifications. If pure diffusion SV models are chosen over jump diffusions, it has important implications for hedging strategies. If logaritmic models are chosen over affine ones, it may seriously complicate option pricing. Comparing many different specifications of pure diffusion multi-factor models and jump diffusion models, we find that (1) log linear models have to be extented to 2 factors with feedback in the mean reverting factor, (2) affine models have to have a jumps in r eturns, stochastic volatility and probably both. Models (1) and (2) are observationally equivalent on the data set in hand. In either (1) or (2) the key is that the volatility can move violently. As we obtain models with comparable empirical fit, one must make a choice based on arguments other than statistical goodness of fit criteria. The considerations include facility to price options, to hedge and parsimony. The affine specification with jumps in volatility might therefore be preferred because of the closed-form derivatives prices. * We would like to thank Torben Andersen, the Editor, two anonymous referees and Nour Medahi, the third referee, for comments that substantially improved the paper. We are also grateful to Luca Benzoni, Paul Glasserman, Micheal Johannes, David Robinson, the conference and seminar participants at the CAP Mathematical Finance Workshop, Columbia University, the Conference on Risk Neutral and Objective Probability Distributions, Fuqua School of Business, Duke University, CIRANO and Vanderbilt University for their comments. All remaining errors are our own. This paper subsumes part of the material presented in the working paper titled. "A New Class of Stochastic Volatility Models with Jumps: Theory and Estimation."

No abstract

No abstract