Preface ix
Acknowledgments xi
CHAPTER 1 Setting the Stage 1
Why Is This Book Different? 2
Road Map of the Book 3
References 5
CHAPTER 2 Building Zero Curves 7
Market Instruments 8
Linear Interpolation 16
Cubic Splining 25
Appendix: Finding Swap Rates Using a Floating Coupon
Bond Approach 41
References 43
CHAPTER 3 Valuing Vanilla Options 45
Black-Scholes Formulae 47
Adaptations of the Black-Scholes Formulae 53
Limitations of the Black-Scholes Formulae 70
Application in Currency Risk Management 74
Appendix 78
References 80
CHAPTER 4 Simulations 81
Uniform Number Generation 82
Non-Uniform Number Generation 86
Applications of Simulations 93
Variance Reduction Techniques 100
References 104
CHAPTER 5 Valuing Exotic Options 107
Valuing Path-Independent, European-Style Options on a Single Variable 108
Valuing Path-Dependent, European-Style Options on a Single Variable 114
Valuing Path-Independent, European-Style Options on Two Variables 135
Valuing Path-Dependent, European-Style Options on Multiple Variables 152
References 157
CHAPTER 6 Estimating Model Parameters 159
Calibration of Parameters in the Black-Scholes Model 161
Using Implied Black-Scholes Volatility Surface and Zero Rate Term Structure to Value Options 169
Using Volatility Surface 178
Calibration of Interest Rate Option Model Parameters 190
Statistical Estimation 196
References 203
CHAPTER 7 The Effectiveness of Hedging Strategies 205
Delta Hedging 206
Assumptions Underlying Delta Hedging 216
Beyond Delta Hedging 223
Testing Hedging Strategies 230
Analysis Associated with the Hedging of a European-Style Vanilla Put Option 235
References 244
CHAPTER 8 Valuing Variable Annuity Guarantees 245
Basic GMDB 246
Death Benefit Riders 261
Other Details Associated with GMDB Products 269
Improving Modeling Assumptions 273
Living Benefit Riders 276
References 279
CHAPTER 9 Real Options 281
Surrendering a GMAB Rider 282
Adding Servers in a Queue 300
References 314
CHAPTER 10 Parting Thoughts 315
About the Author 317
About the Website 319
Index 321