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図書
図書
1. Mathematical finance : theory, modeling, implementation
Christian Fries
出版情報: New Jersey : John Wiley & Sons, c2007  xxii, 520 p. ; 25 cm
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電子ブック
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2. Mathematical finance : theory, modeling, implementation (: electronic bk)
Christian Fries
出版情報: [S.l.] : Wiley Online Library, [20--]  1 online resource (xxii, 520 p.)
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目次情報: 続きを見る
Introduction / 1：
Theory, Modeling and Implementation / 1.1：
Interest Rate Models and Interest Rate Derivatives / 1.2：
How to Read this Book / 1.3：
Abridged Versions / 1.3.1：
Special Sections / 1.3.2：
Notation / 1.3.3：
Foundations / I：
Probability Theory / 2：
Stochastic Processes / 2.2：
Filtration / 2.3：
Brownian Motion / 2.4：
Wiener Measure, Canonical Setup / 2.5：
Itô Calculus / 2.6：
Itô Integral / 2.6.1：
Itô Process / 2.6.2：
Itô Lemma and Product Rule / 2.6.3：
Brownian Motion with Instantaneous Correlation / 2.7：
Martingales / 2.8：
Change of Measure (Girsanov, Cameron, Martin / 2.8.1 Martingale Representation Theorem：
Stochastic Integration / 2.10：
Partial Differential Equations (PDE / 2.11：
Feynman-Kac Theorem / 2.11.1：
List of Symbols / 2.12：
Replication / 3：
Replication Strategies / 3.1：
Replication in a discrete Model / 3.1.1：
Foundations: Equivalent Martingale Measure / 3.2：
Challenge and Solution Outline / 3.2.1：
Steps towards the Universal Pricing Theorem / 3.2.2：
Excursus: Relative Prices and Risk Neutral Measures / 3.3：
Why relative prices? / 3.3.1：
Risk Neutral Measure / 3.3.2：
First Applications / II：
Pricing of a European Stock Option under the Black-Scholes Model / 4：
Excursus: The Density of the Underlying of a European Call Option / 5：
Excursus: Interpolation of European Option Prices / 6：
No-Arbitrage Conditions for Interpolated Prices / 6.1：
Arbitrage Violations through Interpolation / 6.2：
Example (1): Interpolation of four Prices / 6.2.1：
Example (2): Interpolation of two Prices / 6.2.2：
Arbitrage-Free Interpolation of European Option Prices / 6.3：
Hedging in Continuous and Discrete Time and the Greeks / 7：
Deriving the Replications Strategy from Pricing Theory / 7.1：
Deriving the Replication Strategy under the Assumption of a Locally Riskless Product / 7.2.1：
The Black-Scholes Differential Equation / 7.2.2：
Example: Replication Portfolio and PDE under a Black-Scholes Model / 7.2.3：
Greeks / 7.3：
Greeks of a European Call-Option under the Black-Scholes model / 7.3.1：
Hedging in Discrete Time: Delta and Delta-Gamma Hedging / 7.4：
Delta Hedging / 7.4.1：
Error Propagation / 7.4.2：
Delta-Gamma Hedging / 7.4.3：
Vega Hedging / 7.4.4：
Hedging in Discrete Time: Minimizing the Residual Error (Bouchaud-Sornette Method / 7.5：
Minimizing the Residual Error at Maturity T / 7.5.1：
Minimizing the Residual Error in each Time Step / 7.5.2：
Interest Rate Structures, Interest Rate Products And Analytic Pricing Formulas / III：
Interest Rate Structures / Motivation and Overview：
Fixing Times and Tenor Times / 8.1：
Definitions / 8.2：
Interest Rate Curve Bootstrapping / 8.3：
Interpolation of Interest Rate Curves / 8.4：
Implementation / 8.5：
Simple Interest Rate Products / 9：
Interest Rate Products Part 1: Products without Optionality / 9.1：
Fix, Floating and Swap / 9.1.1：
