衍生證券與差分析（簡體書）

作者：（美國）朱友蘭

《衍生證券與差分法(英文)》通篇包括練習，可以吸引大量的計量金融中的學生和科研人員，以及金融工業和編碼方面的工作者。

Part Ⅰ Partial Differential Equations in Finance
Introduction
1.1 Assets
1.2 Derivative Securities
1.2.1 Forward and Futures Contracts
1.2.2 Options
1.2.3 Interest Rate Derivatives
1.2.4 Factors Affecting Derivative Prices
1.2.5 Functions of Derivative Securities
Problems
Basic Options
2.1 Asset Price Model and It(o)'s Lemma
2.1.1 A Model for Asset Prices
2.1.2 It(o)'s Lemma
2.1.3 Expectation and Variance of Lognormal Random Variables
2.2 Derivation of the Black-Scholes Equation
2.2.1 Arbitrage Arguments
2.2.2 The Black-Schotes Equation
2.2.3 Final Conditions for the Black-Scholes Equation
2.2.4 Hedging and Greeks
2.3 Two Transformations on the Black-Scholes Equation
2.3.1 Converting the Black-Scholes Equation into a Heat Equation
2.3.2 Transforming the Black-Scholes Equation into an Equation Defined on a Finite Domain
2.4 Solutions of European Options
2.4.1 The Solutions of Parabolic Equations
2.4.2 Solutions of the Black-Scholes Equation
2.4.3 Prices of Forward Contracts and Delivery Prices
2.4.4 Derivation of the Black-Scholes Formulae
2.4.5 Put-Call Parity Relation
2.4.6 An Explanation in Terms of Probability
2.5 American Option Problems as Linear Complementarity Problems
2.5.1 Constraints on American Options
2.5.2 Formulation of the Linear Complementarity Problem in (S,t)-Plane
2.5.3 Formulation of the Linear Complementarity Problem in (S,t)-Plane
2.5.4 Formulation of the Linear Complementarity Problem on a Finite Domain
2.5.5 More General Form of the Linear Complementarity Problems
2.6 American Option Problems as Free-Boundary Problems
2.6.1 Free Boundaries
2.6.2 Free-Boundary Problems
2.6.3 Put-Call Symmetry Relations
2.7 Equations for Some Greeks
2.8 Perpetual Options
2.9 General Equations for Derivatives
2.9.1 Models for Random Variables
2.9.2 Generalization of It(o)'s Lemma
2.9.3 Derivation of Equations for Financial Derivatives
2.9.4 Three Types of State Variables
2.9.5 Uniqueness of Solutions
2.10 Jump Conditions
2.10.1 Hyperbolic Equations with a Dirac Delta Function
2.10.2 Jump Conditions for Options with Discrete Dividends and Discrete Sampling
2.11 More Arbitrage Theory
2.11.1 Three Conclusions and Some Portfolios
2.11.2 Bounds of Option Prices
2.11.3 Relations Between Call and Put Prices
Problems
3 Exotic Options
3.1 Introduction
3.2 Barrier Options
3.2.1 Knock-Out and Knock-In Options
3.2.2 Closed-Form Solutions of Some European Barrier Options
3.2.3 Formulation of American Barrier Options
3.2.4 Parisian Options
3.3 Asian Options
3.3.1 Average Strike,Average Price,and Double Average Options
3.3.2 Continuously and Discretely Sampled Arithmetic Averages
3.3.3 Derivation of Equations
3.3.4 Reducing to One-Dimensional Problems
3.3.5 Jump Conditions
3.3.6 American Asian Options
3.3.7 Some Examples
3.4 Lookback Options
3.4.1 Equations for Lookback Options
3.4.2 Reducing to One-Dimensional Problems
3.4.3 Closed-Form Solutions for European Lookback Options
3.4.4 American Options Formulated as Free-Boundary Problems
3.4.5 A Closed-Form Solution for a Perpetual American Lookback Option
3.4.6 Lookback-Asian Options
3.4.7 Some Examples
3.5 Multi-Asset Options
3.5.1 Equations for Multi-Asset Options and Green's Formula
3.5.2 Exchange Options
3.5.3 Options on the Extremum of Several Assets
3.5.4 Formulation of Multi-Asset Option Problems on a Finite Domain
3.6 Some Other Exotic Options
3.6.1 Binary Options
3.6.2 Forward Start Options (Delayed Strike Options)
3.6.3 Compound Options
3.6.4 Chooser Options
Problems
4 Interest Rate Derivative Securities
4.1 Introduction
4.2 Bonds
4.2.1 Bond Values for Deterministic Spot Rates
4.2.2 Bond Equations for Random Spot Rates
4.3 Some Explicit Solutions of Bond Equations
4.3.1 Analytic Solutions for the Vasicek and Cox-Ingersoll-Ross Models
4.3.2 Explicit Solutions for the Ho-Lee and Hull-White Models
4.4 Inverse Problem on the Market Price of Risk
4.5 Application of Bond Equations
4.5.1 Bond Options and Options on Bond Futures Contracts
4.5.2 Interest Rate Swaps and Swaptions
4.5.3 Interest Rate Caps,Floors,and Collars
4.6 Multi-Factor Interest Rate Models
4.6.1 Brief Description of Several Multi-Factor Interest Rate Models
4.6.2 Reducing the Randomness of a Zero-Coupon Bond Curve to That of a Few Zero-Coupon Bonds
4.6.3 A Three-Factor Interest Rate Model and the Equation for Interest Rate Derivatives
4.7 Two-Factor Convertible Bonds
Problems
Part Ⅱ Numerical Methods for Derivative Securities
Basic Numerical Methods
5.1 Approximations
5.1.1 Interpolation
5.1.2 Approximation of Partial Derivatives
5.1.3 Approximate Integration
5.1.4 Least Squares Approximation
5.2 Solution of Systems and Eigenvalue Problems
5.2.1 LU Decomposition of Linear Systems
5.2.2 Iteration Methods for Linear Systems
5.2.3 Iteration Methods for Nonlinear Systems
5.2.4 Obtaining Eigenvalues and Eigenvectors
5.3 Finite-Difference Methods
5.4 Stability and Convergence Analysis
5.4.1 Stability
5.4.2 Convergence
5.5 Extrapolation of Numerical Solutions
5.6 Determination of Parameters in Models
5.6.1 Constant Variances and Covariances
5.6.2 Variable Parameters
Problems
Projects
Initial-Boundary Value and LC Problems
6.1 Explicit Methods
6.1.1 Pricing European Options by Using Variables
6.1.2 Projected Methods for LC Problems
6.1.3 Binomial and Trinomial Methods
……
7 Free-Boundary Problems
8 Interest Rate Modeling
References
Index