[In a one-period model of market making with many exogenously informed traders, we first show that the variance of prices and expected trading volume depend on the public information released at the start of trading. This is accomplished by representing beliefs with elliptically contoured distributions, for which the form of optimal decision rules does not depend on the specific distribution used. Second, if the model is altered so that the decision to become informed is made endogenous, then the decision rules of the market-maker and informed traders depend on the public information. Third, in a multiperiod model with many informed traders and long-lived private information, recursion formulas similar to those of Kyle (1985) hold for all elliptically contoured distributions, trading volume is autocorrelated, and, unless per period liquidity trading is bounded away from zero as new trading periods are added, informed traders' profits vanish.]

The authors argue that arbitrage pricing theories (APT) imply the existence of a low-dimensional nonnegative nonlinear pricing kernel. In contrast to standard constructs of the APT, they do not assume a linear factor structure on the payoffs. This allows the authors to price both primitive and derivative securities. Seminonparametric techniques are used to estimate the pricing kernel and test the theory. Empirical results using size-based portfolio returns and yields on bonds reject the nested capital asset pricing model and linear APT and support the nonlinear APT. Diagnostics show that the nonlinear model is more capable of explaining variations in small firm returns.

Patterns in stock market trading volume, trading costs, and return volatility are examined using New York Stock Excha nge data from 1988. Intraday test results indicate that, for actively traded firms trading volume, adverse selection costs, and return volatility are higher in the first half-hour of the day. This eviden ce is inconsistent with the Admati and Pfleiderer (1988) model which predicts that trading costs are low when volume and return volatilit y are high. Interday test results show that, for actively traded firms , trading volume is low and adverse selection costs are high on Monday , which is consistent with the predictions of the Foster and Viswanath an (1990) model.

F. Douglas Foster, S. Viswanathan, Variations in Trading Volume, Return Volatility, and Trading Costs: Evidence on Recent Price Formation Models, The Journal of Finance, Vol. 48, No. 1 (Mar., 1993), pp. 187-211

In a one-period model of market making with many exogenously informed traders, we first show that the variance of prices and expected trading volume depend on the public information released at the start of trading. This is accomplished by representing beliefs with elliptically contoured distributions, for which the form of optimal decision rules does not depend on the specific distribution used. Second, if the model is altered so that the decision to become informed is made endogenous, then the decision rules of the market-maker and informed traders depend on the public information. Third, in a multiperiod model with many informed traders and long-lived private information, recursion formulas similar to those of Kyle (1985) hold for all elliptically contoured distributions, trading volume is autocorrelated and, unless per period liquidity trading is bounded away from zero as new trading periods are added, informed traders’ profits vanish.

This paper uses a nonlinear arbitrage-pricing model, a conditional linear model, and an unconditional linear model to price international equities, bonds, and forward currency contracts. Unlike linear models, the nonlinear arbitrage-pricing model requires no restrictions on the payoff space, allowing it to price payoffs of options, forward contracts, and other derivative securities. Only the nonlinear arbitrage-pricing model does an adequate job of explaining the time-series behavior of a cross section of international returns.

ABSTRACT Patterns in stock market trading volume, trading costs, and return volatility are examined using New York Stock Exchange data from 1988. Intraday test results indicate that, for actively traded firms trading volume, adverse selection costs, and return volatility are higher in the first half‐hour of the day. This evidence is inconsistent with the Admati and Pfleiderer (1988) model which predicts that trading costs are low when volume and return volatility are high. Interday test results show that, for actively traded firms, trading volume is low and adverse selection costs are high on Monday, which is consistent with the predictions of the Foster and Viswanathan (1990) model.

This paper uses a nonlinear arbitrage-pricing model, a conditional linear model, and an unconditional linear model to price international equities, bonds, and forward currency contracts. Unlike linear models, the nonlinear arbitrage-pricing model requires no restrictions on the payoff space, allowing it to price payoffs of options, forward contracts, and other derivative securities. Only the nonlinear arbitrage-pricing model does an adequate job of explaining the time series behavior of a cross section of international returns.

ABSTRACT We argue that arbitrage‐pricing theories (APT) imply the existence of a low‐dimensional nonnegative nonlinear pricing kernel. In contrast to standard constructs of the APT, we do not assume a linear factor structure on the payoffs. This allows us to price both primitive and derivative securities. Semi‐nonparametric techniques are used to estimate the pricing kernel and test the theory. Empirical results using size‐based portfolio returns and yields on bonds reject the nested capital asset‐pricing model and linear APT and support the nonlinear APT. Diagnostics show that the nonlinear model is more capable of explaining variations in small firm returns.