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Risk Neutral Pricing and Financial Mathematics,

Edition 1 A Primer

Editors: By Peter M. Knopf and John L. Teall

Publication Date: 18 Aug 2015

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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

About the author

By Peter M. Knopf, Dyson College of Arts and Sciences, Pace University, Pleasantville, NY, USA and John L. Teall, Johns Hopkins University

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

Title Reviews

"A self-contained and well-balanced financial modeling textbook ideally suitable for both business school and engineering school. It also offers an intuitive and applied orientation approach for professional training and self-study." —K.C. Chang, George Mason University¿

ISBN: 9780128015346

Page Count: 348

Retail Price (USD) :

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Risk Neutral Pricing and Financial Mathematics,

Editors: By Peter M. Knopf and John L. Teall

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