Financial models and price formation : applications to sport betting.

Summary This thesis is composed of four chapters. The first chapter deals with the valuation of financial products in a model with a jump for the risk asset. This jump represents the bankruptcy of the corresponding firm. We then study the valuation of option prices by utility indifference in an exponential utility framework. Using dynamic programming techniques, we show that the price of a Bond is a solution of a differential equation and the price of asset-dependent options is a solution of a Hamilton-Jacobi-Bellman partial drift equation. The jump in the dynamics of the risky asset induces differences with the Merton model that we try to quantify. The second chapter deals with a market with jumps: soccer betting. We recall the different families of models for a soccer game and introduce a complete model allowing us to evaluate the prices of the different products that have appeared on this market over the last ten years. The complexity of this model leads us to study a simplified model whose implications we study and calculate the prices obtained, which we compare with reality. We notice that the implicit calibration obtained generates very good results by producing prices very close to reality. The third chapter develops the problem of price setting by a monopolistic market maker in the binary betting market. This work is a direct extension of the problem introduced by Levitt [Lev04]. We generalize his work to the case of European bets and propose a method to estimate the pricing method used by the bookmaker. We show that two inextricable hypotheses can explain this price fixing. On the one hand, the public's uncertainty about the true value and on the other hand, the bookmaker's extreme risk-averse character. The fourth chapter extends this approach to the case of non-binary financial products. We examine different supply and demand models and derive, by dynamic programming techniques, partial differential equations dictating the formation of the buying and selling prices. We finally show that the spread between the buying and selling price does not depend on the position of the market maker in the asset under consideration. However, the average price depends strongly on the quantity held by the market maker. A simplified approach is finally proposed in the multidimensional case.