Credit networks and agent games
This thesis is divided into three parts; an intensity based network model of firm default, an agent based network model of firm default, and an agent based model of feedback effects from dynamic hedging. The common theme among all three parts is the application of ideas from both physics and mathematics to the solution of problems motivated by the financial markets. Less broadly, in the first two parts, the common themes are credit markets, networks, and dependent defaults. Part one tackles the problem of default dependence from a probabilistic perspective, modeling the default of companies as generalised Poisson processes, with the default dependence structure given by a network. We present a mathematical framework to solve a generalised version of the Jarrow Yu model of looping defaults  and study the relationship between network structure and the resilience of a network of firms to default events. Using this model we then show how to price simple multi-name credit products such as kth to default baskets. Part two again considers dependent defaults, but here the network is dynamic and firms are modelled as simple agents, defined by strategies, whose interactions determine a network of trading links. Using our agent based network model of firm default we study network structure and their degree distributions, firm lifetimes, and look for evidence of agent learning and default clustering. We then study the effect of default on a network of firms and the response of remaining firms to that default event. Part three considers a relatively more established agent based framework, called the Minority Game. We first describe in detail the Minority Game and discuss its suitability as a market model. We then show how it may be applied to modelling the actions of traders delta hedging a short option position. We show that for a variety of option positions, in a sufficiently illiquid market feedback effects arise from the actions of the traders as their trades impact upon the underlying market.