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    SABR/LIBOR Market Model Pricing, Calibration and Hedging for Complex Interest-Rate Derivatives

    ISBN-10: 0470740051
    ISBN-13: 9780470740057
    Author(s): Riccardo Rebonato, Kenneth D. McKay, Richard White
    Buy it from: $84.75
    This item will ship on Friday, December 26 .

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    Publisher: John Wiley & Sons, Limited
    Binding: Hardcover
    Pages: 296
    Size: 7.00" wide x 10.00" long x 1.00" tall
    Weight: 1.430
    Language: English

    Introduction.
    The Theoretical Set-Up.
    The LIBOR Market Model.
    Definitions
    The Volatility Functions
    Separating the Correlation from the Volatility Term
    The Caplet-Pricing Condition Again
    The Forward-Rate/Forward-Rate Correlation
    Possible Shapes of the Doust Correlation Function
    The Covariance Integral Again
    The SABR Model.
    The SABR Model (and Why It Is a Good Model
    Description of the Model
    The Option Prices Given by the SABR Model
    Special Cases
    Qualitative Behaviour of the SABR Model
    The Link Between the Exponent, _, and the Volatility of Volatility, _
    Volatility Clustering in the (LMM)-SABR Model
    The Market
    How Do We Know that the Market Has Chosen _ = 0:5?
    The Problems with the SABR Model
    The LMM-SABR Model.
    The Equations of Motion
    The Nature of the Stochasticity Introduced by Our Model
    A Simple Correlation Structure
    A More General Correlation Structure
    Observations on the Correlation Structure
    The Volatility Structure
    What We Mean by Time Homogeneity
    The Volatility Structure in Periods of Market Stress
    A More General Stochastic Volatility Dynamics
    Calculating the No-Arbitrage Drifts
    IMPLEMENTATION AND CALIBRATION.
    Calibrating the LMM-SABR model to Market Caplet Prices.
    The Caplet-Calibration Problem
    Choosing the Parameters of the Function, g (_), and the Initial Values, kT 0
    Choosing the Parameters of the Function h(_
    Choosing the Exponent, _, and the Correlation, _SABR
    Results
    Calibration in Practice: Implications for the SABR Model
    Implications for Model Choice
    Calibrating the LMM-SABR model to Market Swaption Prices.
    The Swaption Calibration Problem
    Swap Rate and Forward Rate Dynamics
    Approximating the Instantaneous Swap Rate Volatility, St
    Approximating the Initial Value of the Swap Rate Volatility, _0 (First Route
    Approximating _0
    Approximating the Swap-Rate/Swap-Rate-Volatility Correlation, RSABR
    Approximating the Swap Rate Exponent, B
    Results
    Conclusions and Suggestions for Future Work
    Appendix: Derivation of Approximate Swap Rate Volatility
    Appendix: Derivation of Swap-Rate/Swap-Rate-Volatility Correlation, RSABR
    Appendix: Approximation of
    Calibrating the Correlation Structure.
    Statement of the Problem
    Creating a Valid Model Matrix
    A Case Study: Calibration Using the Hypersphere Method
    Which Method Should One Choose?
    Appendix1
    EMPIRICAL EVIDENCE.
    The Empirical Problem.
    Statement of the Empirical Problem
    What Do We know from the Literature?
    Data Description
    Distributional Analysis and Its Limitations
    What Is the True Exponent _?
    Appendix: Some Analytic Results
    Estimating the Volatility of the Forward Rates.
    Expiry-Dependence of Volatility of Forward Rates
    Direct Estimation
    Looking at the Normality of the Residuals
    Maximum-Likelihood and Variations on the Theme
    Information About the Volatility from the Options Market
    Overall Conclusions
    Estimating the Correlation Structure.
    What We Are Trying To Do
    Some Results from Random Matrix Theory
    Empirical Estimation
    Descriptive Statistics
    Signal and Noise in the Empirical Correlation Blocks
    What Does Random Matrix Theory Really Tell Us?
    Calibrating the Correlation Matrices
    How Much Information Do the Proposed Models Retain?
    HEDGING.
    Various Types of Hedging.
    Statement of the Problem
    Three Types of Hedging
    Definitions
    First-Order Derivatives with Respect to the Underlyings
    Second-Order Derivatives with Respect to the Underlyings
    Generalizing Functional-Dependence Hedging
    How Does the Model Know about Volga and Vanna?
    Choice of Hedging Instrument
    Hedging Against Moves in the Forward Rate and in the Volatility.
    Delta Hedging in the SABR-(LMM) Model
    Vega Hedging in the SABR-(LMM) Model
    (LMM)-SABR Hedging in Practice: Evidence from Market Data.
    Purpose of this Chapter
    Notation
    Hedging Results for the SABR Model
    Hedging Results for the LMM-SABR Model
    Conclusions
    Hedging the Correlation Structure.
    The Intuition Behind the Problem
    Hedging the Forward-Rate Block
    Hedging the Volatility-Rate Block
    Hedging the Forward-Rate/Volatility Block
    Final Considerations
    Hedging in Conditions of Market Stress.
    Statement of the Problem
    The Volatility Function
    The Case Study
    Hedging
    Results
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