[Numerical Methods in Finance and Economics]基于MATLAB的经济金融数值分析-经管之家官网！

Amazon的链接
http://www.amazon.com/Numerical-Methods-Finance-Economics-MATLAB-Based/dp/0471745030
目录
Part I Background
1 Motivation
1.1 Need for numerical methods
1.2 Need for numerical computing environments:
why MATLAB?
1.3 Need for theory
For further reading
References
2 Financial Theory
2.1 Modeling uncertainty
2.2 Basic financial assets and related issues
2.2.1 Bonds
2.2.2 Stocks
vii
viii CONTENTS
2.2.3 Derivatives
2.2.4 Asset pricing, portfolio optimization, and
risk management
2.3 Fixed-income securities: analysis and portfolio
immunization
2.3.1 Basic theory of interest rates: compounding
and present value
2.3.2 Basic pricing of fixed-income securities 49
2.3.3 Interest rate sensitivity and bond portfolio
immunization
2.3.4 MATLAB functions to deal with fixedincome
securities
2.3.5 Critique
2.4 Stock portfolio optimization
2.4.1 Utility theory
2.4.2 Mean-variance portfolio optimization
2.4.3 MATLAB functions to deal with meanvariance
portfolio optimization
2.4.4 Critical remarks
2.4.5 Alternative risk measures: Value at Risk
and quantile-based measures
2.5 Modeling the dynamics of asset prices
2.5.1 From discrete to continuous time
2.5.2 Standard Wiener process
2.5.3 Stochastic integrals and stochastic
differential equations
2.5.4 Ito’s lemma
2.5.5 Generalizations
2.6 Derivatives pricing
2.6.1 Simple binomial model for option pricing
2.6.2 Black–Scholes model
2.6.3 Risk-neutral expectation and Feynman–
Kaˇc formula
2.6.4 Black–Scholes model in MATLAB
2.6.5 A few remarks on Black–Scholes formula
2.6.6 Pricing American options
2.7 Introduction to exotic and path-dependent options
2.7.1 Barrier options
2.7.2 Asian options
2.7.3 Lookback options
CONTENTS ix
2.8 An outlook on interest-rate derivative
2.8.1 Modeling interest-rate dynamics
2.8.2 Incomplete markets and the market price
of risk
For further reading
References
Part II Numerical Methods
3 Basics of Numerical Analysis
3.1 Nature of numerical computation
3.1.1 Number representation, rounding, and
truncation
3.1.2 Error propagation, conditioning, and
instability
3.1.3 Order of convergence and computational
complexity
3.2 Solving systems of linear equations
3.2.1 Vector and matrix norms
3.2.2 Condition number for a matrix
3.2.3 Direct methods for solving systems of
linear equations
3.2.4 Tridiagonal matrices
3.2.5 Iterative methods for solving systems of
linear equations
3.3 Function approximation and interpolation
3.3.1 Ad hoc approximation
3.3.2 Elementary polynomial interpolation
3.3.3 Interpolation by cubic splines
3.3.4 Theory of function approximation by least
squares
3.4 Solving non-linear equations
3.4.1 Bisection method
3.4.2 Newton’s method
3.4.3 Optimization-based solution of non-linear
equations
3.4.4 Putting two things together: solving
a functional equation by a collocation
method
x CONTENTS
3.4.5 Homotopy continuation methods
For further reading
References
4 Numerical Integration: Deterministic and Monte Carlo
Methods
4.1 Deterministic quadrature
4.1.1 Classical interpolatory formulas
4.1.2 Gaussian quadrature
4.1.3 Extensions and product rules
4.1.4 Numerical integration in MATLAB
4.2 Monte Carlo integration
4.3 Generating pseudorandom variates
4.3.1 Generating pseudorandom numbers
4.3.2 Inverse transform method
4.3.3 Acceptance–rejection method
4.3.4 Generating normal variates by the polarapproach
4.4 Setting the number of replications
4.5 Variance reduction techniques
