Fixed Odds Bookmaking with Stochastic Betting Demands

Abstract

This paper studies fixed odds bookmaking in the market for bets in a British horse race. The bookmaker faces the risk of unbalanced liability exposures. Even random shocks in the noisy betting demands are costly to the bookmaker since his book could become less balanced. In our model, the bookmaker sets appropriate odds to influence the betting flow to mitigate the risk. The stylised fact of the favourite-longshot bias only arises from the model under specific assumptions. Our model offers insights into the complexity of managing a series of state contingent exposures such as options.

Optimal Bookmaking

“…Unlike our paper, Hodges et al (2013) do not allow the bookmaker to dynamically adjust prices as bets come in nor do they find an analytic solution for the bookmaker's optimal control. As far as we are aware, our paper is the first to provide a general framework for studying optimal bookmaking in a dynamic setting.…”

“…Existing literature on optimal bookmaking in the context of stochastic control appears to be rather scarce. In one of the few existing papers on the topic, Hodges et al (2013) consider the bookmaker of a horse race. In their paper, the probability that a given horse wins the race is fixed and the number of bets placed on a given horse is a normally distributed random variable with a mean that is proportional to the probability that the horse will win and inversely proportional to the price set by the bookmaker.…”

Bookmakers’ mispricing of the disappeared home advantage in the German Bundesliga after the COVID-19 break

“…The again so-called home bias refers to increased payouts (equivalent to higher odds) for the home team compared to the fair odds. Such biased odds can arise from the bookmakers' difficulty to assess the exact magnitude of the home advantage, their knowledge that fans are somewhat unable to assess teams' strength (Na, Su, and Kunkel 2019) or their goal to have a so-called balanced book, which is given if wagers on both outcomes (home and away win) level out such that bookmakers secure a profit independent of the game outcome (Hodges, Lin, and Liu 2013). Since bettors rather bet on underdogs than favourites, bookmakers offer favourable odds on home wins (Franke 2020).…”

New entry, strategic diversity and efficiency in soccer betting markets: the creation and suppression of arbitrage opportunities

“…An alternative view is that the objective of bookmakers is to balance their books, and as a result, secure profit independent of the event's outcome (Magee, 1990;Woodland andWoodland 1991, Hodges, Lin, andLiu, 2013). Such bookmakers will change their odds frequently in order to account for inventory imbalance.…”