Abstract: The impact of large trades on market prices is a widely discussed but rarely measured phenomenon, of essential importance to selland buy-side participants. We analyse a large data set from the Citigroup US equity trading desks, using a simple but realistic theoretical framework. We fit the model across a wide range of stocks, determining the dependence of the coefficients on parameters such as volatility, average daily volume, and turnover. We reject the common square-root model for temporary impact as function of trade rate, in favor of a 3/5 power law across the range of order sizes considered. Our results can be directly incorporated into optimal trade scheduling algorithms and pre- and post-trade cost estimation.

Abstract: This paper studies the “overpriced puts puzzle” – the finding that historical prices of the S&P 500 put options have been too high and incompatible with the canonical asset-pricing models, such as CAPMand Rubinstein (1976) model. Simple trading strategies that involve selling at-the-money and out-of-the-money puts would have earned extraordinary profits. To investigate whether put returns could be rationalized by another, possibly nonstandard equilibrium model, we implement a new methodology. The methodology is “model-free” in the sense that it requires no parametric assumptions on investors’ preferences. Furthermore, the methodology can be applied even when the sample is affected by certain selection biases (such as the Peso problem) and when investors’ beliefs are incorrect. We find that no model within a fairly broad class of models can possibly explain the put anomaly.

Abstract: Gene expression programming, a genotype/phenotype genetic algorithm (linear and ramified), is presented here for the first time as a new technique for the creation of computer programs. Gene expression programming uses character linear chromosomes composed of genes structurally organized in a head and a tail. The chromosomes function as a genome and are subjected to modification by means of mutation, transposition, root transposition, gene transposition, gene recombination, and one- and two-point recombination. The chromosomes encode expression trees which are the object of selection. The creation of these separate entities (genome and expression tree) with distinct functions allows the algorithm to perform with high efficiency that greatly surpasses existing adaptive techniques. The suite of problems chosen to illustrate the power and versatility of gene expression programming includes symbolic regression, sequence induction with and without constant creation, block stacking, cellular automata rules for the density-classification problem, and two problems of boolean concept learning: the 11-multiplexer and the GP rule problem.