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| Introduction | |
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| Uncertain Volatility Scenarios and Exotic Options | |
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| Volatility Shock Scenarios | |
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| Object-Oriented Implementation | |
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| User Interfaces: Scripting and Mathematica | |
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| How to Best Read This Book | |
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| Computational Finance: Theory | |
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| Notation and Basic Definitions | |
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| Linear Algebra | |
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| Probability and Stochastic Processes | |
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| Partial Portfolios and Positions | |
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| Accents, Superscript, Subscript | |
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| Continuous Time Finance | |
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| Deterministic Volatility | |
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| One-Factor Black-Scholes Analysis | |
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| Hedging with Black-Scholes | |
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| Interest Rate Models | |
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| Stochastic Volatility | |
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| Tradable and Nontradable Factors | |
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| Some Concrete One-Dimensional Models | |
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| Model Calibration | |
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| Parametric Methods | |
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| Non-Parametric Methods | |
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| Scenario-Based Evaluation and Uncertainty | |
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| Preliminaries | |
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| The Worst-Case Volatility Scenario | |
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| Worst-Case Pricing | |
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| The Optimal Hedge Portfolio | |
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| Calibration to the Worst Case | |
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| Minimum-Entropy Calibration | |
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| Scenarios and Nonlinearity | |
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| Algorithms for Uncertain Volatility Models | |
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| A Lattice Framework | |
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| Multi-Lattice Dynamic Programming | |
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| Data Structures | |
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| Dataflow for Explicit Methods | |
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| Dataflow for Mixed Explicit/Implicit Methods | |
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| Numerical Issues | |
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| Algorithms for Vanilla Options | |
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| Algorithms for Barrier Options | |
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| The Hierarchy of PDE�s | |
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| Construction | |
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| Complexity | |
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| Empirical Results | |
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| Numerical Convergence | |
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| Introducing Uncertainty | |
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| Algorithms for American Options | |
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| Early Exercise Combinations | |
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| Long and Short Positions | |
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| Best Worst-Case Evaluation Formalized | |
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| Speedup Techniques | |
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| Maintaining the Corridor of Uncertainty | |
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| Collapsing the Corridor of Uncertainty | |
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| Miscellaneous Issues | |
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| Empirical Results | |
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| Computational Complexity | |
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| Stress Tests | |
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| American Options and Calibration | |
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| Exotic Volatility Scenarios | |
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| Volatility Shocks for Portfolios of Vanilla Options | |
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| Worst-Case Volatility Shocks | |
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| Empirical Results | |
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| Volatility Shocks and Exotic Options | |
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| Object-Oriented Implementation | |
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| The Architecture of Mtg | |
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| The Class Hierarchy of MtgLib-External | |
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| Instruments | |
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| Portfolios | |
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| Models | |
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| Model Coefficients | |
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| The Base Class tTermStruct | |
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| Classes Derived from tTermStruct | |
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| Classes with tTermStruct Components | |
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| Scenarios | |
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| The Base Class tScenario | |
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| Classes Derived from tScenario | |
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| Numerical Methods | |
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| Lattice Templates and Instances | |
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| Finite Difference Solvers | |
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| Evaluators | |
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| The Class Hierarchy of MtgLib-Internal | |
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| Compute Engines | |
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| The Abstract Class tEngine | |
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| The Abstract Class tFDEngine | |
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| The Abstract Class tOFEngine | |
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| The Concrete Class tGeoEngine | |
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| The Concrete Class tShockEngine | |
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| Other Groups of Classes | |
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| Extensions for Monte-Carlo Pricing and Calibration | |
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| The Network Application MtgClt/MtgSvr | |
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| The Scripting Language MtgScript | |
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| Factor Objects | |
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| Claim and Portfolio Objects | |
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| Model, Drift and Volatility Objects | |
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| Lattice and Path Space Objects | |
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| Bootstrapping, Curve and Image Objects | |
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| Scenario and Optimizer Objects | |
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| Evaluation Objects and Examples | |
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| Mathematica Extensions | |
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| The Syntax of Object Expressions | |
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| Turning Scripts into Functions | |
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| Profiling and Diagrams | |
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| References | |
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| Index | |