Introduction to Financial Mathematics With Computer Applications

This book’s primary objective is to educate aspiring finance professionals about mathematics and computation in the context of financial derivatives. The authors offer a balance of traditional coverage and technology to fill the void between highly mathematical books and broad finance books. The focus of this book is twofold: To partner mathematics with corresponding intuition rather than diving so deeply into the mathematics that the material is inaccessible to many readers. To build reader intuition, understanding and confidence through three types of computer applications that help the reader understand the mathematics of the models. Unlike many books on financial derivatives requiring stochastic calculus, this book presents the fundamental theories based on only undergraduate probability knowledge. A key feature of this book is its focus on applying models in three programming languages –R, Mathematica and EXCEL. Each of the three approaches offers unique advantages. The computer applications are carefully introduced and require little prior programming background. The financial derivative models that are included in this book are virtually identical to those covered in the top financial professional certificate programs in finance. The overlap of financial models between these programs and this book is broad and deep.

Contents Preface to the Instructor ......................................................................................xvPreface to the Student.........................................................................................xixAcknowledgments...............................................................................................xxiAbout the Authors ........................................................................................... xxiii 1. Introduction to Financial Derivatives and Valuation ...........................................1 2. Introduction to Interest Rates, Bonds, and Equities............................................63 3. Fundamentals of Financial Derivative Pricing ....................................................111 4. More about Derivative Pricing .........................................................................211 5. Risk Management and Hedging Strategies .......................................................263 6. Portfolio Management .....................................................................................351 7. Interest Rate Derivatives Modeling and Risk Management in the HJM Framework...................................................................407 8. Credit Risk and Credit Derivatives....................................................................471 Index ..................................................................................................................549

Donald R. Chambers served as the Walter E. Hanson KPMG Chair in Finance at Lafayette College in Easton Pennsylvania for 25 years. During that time he worked closely with economics and math-economics undergraduate majors, providing him with an understanding of the needs and abilities of students interested in the intersection of math and finance. Professor Chambers has authored or co-authored approximately 50 research papers in scholarly journals and six books. Professor Chambers served previously as Associate Director of Programs at the CAIA Association, a risk management consultant to the Bank of New York in Manhattan and as a senior portfolio strategist with Karpus Investment Management. He currently serves as a Chief Investment Officer at Biltmore Capital Advisors. These experiences have provided him with a deep and broad knowledge of the practical applications of mathematical finance. Qin Lu has taught Mathematics at Lafayette College in Easton Pennsylvania for the last 21 years. Trained as an Algebraic Topologist, Professor Lu began her journey in Mathematical Finance in 2003 by taking CFA (Charted Financial Analyst) exams. By passing three rigid tests during three-year period, Professor Lu became CFA charter holder in 2006. There are very few CFA charter holders who are working at colleges/universities, most of them are working in investment industry. During these years at Lafayette, Professor Lu has taught financial mathematics course many times. In addition, she has been NSF REU (Research Experiences for Undergraduates) PI and mentor for multiple years and has guided a lot of undergraduate research through honors thesis and REU program. Professor Chambers and Professor Lu have co-authored 8 papers, one of which was published in a top-three finance journal and it had an undergraduate student coauthor.