4.5.1 Antithetic sampling
4.5.2 Common random numbers
4.5.3 Control variates
4.5.4 Variance reduction by conditioning
4.5.5 Stratified sampling
4.5.6 Importance sampling
4.6 Quasi-Monte Carlo simulation
4.6.1 Generating Halton low-discrepancy sequences
4.6.2 Generating Sobol low-discrepancy sequences
For further reading
References
5 Finite Difference Methods for Partial Differential
Equations
5.1 Introduction and classification of PDEs
5.2 Numerical solution by finite difference methods
5.2.1 Bad example of a finite difference scheme
CONTENTS xi
5.2.2 Instability in a finite difference scheme
5.3 Explicit and implicit methods for the heat
equation
5.3.1 Solving the heat equation by an explicit
method
5.3.2 Solving the heat equation by a fully
implicit method
5.3.3 Solving the heat equation by the Crank–
Nicolson method
5.4 Solving the bidimensional heat equation
5.5 Convergence, consistency, and stability
For further reading 324
References 324
6 Convex Optimization 327
6.1 Classification of optimization problems 328
6.1.1 Finite- vs. infinite-dimensional problems 328
6.1.2 Unconstrained vs. constrained problems 333
6.1.3 Convex vs. non-convex problems 333
6.1.4 Linear vs. non-linear problems 335
6.1.5 Continuous vs. discrete problems 337
6.1.6 Deterministic vs. stochastic problems 337
6.2 Numerical methods for unconstrained optimization 338
6.2.1 Steepest descent method 339
6.2.2 The subgradient method 340
6.2.3 Newton and the trust region methods 341
6.2.4 No-derivatives algorithms: quasi-Newton
method and simplex search 342
6.2.5 Unconstrained optimization in MATLAB 343
6.3 Methods for constrained optimization 346
6.3.1 Penalty function approach 346
6.3.2 Kuhn–Tucker conditions 351
6.3.3 Duality theory 357
6.3.4 Kelley’s cutting plane algorithm 363
6.3.5 Active set method 365
6.4 Linear programming 366
6.4.1 Geometric and algebraic features of linear
programming 368
6.4.2 Simplex method 370
xii CONTENTS
6.4.3 Duality in linear programming 372
6.4.4 Interior point methods 375
6.5 Constrained optimization in MATLAB 377
6.5.1 Linear programming in MATLAB 378
6.5.2 A trivial LP model for bond portfolio
management 380
6.5.3 Using quadratic programming to trace
efficient portfolio frontier 383
6.5.4 Non-linear programming in MATLAB 385
6.6 Integrating simulation and optimization 387
S6.1 Elements of convex analysis 389
S6.1.1 Convexity in optimization 389
S6.1.2 Convex polyhedra and polytopes 393
For further reading 396
References 397
Part III Pricing Equity Options
7 Option Pricing by Binomial and Trinomial Lattices 401
7.1 Pricing by binomial lattices 402
7.1.1 Calibrating a binomial lattice 403
7.1.2 Putting two things together: pricing a
pay-later option 410
7.1.3 An improved implementation of binomial
lattices 411
7.2 Pricing American options by binomial lattices 414
7.3 Pricing bidimensional options by binomial lattices 417
7.4 Pricing by trinomial lattices 422
7.5 Summary 425
For further reading 426
References 426
8 Option Pricing by Monte Carlo Methods 429
8.1 Path generation 430
8.1.1 Simulating geometric Brownian motion 431
8.1.2 Simulating hedging strategies 435
8.1.3 Brownian bridge 439
8.2 Pricing an exchange option 443
CONTENTS xiii
8.3 Pricing a down-and-out put option 446
8.3.1 Crude Monte Carlo 446
8.3.2 Conditional Monte Carlo 447
8.3.3 Importance sampling 450
8.4 Pricing an arithmetic average Asian option 454
8.4.1 Control variates 455
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