Summary of Derivative Securities and Difference Methods
Studies pricing financial derivatives with a partial differential equation approach. This book covers a variety of topics in finance including forward contracts, the Black-Scholes model, European and American type options, free boundary problems, lookback options, interest rate models, interest rate derivatives, swaps, caps, floors, and collars.
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Contents of Derivative Securities and Difference Methods
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
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