Modelling of the In-Play Football Betting Market

This thesis is about modelling the in-play football betting market. Our aim is to apply and extend financial mathematical concepts and models to value and risk-manage in-play football bets. We also apply machine learning methods to predict the outcome of the game using in-play indicators. In-play football betting provides a unique opportunity to observe the interplay between a clearly defined fundamental process, that is the game itself and a market on top of this process, the in-play betting market. This is in contrast with classical finance where the relationship between the fundamentals and the market is often indirect or unclear due to lack of direct connection, lack of information and infrequency or delay of information. What makes football betting unique is that the physical fundamentals are well observable because of the existence of rich high frequency data sets, the games have a limited time horizon of usually 90 minutes which avoids the buildup of long term expectations and finally the payoff of the traded products is directly linked to the fundamentals. In the first part of the thesis we show that a number of results in financial mathematics that have been developed for financial derivatives can be applied to value and risk manage in-play football bets. In the second part we develop models to predict the outcomes of football games using in-play data. First, we show that the concepts of risk-neutral measure, arbitrage freeness and completeness can also be applied to in-play football betting. This is achieved by assuming a model where the scores of the two teams follow standard Poisson processes with constant intensities. We note that this model is analogous to the Black-Scholes model in many ways. Second, we observe that an implied intensity smile does exist in football betting and we propose the so-called Local Intensity model. This is motivated by the local volatility model from finance which was the answer to the problem of the implied volatility smile. We show that the counterparts of the Dupire formulae [31] can also be derived in this setting. Third, we propose a Microscopic Model to describe not only the number of goals scored by the two teams, but also two additional variables: the position of the ball and the team holding the ball. We start from a general model where the model parameters are multi-variate functions of all the state variables. Then we characterise the general parameter surfaces using in-play game data and arrive to a simplified model of 13 scalar parameters only. We then show that a semi-analytic method can be used to solve the model. We use the model to predict scoring intensities for various time intervals in the future and find that the initial ball position and team holding the ball is relevant for time intervals of under 30 seconds. Fourth, we consider in-play indicators observed at the end of the first half to predict the number of goals scored during the second half, we refer to this model as the First Half Indicators Model. We use various feature selection methods to identify relevant indicators and use different machine learning models to predict goal intensities for the second half. In our setting a linear model with Elastic Net regularisation had the best performance. Fifth, we compare the predictive powers of the Microscopic Model and the First Half Indicators Model and we find that the Microscopic Model outperforms the First Half Indicators Model for delays of under 30 seconds because this is the time frame where the initial team having the ball and the initial position of the ball is relevant

Risk-Neutral Pricing and Hedging of In-Play Football Bets

A risk-neutral valuation framework is developed for pricing and hedging in-play football bets based on modelling scores by independent Poisson processes with constant intensities. The Fundamental Theorems of Asset Pricing are applied to this set-up which enables us to derive novel arbitrage-free valuation formulæ for contracts currently traded in the market. We also describe how to calibrate the model to the market and how trades can be replicated and hedged

Orthotropic Strength and Elasticity of Hardwoods in Relation to Composite Manufacture Part III: Orthotropic Elasticity of Structural Veneers

Structural veneers approximately 3.2 mm (1/8 in.) in thickness are widely used as basic constituents in structural composites such as plywood, laminated veneer lumber (LVL), and parallel strand lumber (PSL). The veneer processing operation (peeling) may adversely alter the mechanical properties of the wood substance by introducing compression-set, cracks, and splits, etc. The modulus of elasticity (MOE) in tension of five hardwood species, which are potential raw materials for composite manufacture, was investigated in veneer form. The experimental work included dynamic MOE determination using ultrasound stress wave timing and static MOE measurements for comparison purposes. The orthotropy of MOE in the longitudinal-tangential (LT) plane was also a target of the investigation. Theoretical models were fitted to experimental data that may predict the MOE of the constituents according to their position within the consolidated composites. Experimental and analytical results indicated that a combined model including the Hankinson's formula and an orthotropic tensorial approach is the best estimator for MOE of veneers having inclined grain orientation. Furthermore, the relationship between static and dynamic MOE values may be obtained by second-order polynomial models

Using Acoustic Sensors to Improve the Efficiency of the Forest Value Chain in Canada: A Case Study with Laminated Veneer Lumber

Engineered wood products for structural use must meet minimum strength and stiffness criteria. This represents a major challenge for the industry as the mechanical properties of the wood resource are inherently variable. We report on a case study that was conducted in a laminated veneer lumber (LVL) mill in order to test the potential of an acoustic sensor to predict structural properties of the wood resource prior to processing. A population of 266 recently harvested aspen logs were segregated into three sub-populations based on measurements of longitudinal acoustic speed in wood using a hand tool equipped with a resonance-based acoustic sensor. Each of the three sub-populations were peeled into veneer sheets and graded for stiffness with an ultrasonic device. The average ultrasonic propagation time (UPT) of each subpopulation was 418, 440 and 453 microseconds for the green, blue, and red populations, respectively. This resulted in contrasting proportions of structural veneer grades, indicating that the efficiency of the forest value chain could be improved using acoustic sensors. A linear regression analysis also showed that the dynamic modulus of elasticity (MOE) of LVL was strongly related to static MOE (R2 = 0.83), which suggests that acoustic tools may be used for quality control during the production process