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

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.

ABSTRACT 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.