Multi-asset credit derivatives trade in huge volumes, yet no models exist that are capable of properly accounting for the spread behaviour of dependent companies. In this thesis we consider new ways of incorporating a richer and more realistic dependence structure into multi-firm models. We focus on the structural framework in which firm value is modelled as a geometric Brownian motion, with default as the first hitting time of an exponential default threshold. Specification of a dependence structure consisting of a common driving influence and firm-specific inter-company ties allows for both default causality and default asymmetry and we incorporate default contagion in the first passage framework for the first time. Building on the work by Zhou (2001a), we propose an analytical model for corporate bond yields in the presence of default contagion and two-firm credit default swap baskets. We derive closed-form solutions for credit spreads, and results clearly highlight the importance of dependence assumptions. Extending this framework numerically, we calculate CDS spreads for baskets of three firms with a wide variety of credit dependence specifications. We examine the impact of firm value correlation and credit contagion for symmetric and asymmetric baskets, and incorporate contagion that has a declining impact over time.

How should we model learning behaviour in economic agents? This thesis addresses this question in two distinct ways. In the first set of chapters the assumption is that agents learn through the observation of others. They use Bayesian updating which together with specific informational assumptions can generate the problem known as herding with the potential for significant welfare losses. In the final set of chapters the agent is instead modelled as learning by example. Here the agent cannot learn by observing others, but has a pool of experience to fall back on. This allows us to examine how an economic agent will perform if he sees a particular economic situation (or game) for the first time, but has experience of playing related games. The tool used to capture the notion of learning through example is a neural network. Throughout the thesis the central theme is that economic agents will naturally use as much information as they can to help them make decisions. In many cases this should mean they take into consideration others' actions or their own experiences in similar but non-identical situations. Learning throughout the thesis will be rational or bounded-rational in the sense that either the best possible way to learn will be utilized (so players achieve full rational play, for example, through Bayesian updating), or a suitable local error-minimizing algorithm will be developed (for example, a rule of thumb which optimizes play in a subclass of games, but not in the overall set of possible games). Several themes permeate the whole thesis, including the scope for firms or planners to manipulate the information that is used by agents for their own ends, the role of rules of thumb, and the realism of current theories of learning in economics.

Pricing single asset American options is a hard problem in mathematical finance. There are no closed form solutions available (apart from in the case of the perpetual option), so many approximations and numerical techniques have been developed. Pricing multi–asset (high dimensional) American options is still more difficult. We extend the method proposed theoretically by Glasserman and Yu (2004) by employing regression basis functions that are martingales under geometric Brownian motion. This results in more accurate Monte Carlo simulations, and computationally cheap lower and upper bounds to the American option price. We have implemented these models in QuantLib, the open–source derivatives pricing library. The code for many of the models discussed in this thesis can be downloaded from quantlib.org as part of a practical pricing and risk management library. We propose a new type of multi–asset option, the “Radial Barrier Option” for which we find analytic solutions. This is a barrier style option that pays out when a barrier, which is a function of the assets and their correlations, is hit. This is a useful benchmark test case for Monte Carlo simulations and may be of use in approximating multi–asset American options. We use Laplace transforms in this analysis which can be applied to give analytic results for the hitting times of Bessel processes. We investigate the asymptotic solution of the single asset Black–Scholes–Merton equation in the case of low volatility. This analysis explains the success of some American option approximations, and has the potential to be extended to basket options.

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 [27] 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.

