Introduction to Financial Mathematics
With Computer Applications
- Available for pre-order. Item will ship after May 4, 2021
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.
Table of Contents
Chapter 1. Introduction to Financial Derivatives and Valuation. 1.1. Foundations in Economics and Finance. 1.2. Introduction to the Valuation of Financial Contracts. 1.3. Details Regarding Forward Contracts. 1.4. The Arbitrage-free Pricing of Forward Contracts. 1.5. Introduction to Option Contracts. 1.6. Put-Call Parity and Arbitrage. 1.7. Arbitrage-free Option Pricing. 1.8. Compound Options and Option Strategies. 1.9. The Limits to Arbitrage and Complete Markets. 1.10. Computing System: Mathematica and R. Chapter 2. Introduction to Interest Rates, Bonds and Equities. 2.1. The Time Value of Money and Interest Rates. 2.2. Term Structures, Yield Curves, and Forward Rates. 2.3. Fixed Income Risk Measurement and Management. 2.4. Equities and Equity Valuation. 2.5. Asset Pricing and Equity Risk Management. Chapter 3. Fundamentals of Financial Derivative Pricing. 3.1. Overview of the Three Primary Derivative Pricing Approaches. 3.2. The Binomial Tree Model Approach to Derivative Pricing. 3.3. The Geometric Brownian Motion and Monte-Carlo Simulation. 3.4. Analytical Model Approaches to Derivative Pricing. Chapter 4. More About Derivative Pricing. 4.1. Various Methods to Value Derivatives. 4.2. Various Exotic Derivatives. 4.3. Dividends. 4.4. More on Forward Values, Futures Contracts, and Futures Prices. Chapter 5. Risk Management and Hedging Strategies. 5.1. Simple Hedging Using Forward and Futures Contracts. 5.2. One-to-h Hedging Using Forward and Futures Contracts. 5.3. Delta Hedging of Options Portfolio Using Underlying Asset. 5.4. Delta Hedging Using Futures. 5.5. Greek Letter Hedging of Other Option Risk Factors. 5.6. Duration Hedging of Fixed Income Instruments and Interest Rate Risk. 5.7. Hedging Various Risks Using Swap Contracts. Chapter 6. Portfolio Management. 6.1. Markowitz Frontier. 6.2. Portfolio Optimization: Linear and Quadratic Programming. 6.3. The Optimal Growth Portfolio. Chapter 7. Interest Rate Derivatives Modeling and Risk Management in the HJM Framework. 7.1. Zero Coupon Bonds, Forward rates, Short Rates and Money Markets in a Deterministic World. 7.2. Risk neutral Valuation in a One Factor HJM Model. 7.3. Valuation and Risk Management of Options on Bonds and in a One Factor HJM. 7.4. Valuation and Risk Management of Caps, Floors, and Interest Rate Swaps in a One Factor HJM Model. 7.5. Pricing and Risk Management of Forward and Futures Contracts on a Bond in a One Factor HJM Model. 7.6. Calibrating the HJM Model Parameters from the Market Prices. Chapter 8. Credit Risk and Credit Derivatives. 8.1. Default Probabilities and Extract Default Probabilities from Market. 8.2. Single-Name Credit Derivatives. 8.3. Collateralized Debt Obligations (CDOs) and CDO Model with Independent Bond Defaults. 8.4. Collateralized Debt Obligations (CDOs) Model with Positively Correlated Bond Defaults. 8.5. CDO Squared. 8.6. The Financial Crisis and Credit Derivatives
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.