Description
Book SynopsisLearn how quantitative models can help fight client problems head-on Before financial problems can be solved, they need to be fully understood. Since in-depth quantitative modeling techniques are a powerful tool to understanding the drivers associated with financial problems, one would need a solid grasp of these techniques before being able to unlock their full potential of the methods used. In The Mathematics of Financial Models, the author presents real world solutions to the everyday problems facing financial professionals. With interactive tools such as spreadsheets for valuation, pricing, and modeling, this resource combines highly mathematical quantitative analysis with useful, practical methodologies to create an essential guide for investment and risk-management professionals facing modeling issues in insurance, derivatives valuation, and pension benefits, among others. In addition to this, this resource also provides the relevant tools like matrices, calculu
Table of Contents
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
