Financial Mathematics: A Comprehensive Treatment

Abstract

This book is divided into four main parts with each part consisting of several chapters. There are a total of eighteen chapters, and every chapter (with the exception of Chapter 9 on general probability theory and Chapter 18 on numerical applications) ends with a com-prehensive and exhaustive set of exercises of varying di culty. Part I is an introduction to pricing and management of nancial securities. This part has four chapters. Chapter 1 introduces the reader to time value of money, compounding interest, and the basic concepts of xed income markets. Chapter 2 introduces basic derivative securities and the concept of arbitrage. Chapter 3 covers standard theoretical topics of portfolio management and only requires some very basic linear algebra and optimization. Chapter 4 presents more formal de nitions and gives a thorough discussion on basic options theory, including payo repli-cation, hedging, put-call parity relations, forwards and futures contracts, swaps, American options, and other contracts.