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

Rebonato, Riccardo; McKay, Kenneth D.; White, Richard
ISBN-10: 0470740051
ISBN-13: 9780470740057

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Written by highly experienced, well-respected researchers and practitioners, this book presents a never before published major innovation in interest rate modelling.
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
Are We Getting Something for Nothing?

Edition: 2009
Publisher: John Wiley & Sons, Limited
Binding: Trade Cloth
Pages: 296
Size: 7.00" wide x 10.00" long x 1.00" tall
Weight: 1.43 lbs.
Language: English

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