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1.

図書
図書
1. Security markets : stochastic models
Darrell Duffie
出版情報: Boston ; San Diego ; Tokyo : Academic Press, c1988  xx, 358 p. ; 24 cm
シリーズ名: Economic theory, econometrics, and mathematical economics
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Preface
Introduction
Market Equilibrium / A.：
Equilibrium under Uncertainty / B.：
Security-Spot Market Equilibrium / C.：
State Pricing Model of Securities / D.：
Binomial Arbitrage Pricing Model of Securities / E.：
Capital Asset Pricing Model / F.：
Stochastic Control Pricing Model / G.：
The Potential-Price Matrix / H.：
Ito's Lemma--A Simple Case / I.：
Continuous-Time Portfolio Control / J.：
Black-Scholes Option Pricing Formula / K.：
Representative Agent Asset Pricing / L.：
Exercises
Notes
Static Economies / Chapter I.：
The Geometry of Choices and Prices / 1.：
Vector Spaces
Normed Spaces
Convexity and Cones
Function Spaces
Topology
Duality
Dual Representation
Preferences / 2.：
Preference Relations
Preference Continuity and Convexity
Utility Functions
Utility Representation
Quasi-Concave Utility
Monotonicity
Non-Satiation
Primitives of an Economy / 3.：
Equilibria
Exchange and Net Trade Economies
Production and Exchange Equilibria
Equilibrium and Efficiency
Efficiency and Equilibrium
Existence of Equilibria
First Probability Concepts / 4.：
Probability Spaces
Random Variables and Distributions
Measurability, Topology, and Partitions
Almost Sure Events and Versions
Expectation and Integration
Distribution and Density Functions
Expected Utility / 5.：
Von-Neumann-Morgenstern and Savage Models of Preferences
Expected Utility Representation
Preferences over Probability Distributions
Mixture Spaces and the Independence Axiom
Axioms for Expected Utility
Special Choice Spaces / 6.：
Banach Spaces
Measurable Function Spaces
L[superscript q] Spaces
L[superscript [infinity] Spaces
Riesz Representation
Continuity of Positive Linear Functionals
Hilbert Spaces
Portfolios / 7.：
Span and Vector Subspaces
Linearly Independent Bases
Equilibrium on a Subspace
Security Market Equilibria
Constrained Efficiency
Optimization Principles / 8.：
First Order Necessary Conditions
Saddle Point Theorem
Kuhn-Tucker Theorem
Superdifferentials and Maxima
Second Probability Concepts / 9.：
Changing Probabilities
Changing Information
Conditional Expectation
Properties of Conditional Expectation
Expectation in General Spaces
Jensen's Inequality
Independence and The Law of Large Numbers
Risk Aversion / 10.：
Defining Risk Aversion
Risk Aversion and Concave Expected Utility
Risk Aversion and Second Order Stochastic Dominance
Equilibrium in Static Markets Under Uncertainty / 11.：
Markets for Assets with a Variance
Beta Models: Mean-Covariance Pricing
The CAPM and APT Pricing Approaches
Variance Aversion
The Capital Asset Pricing Model
Proper Preferences
Stochastic Economies / Chapter II.：
Event Tree Economies / 12.：
Event Trees
Security and Spot Markets
Trading Strategies
Marketed Subspaces and Tight Markets
Dynamic and Static Equilibria
Dynamic Spanning and Complete Markets
A Security Valuation Operator
Dynamically Complete Markets Equilibria
Dynamically Incomplete Markets Equilibria
Generic Existence of Equilibria with Real Securities
Arbitrage Security Valuation and State Prices
A Dynamic Theory of the Firm / 13.：
Stock Market Equilibria
An Example
Security Trading by Firms
Invariance of Stock Values to Security Trading by Firms
Modigliani-Miller Theorem
Invariance of Firm's Total Market Value Process
Firms Issue and Retire Securities
Tautology of Complete Information Models
The Goal of the Firm
Stochastic Processes / 14.：
