Risk Neutral Pricing and Financial Mathematics

A Primer

Peter M. Knopf, John L. Teall

• Publisher: Academic Press
• Year: 2015
• Print ISBN: 9780128015346
• eBook ISBN: 9780128017272
• Topic: Business
• Subtopic: Business Mathematics
• Index: Business

Risk Neutral Pricing and Financial Mathematics: A Primer provides a foundation to financial mathematics for those whose undergraduate quantitative preparation does not extend beyond calculus, statistics, and linear math. It covers a broad range of foundation topics related to financial modeling, including probability, discrete and continuous time and space valuation, stochastic processes, equivalent martingales, option pricing, and term structure models, along with related valuation and hedging techniques. The joint effort of two authors with a combined 70 years of academic and practitioner experience, Risk Neutral Pricing and Financial Mathematics takes a reader from learning the basics of beginning probability, with a refresher on differential calculus, all the way to Doob-Meyer, Ito, Girsanov, and SDEs. It can also serve as a useful resource for actuaries preparing for Exams FM and MFE (Society of Actuaries) and Exams 2 and 3F (Casualty Actuarial Society).- Includes more subjects than other books, including probability, discrete and continuous time and space valuation, stochastic processes, equivalent martingales, option pricing, term structure models, valuation, and hedging techniques- Emphasizes introductory financial engineering, financial modeling, and financial mathematics- Suited for corporate training programs and professional association certification programs

Chapter 1

Preliminaries and Review

Chapter 1 provides a concise review of essential prerequisite material for financial mathematics along with brief discussions of financial securities and markets. The securities and markets sections introduce equity, fixed income, and derivatives instruments along with the markets in which they trade along with essential financial practices such as arbitrage and short selling. Mathematics reviews include matrix arithmetic, vector spaces and span, differential and integral calculus, all illustrated with relevant examples drawn from finance. Matrices are applied to solving systems of equations. Taylor series and LaGrange optimization are discussed along with differentials and Riemann sums. All of these topics are reviewed with the goal of applying their principles to understanding discrete and continuous valuation, basic stochastic calculus, and their applications to valuing and managing equity, fixed income, and derivative instruments.

Keywords

Financial models; market efficiency; arbitrage; derivative securities; matrix; vector; Gauss–Jordan method; linear independence; spanning set of v...

Table of contents

• Cover image
• Title page
• Table of Contents
• Copyright
• Dedication
• About the Authors
• Preface
• Chapter 1. Preliminaries and Review
• Chapter 2. Probability and Risk
• Chapter 3. Discrete Time and State Models
• Chapter 4. Continuous Time and State Models
• Chapter 5. An Introduction to Stochastic Processes and Applications
• Chapter 6. Fundamentals of Stochastic Calculus
• Chapter 7. Derivatives Pricing and Applications of Stochastic Calculus
• Chapter 8. Mean-Reverting Processes and Term Structure Modeling
• Appendix A. The z-table
• Appendix B. Exercise Solutions
• Appendix C. Glossary of Symbols
• Glossary of Terms
• Index