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    Uncertain Volatility Models Theory and Application

    ISBN-10: 3540426574
    ISBN-13: 9783540426578
    Author(s): Robert Buff
    Description: This text describes Uncertain Volatility Models in mathematical finance and their computer implementation for portfolios of vanilla, barrier and American options in equity and FX markets.
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    List Price: $99.00
    Publisher: Springer
    Binding: Mixed Media
    Pages: 244
    Size: 6.00" wide x 9.25" long x 0.50" tall
    Weight: 0.880
    Language: English

    This text describes Uncertain Volatility Models in mathematical finance and their computer implementation for portfolios of vanilla, barrier and American options in equity and FX markets.

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

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