Robert Bajons - Rethinking Goals Above Expectation (GAX): A semiparametric approach

Expected Goals (xG) are the output of a statistical model assigning a probability of success to shot using shot-specific covariates and are one of the most popular metrics in modern football (soccer) analytics. Popular xG models are based on flexible machine learning algorithms, such as extreme gradient boosting machines, that account for non-linear and interaction effects of the shot-specific covariates. As a measure of a shot’s value, it is commonly used to evaluate the shooting skills of players by considering goals over expectation (GAX), i.e., the difference between actual and expected goals for each shot. However, GAX is often criticized for being unstable over seasons and for not providing (direct) means of uncertainty quantification. In this work, we address both issues by showing how the player-specific GAX relates to a score test when the xG model is a logistic regression and using a nonparametric extension which can be based on any xG model derived from sufficiently powerful machine learning algorithms. Thus, we are able to leverage commonly used black-box xG models, while still obtaining valid statistical inferences on the player-specific odds (or probability) of scoring a goal. Moreover, in order to make the results more interpretable, we show how the proposed procedure relates to player-specific effect estimates in a partially linear logistic regression model of additive effects on the log-odds of scoring a goal from a shot. Finally, we apply our framework to the 2015/16 season of the top five European leagues, determine the best shooters, and compare results across state-of-the-art xG models.

Luna Rigby - If Not Now, Then When? Optimal Stopping of the American Put Under Model Risk.

We examine the impact of model misspecification on the optimal exercise strategy for an American put option. We work in a continuous-time economy, where the market maker prices options using the Heston model, which is assumed to be the true model. A smaller bank calibrates a misspecified model to European vanilla option prices stemming from the true model and then determines when to optimally exercise an American put. We first consider the case where the misspecified model is a Black-Scholes model and then move to the more general Dupire framework. Due to the absence of closed-form solutions for American options, we employ numerical simulations, where we make use of the Longstaff-Schwartz algorithm combined with a randomization procedure to estimate the optimal exercise boundaries. We compare the payoff distribution under the true optimal exercise rule to that of the misspecified rule.