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: |