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

Acknowledgements xi

1 Introduction 1

I The Theoretical Set-Up 7

2 The LIBOR Market Model 9

3 The SABR Model 25

4 The LMM-SABR Model 51

II Implementation and Calibration 79

5 Calibrating the LMM-SABR Model to Market Caplet Prices 81

6 Calibrating the LMM-SABR Model to Market Swaption Prices 101

7 Calibrating the Correlation Structure 125

III Empirical Evidence 141

8 The Empirical Problem 143

9 Estimating the Volatility of the Forward Rates 159

10 Estimating the Correlation Structure 181

IV Hedging 203

11 Various Types of Hedging 205

12 Hedging against Moves in the Forward Rate and in the Volatility 221

13 (LMM)-SABR Hedging in Practice: Evidence from Market Data 231

14 Hedging the Correlation Structure 247

15 Hedging in Conditions of Market Stress 257

References 271

Index 275