The deregulation of regional electricity markets has led to more competitive prices but also higher uncertainty in the future electricity price development. Most markets exhibit high volatilities and occasional distinctive price spikes, which results in demand for derivative products which protect the holder against high prices. A good understanding of the stochastic price dynamics is required for the purposes of risk management and pricing derivatives. In this thesis we examine a simple spot price model which is the exponential of the sum of an Ornstein-Uhlenbeck and an independent pure jump process. We derive the moment generating function as well as various approximations to the probability density function of the logarithm of this spot price process at maturity T. With some restrictions on the set of possible martingale measures we show that the risk neutral dynamics remains within the class of considered models and hence we are able to calibrate the model to the observed forward curve and present semi-analytic formulas for premia of path-independent options as well as approximations to call and put options on forward contracts with and without a delivery period. In order to price path-dependent options with multiple exercise rights like swing contracts a grid method is utilised which in turn uses approximations to the conditional density of the spot process. Further contributions of this thesis include a short discussion of interpolation methods to generate a continuous forward curve based on the forward contracts with delivery periods observed in the market, and an investigation into optimal martingale measures in incomplete markets. In particular we present known results of q-optimal martingale measures in the setting of a stochastic volatility model and give a first indication of how to determine the q-optimal measure for q=0 in an exponential Ornstein-Uhlenbeck model consistent with a given forward curve.

The field of algorithmic mechanism design is concerned with the design of computationally efficient algorithms for use when inputs are provided by rational agents, who may misreport their private values in order to strategically manipulate the algorithm for their own benefit. We revisit classic problems in this field by considering settings of incomplete information, where the players' private values are drawn from publicly-known distributions. Such Bayesian models of partial information are common in economics, but have been largely unexplored by the computer science community. In the first part of this thesis we show that, for a very broad class of single-parameter problems, any computationally efficient algorithm can be converted without loss into a mechanism that is truthful in the Bayesian sense of partial information. That is, we exhibit a transformation that generates mechanisms for which it is in each agent's best (expected) interest to refrain from strategic manipulation. The problem of constructing mechanisms for use by rational agents therefore reduces to the design of approximation algorithms without consideration of game-theoretic issues. We furthermore prove that no such general transformation is possible if we require mechanisms that are truthful in the stronger non-Bayesian sense of dominant strategies. In the second part of the thesis we study simple greedy methods for resolving complex auctions. We show that while such greedy algorithms are not truthful, they suffer very little loss in worst-case performance bounds when agents apply strategies at equilibrium, even in settings of partial information. Our analysis applies to various different equilibrium concepts, including Bayes-Nash equilibrium, regret-minimizing strategies, and asynchronous best-response dynamics. Thus, even though greedy auctions are not truthful, they may be appropriate for use as mechanisms under the goal of achieving high social efficiency at equilibrium. Moreover, we prove that no algorithm in a broad class of greedy-like methods can be used to create a deterministic truthful mechanism while retaining a non-trivial approximation to the optimal social welfare. Our overall conclusion is that while full-information models of agent rationality currently dominate the algorithmic mechanism design literature, a relaxation to settings of partial information is well-motivated and provides additional power in solving central problems in the field.

The field of algorithmic mechanism design is concerned with the design of computationally efficient algorithms for use when inputs are provided by rational agents, who may misreport their private values in order to strategically manipulate the algorithm for their own benefit. We revisit classic problems in this field by considering settings of incomplete information, where the players' private values are drawn from publicly-known distributions. Such Bayesian models of partial information are common in economics, but have been largely unexplored by the computer science community. In the first part of this thesis we show that, for a very broad class of single-parameter problems, any computationally efficient algorithm can be converted without loss into a mechanism that is truthful in the Bayesian sense of partial information. That is, we exhibit a transformation that generates mechanisms for which it is in each agent's best (expected) interest to refrain from strategic manipulation. The problem of constructing mechanisms for use by rational agents therefore reduces to the design of approximation algorithms without consideration of game-theoretic issues. We furthermore prove that no such general transformation is possible if we require mechanisms that are truthful in the stronger non-Bayesian sense of dominant strategies. In the second part of the thesis we study simple greedy methods for resolving complex auctions. We show that while such greedy algorithms are not truthful, they suffer very little loss in worst-case performance bounds when agents apply strategies at equilibrium, even in settings of partial information. Our analysis applies to various different equilibrium concepts, including Bayes-Nash equilibrium, regret-minimizing strategies, and asynchronous best-response dynamics. Thus, even though greedy auctions are not truthful, they may be appropriate for use as mechanisms under the goal of achieving high social efficiency at equilibrium. Moreover, we prove that no algorithm in a broad class of greedy-like methods can be used to create a deterministic truthful mechanism while retaining a non-trivial approximation to the optimal social welfare. Our overall conclusion is that while full-information models of agent rationality currently dominate the algorithmic mechanism design literature, a relaxation to settings of partial information is well-motivated and provides additional power in solving central problems in the field.

