Quantitative Finance

A graduate-level, mathematically rigorous introduction to the tools, methods, and approaches used in contemporary quantitative finance This book offers a theory-oriented introduction to investments, asset pricing, and derivatives. Designed for a quantitative master's program in finance, it is grounded by what works in the classroom. Presenting its topics in a unified, self-contained framework, the book is specifically appropriate for courses in asset pricing and derivatives pricing but may also be used for courses in investments, asset management, and portfolio management. Students will learn how to make decisions under uncertainty and over time, how to choose an investment portfolio, and how to characterize the prices and returns of financial assets in equity, bond, and derivative markets. The book focuses on a number of classical models and theories in quantitative finance and covers selected advanced and newer topics in its final section. Proofs and in-depth theoretical results within quantitative finance appear throughout the book along with examples and end-of-chapter exercises to facilitate and support the learning process. Part one covers the capital asset pricing model, the Lucas model, the static Arrow-Debreu model, consumption-based asset pricing, and the arbitrage pricing theory, and introduces preliminary theories of decision making and portfolio choice Part two covers no-arbitrage theory, with applications to derivatives and bond markets, beginning with a static economy and then gradually moving to the continuous-time setting; it includes the advanced mathematical tools needed for continuous-time finance Part three covers selected advanced and newer topics, including equilibrium models in continuous time, the variance gamma option pricing model, and the Ross recovery theorem An appendix presents mathematical concepts and results from set theory, topology, linear algebra, matrix theory, and analysis