Risk Neutral Pricing and Financial Mathematics
A Primer
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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).
Key Features
- 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
Readership
Upper-division undergraduates and first-year graduate students worldwide in financial engineering, quantitative finance, computational finance and mathematical finance. Also professionals working in financial institutions, insurance, and risk management.
Table of Contents
- Dedication
- About the Authors
- Preface
- Chapter 1. Preliminaries and Review
- 1.1 Financial Models
- 1.2 Financial Securities and Instruments
- 1.3 Review of Matrices and Matrix Arithmetic
- 1.4 Review of Differential Calculus
- 1.5 Review of Integral Calculus
- 1.6 Exercises
- Notes
- Chapter 2. Probability and Risk
- 2.1 Uncertainty in Finance
- 2.2 Sets and Measures
- 2.3 Probability Spaces
- 2.4 Statistics and Metrics
- 2.5 Conditional Probability
- 2.6 Distributions and Probability Density Functions
- 2.7 The Central Limit Theorem
- 2.8 Joint Probability Distributions
- 2.9 Portfolio Mathematics
- 2.10 Exercises
- References
- Notes
- Chapter 3. Discrete Time and State Models
- 3.1 Time Value
- 3.2 Discrete Time Models
- 3.3 Discrete State Models
- 3.4 Discrete Time–Space Models
- 3.5 Exercises
- Notes
- Chapter 4. Continuous Time and State Models
- 4.1 Single Payment Model
- 4.2 Continuous Time Multipayment Models
- 4.3 Continuous State Models
- 4.4 Exercises
- References
- Notes
- Chapter 5. An Introduction to Stochastic Processes and Applications
- 5.1 Random Walks and Martingales
- 5.2 Binomial Processes: Characteristics and Modeling
- 5.3 Brownian Motion and Itô Processes
- 5.4 Option Pricing: A Heuristic Derivation of Black–Scholes
- 5.5 The Tower Property
- 5.6 Exercises
- References
- Notes
- Chapter 6. Fundamentals of Stochastic Calculus
- 6.1 Stochastic Calculus: Introduction
- 6.2 Change of Probability and the Radon–Nikodym Derivative
- 6.3 The Cameron–Martin–Girsanov Theorem and the Martingale Representation Theorem
- 6.4 Itô’s Lemma
- 6.5 Exercises
- References
- Notes
- Chapter 7. Derivatives Pricing and Applications of Stochastic Calculus
- 7.1 Option Pricing Introduction
- 7.2 Self-Financing Portfolios and Derivatives Pricing
- 7.3 The Black–Scholes Model
- 7.4 Implied Volatility
- 7.5 The Greeks
- 7.6 Compound Options
- 7.7 The Black–Scholes Model and Dividend Adjustments
- 7.8 Beyond Plain Vanilla Options on Stock
- 7.9 Exercises
- References
- Notes
- Chapter 8. Mean-Reverting Processes and Term Structure Modeling
- 8.1 Short- and Long-Term Rates
- 8.2 Ornstein–Uhlenbeck Processes
- 8.3 Single Risk Factor Interest Rate Models
- 8.4 Alternative Interest Rate Processes
- 8.5 Where Do We Go from Here?
- 8.6 Exercises
- References
- Notes
- Appendix A. The z-table
- Appendix B. Exercise Solutions
- Chapter 1
- Chapter 2
- Chapter 3
- Chapter 4
- Chapter 5
- Chapter 6
- Chapter 7
- Chapter 8
- Appendix C. Glossary of Symbols
- Lower Case Letters
- Upper Case Letters
- Greek Letters
- Special Symbols
- Glossary of Terms
- Index
Product details
- No. of pages: 348
- Language: English
- Copyright: © Academic Press 2015
- Published: May 1, 2015
- Imprint: Academic Press
- Paperback ISBN: 9780128015346
- eBook ISBN: 9780128017272
About the Authors
Peter Knopf
Peter Knopf obtained his Ph.D. from Cornell University and subsequently taught at Texas A&M University and Rutgers University. He is currently Professor of Mathematics at Pace University. He has numerous research publications in both pure and applied mathematics. His recent research interests have been in the areas of difference equations and stochastic delay equation models for pricing securities.
Affiliations and Expertise
Dyson College of Arts and Sciences, Pace University, Pleasantville, NY, USA
John Teall
John Teall is a visiting professor at LUISS Business School in Rome, Italy. He is a former member of the American Stock Exchange and has served as a consultant to Deutsche Bank, Goldman Sachs, and other financial institutions.
Affiliations and Expertise
Johns Hopkins University
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