Money-Market Account / 9.1.2：
Interest Rate Products Part 2: Simple Options / 9.2：
Cap, Floor, Swaption / 9.2.1：
Foreign Caplet, Quanto / 9.2.2：
The Black Model for a Caplet / 10：
Pricing of a Quanto Caplet / Modeling the FFX11：
Choice of Numéraire / 11.1：
Exotic Derivatives / 12：
Prototypical Product Properties / 12.1：
Interest Rate Products Part 3: Exotic Interest Rate Derivatives / 12.2：
Structured Bond, Structured Swap, Zero Structure / 12.2.1：
Bermudan Option / 12.2.2：
Bermudan Callable and Bermudan Cancelable / 12.2.3：
Compound Options / 12.2.4：
Trigger Products / 12.2.5：
Structured Coupons / 12.2.6：
Shout Options / 12.2.7：
Product Toolbox / 12.3：
Discretization And Numerical Valuation Methods / IV：
Discretization of time and state space / 13：
Discretization of Time: The Euler and the Milstein Scheme / 13.1：
Time-Discretization of a Lognormal Process / 13.1.1：
Discretization of Paths (Monte-Carlo Simulation) / 13.2：
Monte-Carlo Simulation / 13.2.1：
Weighted Monte-Carlo Simulation / 13.2.2：
Review / 13.2.3：
Discretization of State Space / 13.3：
Backward-Algorithm / 13.3.1：
Path Simulation through a Lattice: Two Layers / 13.3.3：
Numerical Methods for Partial Differential Equations / 14：
Pricing Bermudan Options in a Monte Carlo Simulation / 15：
Bermudan Options: Notation / 15.1：
Bermudan Callable / 15.2.1：
Relative Prices / 15.2.2：
Bermudan Option as Optimal Exercise Problem / 15.3：
Bermudan Option Value as single (unconditioned) Expectation: The Optimal Exercise Value / 15.3.1：
Bermudan Option Pricing - The Backward Algorithm / 15.4：
Re-simulation / 15.5：
Perfect Foresight / 15.6：
Conditional Expectation as Functional Dependence / 15.7：
Binning / 15.8：
Binning as a Least-Square Regression / 15.8.1：
Foresight Bias / 15.9：
Regression Methods - Least Square Monte-Carlo / 15.10：
Least Square Approximation of the Conditional Expectation / 15.10.1：
Example: Evaluation of a Bermudan Option on a Stock / Backward Algorithm with Conditional Expectation Estimator15.10.2：
Example: Evaluation of a Bermudan Callable / 15.10.3：
Binning as linear Least-Square Regression / 15.10.4：
Optimization Methods / 15.11：
Andersen Algorithm for Bermudan Swaptions / 15.11.1：
Review of the Threshold Optimization Method / 15.11.2：
Optimization of Exercise Strategy: A more general Formulation / 15.11.3：
Comparison of Optimization Method and Regression Method / 15.11.4：
Duality Method: Upper Bound for Bermudan Option Prices / 15.12：
American Option Evaluation as Optimal Stopping Problem / 15.12.1：
Primal-Dual Method: Upper and Lower Bound / 15.13：
Pricing Path-Dependent Options in a Backward Algorithm / 16：
Evaluation of a Snowball / Memory in a Backward Algorithm / 16.1：
Evaluation of a Flexi Cap in a Backward Algorithm / 16.2：
Sensitivities / Partial Derivatives) of Monte Carlo Prices17：
Problem Description / 17.1：
Pricing using Monte-Carlo Simulation / 17.2.1：
Sensitivities from Monte-Carlo Pricing / 17.2.2：
Example: The Linear and the Discontinuous Payout / 17.2.3：
Example: Trigger Products / 17.2.4：
Generic Sensitivities: Bumping the Model / 17.3：
Sensitivities by Finite Differences / 17.4：
Example: Finite Differences applied to Smooth and Discontinuous Payout / 17.4.1：
Sensitivities by Pathwise Differentiation / 17.5：
Example: Delta of a European Option under a Black-Scholes Model / 17.5.1：
