A Workout in Computational Finance

Table of contents

1. Cover Page
2. Title Page
3. Copyright
4. Dedication
5. Contents
6. Acknowledgements
7. About the Authors
8. 1 Introduction and Reading Guide
9. 2 Binomial Trees
   1. 2.1 Equities and Basic Options
   2. 2.2 The One Period Model
   3. 2.3 The Multiperiod Binomial Model
   4. 2.4 Black-Scholes and Trees
   5. 2.5 Strengths and Weaknesses of Binomial Trees
   6. 2.6 Conclusion
10. 3 Finite Differences and the Black-Scholes PDE
    1. 3.1 A Continuous Time Model for Equity Prices
    2. 3.2 Black-Scholes Model: From the SDE to the PDE
    3. 3.3 Finite Differences
    4. 3.4 Time Discretization
    5. 3.5 Stability Considerations
    6. 3.6 Finite Differences and the Heat Equation
    7. 3.7 Appendix: Error Analysis
11. 4 Mean Reversion and Trinomial Trees
    1. 4.1 Some Fixed Income Terms
    2. 4.2 Black76 for Caps and Swaptions
    3. 4.3 One-Factor Short Rate Models
    4. 4.4 The Hull-White Model in More Detail
    5. 4.5 Trinomial Trees
12. 5 Upwinding Techniques for Short Rate Models
    1. 5.1 Derivation of a PDE for Short Rate Models
    2. 5.2 Upwind Schemes
    3. 5.3 A Puttable Fixed Rate Bond under the Hull-White One Factor Model
13. 6 Boundary, Terminal and Interface Conditions and their Influence
    1. 6.1 Terminal Conditions for Equity Options
    2. 6.2 Terminal Conditions for Fixed Income Instruments
    3. 6.3 Callability and Bermudan Options
    4. 6.4 Dividends
    5. 6.5 Snowballs and TARNs
    6. 6.6 Boundary Conditions
14. 7 Finite Element Methods
    1. 7.1 Introduction
    2. 7.2 Grid Generation
    3. 7.3 Elements
    4. 7.4 The Assembling Process
    5. 7.5 A Zero Coupon Bond Under the Two Factor Hull-White Model
    6. 7.6 Appendix: Higher Order Elements
15. 8 Solving Systems of Linear Equations
    1. 8.1 Direct Methods
    2. 8.2 Iterative Solvers
16. 9 Monte Carlo Simulation
    1. 9.1 The Principles of Monte Carlo Integration
    2. 9.2 Pricing Derivatives with Monte Carlo Methods
    3. 9.3 An Introduction to the Libor Market Model
    4. 9.4 Random Number Generation
17. 10 Advanced Monte Carlo Techniques
    1. 10.1 Variance Reduction Techniques
    2. 10.2 Quasi Monte Carlo Method
    3. 10.3 Brownian Bridge Technique
18. 11 Valuation of Financial Instruments with Embedded American/Bermudan Options within Monte Carlo Frameworks
    1. 11.1 Pricing American options using the Longstaff and Schwartz algorithm
    2. 11.2 A Modified Least Squares Monte Carlo Algorithm for Bermudan Callable Interest Rate Instruments
    3. 11.3 Examples
19. 12 Characteristic Function Methods for Option Pricing
    1. 12.1 Equity Models
    2. 12.2 Fourier Techniques
20. 13 Numerical Methods for the Solution of PIDEs
    1. 13.1 A PIDE for Jump Models
    2. 13.2 Numerical Solution of the PIDE
    3. 13.3 Appendix: Numerical Integration via Newton-Cotes Formulae
21. 14 Copulas and the Pitfalls of Correlation
    1. 14.1 Correlation
    2. 14.2 Copulas
22. 15 Parameter Calibration and Inverse Problems
    1. 15.1 Implied Black-Scholes Volatilities
    2. 15.2 Calibration Problems for Yield Curves
    3. 15.3 Reversion Speed and Volatility
    4. 15.4 Local Volatility
    5. 15.5 Identifying Parameters in Volatility Models
23. 16 Optimization Techniques
    1. 16.1 Model Calibration and Optimization
    2. 16.2 Heuristically Inspired Algorithms
    3. 16.3 A Hybrid Algorithm for Heston Model Calibration
    4. 16.4 Portfolio Optimization
24. 17 Risk Management
    1. 17.1 Value at Risk and Expected Shortfall
    2. 17.2 Principal Component Analysis
    3. 17.3 Extreme Value Theory
25. 18 Quantitative Finance on Parallel Architectures
    1. 18.1 A Short Introduction to Parallel Computing
    2. 18.2 Different Levels of Parallelization
    3. 18.3 GPU Programming
    4. 18.4 Parallelization of Single Instrument Valuations using (Q)MC
    5. 18.5 Parallelization of Hybrid Calibration Algorithms
26. 19 Building Large Software Systems for the Financial Industry
27. Bibliography
28. Index