The Information Filtration
Informationally Adapted Processes
Information Generated by Processes and Event Trees
Technical Continuity Conditions
Martingales
Brownian Motion and Poisson Processes
Stopping Times, Local Martingales, and Semimartingales
Stochastic Integrals and Gains From Security Trade / 15.：
Discrete-Time Stochastic Integrals
Continuous-Time Primitives
Simple Continuous-Time Integration
The Stochastic Integral
General Stochastic Integrals
Martingale Multiplicity
Stochastic Integrals and Changes of Probability
Stochastic Equilibria / 16.：
Dynamic Spanning
Transformations to Martingale Gains from Trade / 17.：
Introduction: The Finite-Dimensional Case
Dividend and Price Processes
Self-Financing Trading Strategies
Representation of Implicit Market Values
Equivalent Martingale Measures
Choice of Numeraire
A Technicality
Generalization to Many Goods
Generalization to Consumption Through Time
Discrete-Time Asset Pricing / Chapter III.：
Markov Processes and Markov Asset Valuation / 18.：
Markov Chains
Transition Matrices
Metric and Borel Spaces
Conditional and Marginal Distributions
Markov Transition
Transition Operators
Chapman-Kolmogorov Equation
Sub-Markov Transition
Markov Arbitrage Valuation
Abstract Markov Process
Discrete-Time Markov Control / 19.：
Robinson Crusoe Example
Dynamic Programming with a Finite State Space
Borel-Markov Control Models
Existence of Stationary Markov Optimal Control
Measurable Selection of Maxima
Bellman Operator
Contraction Mapping and Fixed Points
Bellman Equation
Finite Horizon Markov Control
Stochastic Consumption and Investment Control
Discrete-Time Equilibrium Pricing / 20.：
Markov Exchange Economies
Optimal Portfolio and Consumption Policies
Conversion to a Borel-Markov Control Problem
Markov Equilibrium Security Prices
Relaxation of Short-Sales Constraints
Markov Production Economies
A Central Planning Stochastic Production Problem
Market Decentralization of a Growth Economy
Markov Stock Market Equilibrium
Continuous-Time Asset Pricing / Chapter IV.：
An Overview of the Ito Calculus / 21.：
Ito Processes and Integrals
Ito's Lemma
Stochastic Differential Equations
Feynman-Kac Formula
Girsanov's Theorem: Change of Probability and Drift
The Black-Scholes Model of Security Valuation / 22.：
Binomial Pricing Model
Black-Scholes Framework
Reduction to a Partial Differential Equation
The Black-Scholes Option Pricing Formula
An Application of the Feynman-Kac Formula
An Extension
Central Limit Theorems
Limiting Binomial Formula
Uniform Integrability
An Application of Donsker's Theorem
An Application of Girsanov's Theorem
An Introduction to the Control of Ito Processes / 23.：
Sketch of Bellman's Equation
Regularity Requirements
Formal Statement of Bellman's Equation
Portfolio Choice with I.I.D. Returns / 24.：
The Portfolio Control Problem
The Solution
Continuous-Time Equilibrium Asset Pricing / 25.：
The Setting
Definition of Equilibrium
Regularity Conditions
Equilibrium Theorem
Conversion to Consumption Numeraire
Equilibrium Interest Rates
The Consumption-Based Capital Asset Pricing Model
The Cox-Ingersoll-Ross Term Structure Model
Bibliography
Author Index
Symbol Glossary
Subject Index
Preface
Introduction
Market Equilibrium / A.：
2.

図書
図書
2. 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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3.

電子ブック
ＥＢ
3. 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：
4.

図書
図書
4. Stochastic volatility modeling
Lorenzo Bergomi
出版情報: Boca Raton : CRC Press, c2016  xvi, 506 p. ; 24 cm
シリーズ名: Chapman & Hall/CRC financial mathematics series
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