Pathwise Differentiation for Discontinuous Payouts / 17.5.2：
Sensitivities by Likelihood Ratio Weighting / 17.6：
Example: Delta of a European Option under a Black-Scholes Model using Pathwise Derivative / 17.6.1：
Example: Variance Increase of the Sensitivity when using Likelihood Ratio Method for Smooth Payouts / 17.6.2：
Sensitivities by Malliavin Weighting / 17.7：
Proxy Simulation Scheme / 17.8：
Proxy Simulation Schemes for Monte Carlo Sensitivities and Importance Sampling / 18：
Full Proxy Simulation Scheme / 18.1：
Calculation of Monte-Carlo weights / 18.1.1：
Sensitivities by Finite Differences on a Proxy Simulation Scheme / 18.2：
Localization / 18.2.1：
Object-Oriented Design / 18.2.2：
Importance Sampling / 18.3：
Example / 18.3.1：
Partial Proxy Simulation Schemes / 18.4：
Linear Proxy Constraint / 18.4.1：
Comparison to Full Proxy Scheme Method / 18.4.2：
Non-Linear Proxy Constraint / 18.4.3：
Transition Probability from a Nonlinear Proxy Constraint / 18.4.4：
Sensitivity with respect to the Diffusion Coefficients - Vega / 18.4.5：
Example: LIBOR Target Redemption Note / 18.4.6：
Example: CMS Target Redemption Note / 18.4.7：
Pricing Models For Interest Rate Derivatives / V：
LIBOR Market Models / 19：
LIBOR Market Model / 19.1：
Derivation of the Drift Term / 19.1.1：
Discretization and (Monte-Carlo) Simulation / 19.1.2：
Calibration - Choice of the free Parameters / 19.1.4：
Interpolation of Forward Rates in the LIBOR Market Model / 19.1.5：
Object Oriented Design / 19.2：
Reuse of Implementation / 19.2.1：
Separation of Product and Model / 19.2.2：
Abstraction of Model Parameters / 19.2.3：
Abstraction of Calibration / 19.2.4：
Swap Rate Market Models (Jamshidian 1997 / 19.3：
The Swap Measure / 19.3.1：
Swap Rate Market Models / 19.3.2：
Terminal Correlation examined in a LIBOR Market Model Example / 20.1：
De-correlation in a One-Factor Model / 20.2.1：
Impact of the Time Structure of the Instantaneous Volatility on Caplet and Swaption Prices / 20.2.2：
The Swaption Value as a Function of Forward Rates / 20.2.3：
Terminal Correlation is dependent on the Equivalent Martingale Measure / 20.3：
Dependence of the Terminal Density on the Martingale Measure / 20.3.1：
Excursus: Instantaneous Correlation and Terminal Correlation / 21：
Short Rate Process in the HJM Framework / 21.1：
The HJM Drift Condition / 21.2：
Heath-Jarrow-Morton Framework: Foundations / 22：
The Market Price of Risk / 22.1：
Overview: Some Common Models / 22.3：
Implementations / 22.4：
Monte-Carlo Implementation of Short-Rate Models / 22.4.1：
Lattice Implementation of Short-Rate Models / 22.4.2：
Short-Rate Models / 23：
Short Rate Models in the HJM Framework / 23.1：
Example: The Ho-Lee Model in the HJM Framework / 23.1.1：
Example: The Hull-White Model in the HJM Framework / 23.1.2：
LIBOR Market Model in the HJM Framework / 23.2：
HJM Volatility Structure of the LIBOR Market Model / 23.2.1：
LIBOR Market Model Drift under the QB Measure / 23.2.2：
LIBOR Market Model as a Short Rate Model / 23.2.3：
Heath-Jarrow-Morton Framwork: Immersion of Short-Rate Models and LIBOR Market Model / 24：
Model / 24.1：
Interpretation of the Figures / 24.2：
Mean Reversion / 24.3：
Factors / 24.4：
Exponential Volatility Function / 24.5：
Instantaneous Correlation / 24.6：
Excursus: Shape of teh Interst Rate Curve under Mean Reversion and a Multifactor Model / 25：
Cheyette Model / 25.1：
