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Risk Neutral Pricing and Financial Mathematics: A Primer

Book Description

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

Table of Contents

  1. Cover image
  2. Title page
  3. Table of Contents
  4. Copyright
  5. Dedication
  6. About the Authors
  7. Preface
  8. Chapter 1. Preliminaries and Review
    1. 1.1 Financial Models
    2. 1.2 Financial Securities and Instruments
    3. 1.3 Review of Matrices and Matrix Arithmetic
    4. 1.4 Review of Differential Calculus
    5. 1.5 Review of Integral Calculus
    6. 1.6 Exercises
    7. Notes
  9. Chapter 2. Probability and Risk
    1. 2.1 Uncertainty in Finance
    2. 2.2 Sets and Measures
    3. 2.3 Probability Spaces
    4. 2.4 Statistics and Metrics
    5. 2.5 Conditional Probability
    6. 2.6 Distributions and Probability Density Functions
    7. 2.7 The Central Limit Theorem
    8. 2.8 Joint Probability Distributions
    9. 2.9 Portfolio Mathematics
    10. 2.10 Exercises
    11. References
    12. Notes
  10. Chapter 3. Discrete Time and State Models
    1. 3.1 Time Value
    2. 3.2 Discrete Time Models
    3. 3.3 Discrete State Models
    4. 3.4 Discrete Time–Space Models
    5. 3.5 Exercises
    6. Notes
  11. Chapter 4. Continuous Time and State Models
    1. 4.1 Single Payment Model
    2. 4.2 Continuous Time Multipayment Models
    3. 4.3 Continuous State Models
    4. 4.4 Exercises
    5. References
    6. Notes
  12. Chapter 5. An Introduction to Stochastic Processes and Applications
    1. 5.1 Random Walks and Martingales
    2. 5.2 Binomial Processes: Characteristics and Modeling
    3. 5.3 Brownian Motion and Itô Processes
    4. 5.4 Option Pricing: A Heuristic Derivation of Black–Scholes
    5. 5.5 The Tower Property
    6. 5.6 Exercises
    7. References
    8. Notes
  13. Chapter 6. Fundamentals of Stochastic Calculus
    1. 6.1 Stochastic Calculus: Introduction
    2. 6.2 Change of Probability and the Radon–Nikodym Derivative
    3. 6.3 The Cameron–Martin–Girsanov Theorem and the Martingale Representation Theorem
    4. 6.4 Itô’s Lemma
    5. 6.5 Exercises
    6. References
    7. Notes
  14. Chapter 7. Derivatives Pricing and Applications of Stochastic Calculus
    1. 7.1 Option Pricing Introduction
    2. 7.2 Self-Financing Portfolios and Derivatives Pricing
    3. 7.3 The Black–Scholes Model
    4. 7.4 Implied Volatility
    5. 7.5 The Greeks
    6. 7.6 Compound Options
    7. 7.7 The Black–Scholes Model and Dividend Adjustments
    8. 7.8 Beyond Plain Vanilla Options on Stock
    9. 7.9 Exercises
    10. References
    11. Notes
  15. Chapter 8. Mean-Reverting Processes and Term Structure Modeling
    1. 8.1 Short- and Long-Term Rates
    2. 8.2 Ornstein–Uhlenbeck Processes
    3. 8.3 Single Risk Factor Interest Rate Models
    4. 8.4 Alternative Interest Rate Processes
    5. 8.5 Where Do We Go from Here?
    6. 8.6 Exercises
    7. References
    8. Notes
  16. Appendix A. The z-table
  17. Appendix B. Exercise Solutions
    1. Chapter 1
    2. Chapter 2
    3. Chapter 3
    4. Chapter 4
    5. Chapter 5
    6. Chapter 6
    7. Chapter 7
    8. Chapter 8
  18. Appendix C. Glossary of Symbols
    1. Lower Case Letters
    2. Upper Case Letters
    3. Greek Letters
    4. Special Symbols
  19. Glossary of Terms
  20. Index