Bayesian Trading Cost Analysis and Ranking of Broker Algorithms

We present a formulation of the transaction cost analysis (TCA) in the Bayesian framework for the primary purpose of comparing broker algorithms using standardized benchmarks. Our formulation allows effective calculation of the expected value of trading benchmarks with only a finite sample of data relevant to practical applications. We discuss the nature of distribution of implementation shortfall, volume-weighted average price, participation-weighted price and short-term reversion benchmarks. Our model takes into account fat tails, skewness of the distributions and heteroscedasticity of benchmarks. The proposed framework allows the use of hierarchical models to transfer approximate knowledge from a large aggregated sample of observations to a smaller sample of a particular algorithm.