Kerry Back

This book is an outgrowth of notes compiled by the author while teaching courses for undergraduate and masters/MBA ?nance students at Washi- ton University in St. Louis and the Institut fur ¨ H¨ ohere Studien in Vienna. At onetime,acourseinOptionsandFutureswasconsideredanadvanced?nance elective, but now such a course is nearly mandatory for any ?nance major and is an elective chosen by many non-?nance majors as well. Moreover, students are exposed to derivative securities in courses on Investments, International Finance, Risk Management, Investment Banking, Fixed Income, etc. This - pansion of education in derivative securities mirrors the increased importance of derivative securities in corporate ?nance and investment management. MBA and undergraduate courses typically (and appropriately) focus on the use of derivatives for hedging and speculating. This is su?cient for many students. However, the seller of derivatives, in addition to needing to und- standbuy-sidedemands,isconfrontedwiththeneedtopriceandhedge.Mo- over,thebuyerofderivatives,dependingonthedegreeofcompetitionbetween sellers, may very likely bene?t from some knowledge of pricing as well. It is “pricing and hedging” that is the primary focus of this book. Through lea- ing the fundamentals of pricing and hedging, students also acquire a deeper understanding of the contracts themselves. Hopefully, this book will also be of use to practitioners and for students in Masters of Financial Engineering programs and, to some extent, Ph.D. students in ?nance.

This book is intended as a textbook for Ph.D. students in finance and as a reference book for academics. It is written at an introductory level but includes detailed proofs and calculations as section appendices. It covers the classical results on single-period, discrete-time, and continuous-time models. It also treats various proposed explanations for the equity premium and risk-free rate puzzles: persistent heterogeneous idiosyncratic risks, internal habits, external habits, and recursive utility. Most of the book assumes rational behavior, but two topics important for behavioral finance are covered: heterogeneous beliefs and non-expected-utility preferences. There are also chapters on asymmetric information and production models. The book includes numerous exercises designed to provide practice with the concepts and also to introduce additional results. Each chapter concludes with a notes and references section that supplies references to additional developments in the field.

This book is an outgrowth of notes compiled by the author while teaching courses for undergraduate and masters/MBA ?nance students at Washi- ton University in St. Louis and the Institut fur ¨ H¨ ohere Studien in Vienna. At onetime,acourseinOptionsandFutureswasconsideredanadvanced?nance elective, but now such a course is nearly mandatory for any ?nance major and is an elective chosen by many non-?nance majors as well. Moreover, students are exposed to derivative securities in courses on Investments, International Finance, Risk Management, Investment Banking, Fixed Income, etc. This - pansion of education in derivative securities mirrors the increased importance of derivative securities in corporate ?nance and investment management. MBA and undergraduate courses typically (and appropriately) focus on the use of derivatives for hedging and speculating. This is su?cient for many students. However, the seller of derivatives, in addition to needing to und- standbuy-sidedemands,isconfrontedwiththeneedtopriceandhedge.Mo- over,thebuyerofderivatives,dependingonthedegreeofcompetitionbetween sellers, may very likely bene?t from some knowledge of pricing as well. It is “pricing and hedging” that is the primary focus of this book. Through lea- ing the fundamentals of pricing and hedging, students also acquire a deeper understanding of the contracts themselves. Hopefully, this book will also be of use to practitioners and for students in Masters of Financial Engineering programs and, to some extent, Ph.D. students in ?nance.

This volume includes the five lecture courses given at the CIME-EMS School on "Stochastic Methods in Finance" held in Bressanone/Brixen, Italy 2003. It deals with innovative methods, mainly from stochastic analysis, that play a fundamental role in the mathematical modelling of finance and insurance: the theory of stochastic processes, optimal and stochastic control, stochastic differential equations, convex analysis and duality theory. Five topics are treated in detail: Utility maximization in incomplete markets; the theory of nonlinear expectations and its relationship with the theory of risk measures in a dynamic setting; credit risk modelling; the interplay between finance and insurance; incomplete information in the context of economic equilibrium and insider trading.