Lookback options are path dependent contingent claims whose payoffs depend on the extrema of a given security's price over a certain period of time. Using probabilistic tools, the authors derive explicit formulas for various European lookback options and provide some results about their American counterparts.

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.

The authors analyze a multiperiod model of trading with differentially informed traders, liquidity traders, and a marketmaker. Each informed trader's initial information is a noisy estimate of the long-term value of the asset and the different signals received by informed traders can have a variety of correlation structures. With this setup, informed traders not only compete with each other for trading profits, they also learn about other traders' signals from the observed order flow. The authors' work suggests that the initial correlation among the informed traders' signals has a significant effect on the informed traders' profits and the informativeness of prices.

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

The practices of preferencing and internalization have been alleged to support collusion, cause worse execution, and lead to wider spreads in dealership style markets relative to auction style markets. For a sample of London Stock Exchange stocks, we find that preferenced trades pay higher spreads, however they do not generate higher dealer profits. Internalized trades pay lower, not higher, spreads. We do not find a relation between the extent of preferencing or internalization and spreads across stocks. These results do not lend support to the “collusion” hypothesis but are consistent with a “costly search and trading relationships” hypothesis.

Using London Stock Exchange data, we test the central implication of the canonical model of Ho and Stoll (1983) that relative inventory differences determine dealer behavior. We find that relative inventories explain which dealers obtain large trades and show that movements between best ask, best bid, and straddle are highly correlated with both standardized and relative inventory changes. We show that the mean reversion in inventories is highly nonlinear and increasing in inventory levels. We show that a key determinant of variations in interdealer trading is inventories and that interdealer trading plays an important role in managing large inventory positions.

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 Lookback options are path dependent contingent claims whose payoffs depend on the extrema of a given security's price over a certain period of time. Using probabilistic tools, we derive explicit formulas for various European lookback options, and provide some results about their American counterparts.

Lookback options are path dependent contingent claims whose payoffs depend on the extrema of a given security's price over a certain period of time. Using probabilistic tools, we derive explicit formulas for various European lookback options, and provide some results about their American counterparts.