Ritchken-Sakarasubramanian Framework: JHM with Low Markov Dimension / 26：
The Markov Functional Assumption / independent of the model considered)26.1：
Outline of this Chapter / 26.1.2：
Equity Markov Functional Model / 26.2：
Markov Functional Assumption / 26.2.1：
Example: The Black-Scholes Model / 26.2.2：
Numerical Calibration to a Full Two-Dimensional European Option Smile Surface / 26.2.3：
Interest Rates / 26.2.4：
Model Dynamics / 26.2.5：
LIBOR Markov Functional Model / 26.2.6：
LIBOR Markov Functional Model in Terminal Measure / 26.3.1：
LIBOR Markov Functional Model in Spot Measure / 26.3.2：
Remark on Implementation / 26.3.3：
Change of numéraire in a Markov-Functional Model / 26.3.4：
Implementation: Lattice / 26.4：
Convolution with the Normal Probability Density / 26.4.1：
State space discretization Markov Functional Models / 26.4.2：
Extended Models. / Part VI：
Introduction - Different Types of Spreads / 27.1：
Spread on a Coupon / 27.1.1：
Credit Spread / 27.1.2：
Defaultable Bonds / 27.2：
Integrating deterministic Credit Spread into a Pricing Model / 27.3：
Deterministic Credit Spread / 27.3.1：
Receiver's and Payer's Credit Spreads / 27.3.2：
Example: Defaultable Forward Starting Coupon Bond / 27.4.1：
Example: Option on a Defaultable Coupon Bond / 27.4.2：
Credit Spreads / 28：
Cross Currency LIBOR Market Model / 28.1：
Derivation of the Drift Term under Spot-Measure / 28.1.1：
Equity Hybrid LIBOR Market Model / 28.1.2：
Equity-Hybrid Cross-Currency LIBOR Market Model / 28.2.1：
Summary / 28.3.1：
Hybrid Models / 28.3.2：
Elements of Object Oriented Programming: Class and Objects / 29.1：
Example: Class of a Binomial Distributed Random Variable / 29.1.1：
Constructor / 29.1.2：
Methods: Getter, Setter, Static Methods / 29.1.3：
Principles of Object Oriented Programming / 29.2：
Encapsulation and Interfaces / 29.2.1：
Abstraction and Inheritance / 29.2.2：
Polymorphism / 29.2.3：
Example: A Class Structure for One Dimensional Root Finders / 29.3：
Root Finder for General Functions / 29.3.1：
Root Finder for Functions with Analytic Derivative: Newton Method / 29.3.2：
Root Finder for Functions with Derivative Estimation: Secant Method / 29.3.3：
Anatomy of a JavaÖ Class / 29.4：
Libraries / 29.5：
JavaÖ2 Platform, Standard Edition (j2se / 29.5.1：
JavaÖ2 Platform, Enterprise Edition (j2ee / 29.5.2：
Colt / 29.5.3：
Commons-Math: The Jakarta Mathematics Library / 29.5.4：
Some Final Remarks / 29.6：
Object Oriented Design (OOD) / Unified Modeling Language / 29.6.1：
Appendices / Part VII：
A small Collection of Common Misconceptions / A：
Tools (Selection / B：
Linear Regression / B.1：
Generation of Random Numbers / B.2：
Uniform Distributed Random Variables / B.2.1：
Transformation of the Random Number Distribution via the Inverse Distribution Function / B.2.2：
Normal Distributed Random Variables / B.2.3：
Poisson Distributed Random Variables / B.2.4：
Generation of Paths of an n-dimensional Brownian Motion / B.2.5：
Factor Decomposition - Generation of Correlated Brownian Motion / B.3：
Factor Reduction / B.4：
Optimization (one-dimensional): Golden Section Search / B.5：
Convolution with Normal Density / B.6：
Exercises / C：
JavaÖ Source Code (Selection / D：
JavaÖ Classes for Chapter 29 / E.1：
Introduction / 1：
Theory, Modeling and Implementation / 1.1：
Interest Rate Models and Interest Rate Derivatives / 1.2：
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