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Contents of Derivative Securities and Difference Methods |
PART I: Partial Differential Equations in Finance
1. Introduction
1.1 Assets
1.2 Derivative Securities
Problems
2. Basic Options
2.1 Asset Price Model and Ito's Lemma
2.2 Derivation of the Black–Scholes Equation
2.3 Two Transformations on the Black–Scholes Equation
2.4 Solutions of European Options
2.5 American Option Problems as LC Problems
2.6 American Option Problems as FBPs
2.7 Equations for Some Greeks
2.8 Perpetual Options
2.9 General Equations for Derivatives
2.10 Jump Conditions
2.11 More Arbitrage Theory
Problems
3. Exotic Options
3.1 Introduction
3.2 Barrier Options
3.3 Asian Options
3.4 Lookback Options
3.5 Multi-Asset Options
3.6 Some Other Exotic Options
Problems
4. Interest Rate Derivative Securities
4.1 Introduction
4.2 Bonds
4.3 Some Explicit Solutions of Bond Equations
4.4 Inverse Problem on the Market Price of Risk
4.5 Application of Bond Equations
4.6 Multi-Factor Interest Rate Models
4.7 Two-Factor Convertible Bonds
Problems
PART II: Numerical Methods for Derivative Securities
5. Basic Numerical Methods
5.1 Approximations
5.2 Solution of Systems and Eigenvalue Problems
5.3 Finite-Difference Methods
5.4 Stability and Convergence Analysis
5.5 Extrapolation of Numerical Solutions
5.6 Determination of Parameters in Models
Problems
Projects
6. Initial-Boundary Value and LC Problems
6.1 Explicit Methods
6.2 Implicit Methods
6.3 Singularity-Separating Method
6.4 Pseudo-Spectral Methods
Problems
Projects
7. Free-Boundary Problems
7.1 SSM for Free-Boundary Problems
7.2 Implicit Finite-Difference Methods
7.3 Pseudo-Spectral Methods
Problems
Projects
8. Interest Rate Modelling
8.1 Inverse Problems
8.2 Numerical Results of One-Factor Models
8.3 Pricing Derivatives with Multi-Factor Models
Problems
Projects
References
Index
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