We propose a model selection method to systematically evaluate the contribution to asset pricing of any new factor, above and beyond what a high-dimensional set of existing factors explains. Our methodology accounts for model selection mistakes that produce a bias due to omitted variables, unlike standard approaches that assume perfect variable selection. We apply our procedure to a set of factors recently discovered in the literature. While most of these new factors are shown to be redundant relative to the existing factors, a few have statistically significant explanatory power beyond the hundreds of factors proposed in the past.

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We propose a model-selection method to systematically evaluate the contribution to asset pricing of any new factor, above and beyond what a high-dimensional set of existing factors explains. Our methodology explicitly accounts for potential model-selection mistakes, unlike the standard approaches that assume perfect variable selection, which rarely occurs in practice and produces a bias due to the omitted variables. We apply our procedure to a set of factors recently discovered in the literature. While most of these new factors are found to be redundant relative to the existing factors, a few-such as profitability-have statistically significant explanatory power beyond the hundreds of factors proposed in the past. In addition, we show that our estimates and their significance are stable, whereas the model selected by simple LASSO is not.

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This paper employs a Skellam process to represent real-time betting odds for English Premier League (EPL) soccer games. Given a matrix of market odds on all possible score outcomes, we estimate the expected scoring rates for each team. The expected scoring rates then define the implied volatility of an EPL game. As events in the game evolve, we re-estimate the expected scoring rates and our implied volatility measure to provide a dynamic representation of the market's expectation of the game outcome. Using a dataset of 1520 EPL games from 2012-2016, we show how our model calibrates well to the game outcome. We illustrate our methodology on real-time market odds data for a game between Everton and West Ham in the 2015-2016 season.We show how the implied volatility for the outcome evolves as goals, red cards, and corner kicks occur. Finally, we conclude with directions for future research.