The worlds of Wall Street and The City have always held a certain allure, but in recent years have left an indelible mark on the wider public consciousness and there has been a need to become more financially literate. The quantitative nature of complex financial transactions makes them a fascinating subject area for mathematicians of all types, whether for general interest or because of the enormous monetary rewards on offer. An Introduction to Quantitative Finance concerns financial derivatives - a derivative being a contract between two entities whose value derives from the price of an underlying financial asset - and the probabilistic tools that were developed to analyse them. The theory in the text is motivated by a desire to provide a suitably rigorous yet accessible foundation to tackle problems the author encountered whilst trading derivatives on Wall Street. The book combines an unusual blend of real-world derivatives trading experience and rigorous academic background. Probability provides the key tools for analysing and valuing derivatives.
The price of a derivative is closely linked to the expected value of its pay-out, and suitably scaled derivative prices are martingales, fundamentally important objects in probability theory. The prerequisite for mastering the material is an introductory undergraduate course in probability. The book is otherwise self-contained and in particular requires no additional preparation or exposure to finance. It is suitable for a one-semester course, quickly exposing readers to powerful theory and substantive problems. The book may also appeal to students who have enjoyed probability and have a desire to see how it can be applied. Signposts are given throughout the text to more advanced topics and to different approaches for those looking to take the subject further.
Stephen Blyth is managing director and head of public markets at the Harvard Management Company, the subsidiary of Harvard University responsible for the management of the University's endowment. He is also Professor of the Practice of Statistics at Harvard University. Before joining Harvard in 2006, Professor Blyth was managing director and head of the Global Rates proprietary trading group at Deutsche Bank in London, and managing director in the Interest Rate Group at Morgan Stanley in New York. Professor Blyth is a frequent speaker at international finance conferences and has written widely on issues facing practitioners in applied quantitative finance and in derivative markets. He holds a PhD in Statistics from Harvard University and an MA in Mathematics with first class honours from Christ's College, Cambridge University, where he is a Lady Margaret Beaufort Fellow. He was formerly a Lecturer in Mathematics at Imperial College London.
I INTRODUCTION AND PRELIMINARIES; II FORWARDS, SWAPS AND OPTIONS; III REPLICATION, RISK-NEUTRALITY AND THE FUNDAMENTAL THEOREM; IV INTEREST RATE OPTIONS; V THROUGH CONTINUOUS TIME