Transportation is important in making supply chain decisions. With the careful consideration of transportation expenses, the performance of each supply chain member, as well as the entire supply chain, could be improved significantly. The purpose of this research is: 1) to explore and identify the various situations that relate to replenishment and transportation activities; and 2) to reveal the strength of the connection between purchase quantity and transportation discounts, and integrate the two discounts to enhance supply-chain coordination. The problem is analyzed and categorized into four representative cases, depending on transportation. To aid the supplier or the carrier to determine the discount that should be offered, in light of the buyer's reaction to that discount, decision models are proposed under three different circumstances. First, assuming a single product, we investigate the quantity discounts from the supplier's perspective, via a noncooperative game-theoretical approach and also a joint decision model. Taking into account the price elasticity of demand, this analysis aids a sole supplier in establishing an all-unit quantity discount policy in light of the buyer's best reaction. The Stackelberg equilibrium and the Pareto-optimal solution set are derived for the noncooperative and joint-decision cases, respectively. Our research indicates that channel efficiency can be improved significantly if the quantity discount decision is made jointly rather than noncooperatively. Moreover, we extend our model in several directions: (a) the product is transported by a private fleet; (b) the buyer may choose to offer her customers a different percentage discount than that she obtained from the supplier; and (c) the case of multiple (heterogeneous) buyers. Numerical examples are employed, here and throughout the thesis, to illustrate the practical applications of the models presented and the sensitivity to model parameters. Secondly, we consider a situation with a family of SKUs for which the supplier will offer a quantity discount, according to the aggregate purchases of the product group. Management of those items is based on the modified periodic policy. From the supplier's point of view, what are the optimal parameters (breakpoint and discount percentage)? For deterministic demand, we discuss the cases in which demand is both constant and price-sensitive. First as a noncooperative Stackelberg game, and then when the two parties make the discount and replenishment decisions jointly, we illustrate the impact of price-sensitivity and joint decision making on the supplier's discount policy. The third approach studies the case in which transportation of the goods by a common carrier (a public, for-hire trucking company) is integrated in the quantity discount decisions. In reality, it is quite difficult for the carrier to determine the proper transportation discount, especially in the case of LTL (less-than-truckload) trucking. This is not only because of the "phantom freight" phenomenon, caused by possible over-declaration of the weight by the shipper, but also due to the fact that the discount relates to both transportation and inventory issues. In this research, we study the problem of coordinating the transportation and quantity discount decisions from the perspectives of the parties who offer the discounts, rather than the ones that take them. By comparison of the noncooperative and cooperative models, we show that cooperation provides better overall results, not only to each party, but also to the entire supply chain. To divide the extra payoffs gained from that cooperation, we further conduct a coalition analysis, based upon the concept of "Shapley Value." A detailed algorithm and numerical examples are provided to illustrate the solution procedure. Finally, the thesis concludes with comprehensive remarks. We summarize the contributions of this thesis, show the overall results obtained here, and present the directions that our research may take in the future.

Thesis (Ph. D.)--University of California, San Diego, 2007. / Title from first page of PDF file (viewed August 7, 2007). Available via ProQuest Digital Dissertations. Vita. Includes bibliographical references (p. 86-90).

Diss--Teilw. zugl.: Univ. of Amsterdam. / Includes bibliographical references and indexes.