Knowledge that Transforms

We study a financial market containing an infinite number of assets, where each asset price is driven by an idiosyncratic random source as well as by a systematic noise term. Introducing ”asymptotic assets“ which correspond to certain infinitely well diversified portfolios we study absence of (asymptotic) arbitrage, and in this context we obtain continuous time extensions of atemporal APT results. We also study completeness and derivative pricing, showing that the possibility of forming infinitely well diversified portfolios has the property of completing the market. It also turns out that models where the all risk is of diffusion type are qualitatively quite different from models where one risk is of diffusion type and the other is of Poisson type. We also present a simple martingale based theory for absence of asymptotic arbitrage.

The model of Foster-Viswanathan (1990, FV) predicts that information heterogeneity among market participants generates patterns in volume, trading costs and volatility. In the Italian Treasury bond market, periodic information asymmetry is related to the arrival of block orders from international investors, which cluster soon after the opening of the market and, respectively, of the US market. Our evidence is that volume is lower and trading costs are higher after the two openings, consistent with FV. We find only weak evidence that volatility behaves as implied by the model.

A three parameter stochastic process, termed the variance gamma process, that generalizes Brownian motion is developed as a model for the dynamics of log stock prices. Theprocess is obtained by evaluating Brownian motion with drift at a random time given by a gamma process. The two additional parameters are the drift of the Brownian motion and the volatility of the time change. These additional parameters provide control over the skewness and kurtosis of the return distribution. Closed forms are obtained for the return density and the prices of European options.The statistical and risk neutral densities are estimated for data on the S&P500 Index and the prices of options on this Index. It is observed that the statistical density is symmetric with some kurtosis, while the risk neutral density is negatively skewed with a larger kurtosis. The additional parameters also correct for pricing biases of the Black Scholes model that is a parametric special case of the option pricing model developed here.

This paper evaluates the welfare implications of front-running by mutual fund managers. It extends the model of Kyle (1985) to a situation in which the insider with fundamentals-information competes against an insider with trade-information and in which noise trading is endogenized. Noise traders are small investors trading through mutual funds to hedge non-tradable or illiquid assets. The insider with trade-information is one of the fund managers. We find that her front-running activity reduces the liquidity costs of her customers, but it also reduces their hedging benefits. As a result, the customers of the front-running manager may be worse off and place smaller orders. The opposite is true, however, for those investors who are not subject to front-running. In aggregate, front-running has either no or positive consequences for welfare. JEL Classification. G14, G23.