Praise for The Mathematics of Financial Models
Dr. Kannoo Ravindran does a great job in using applied quantitative methods to solve financial problems encountered in practice while discussing the practical nuances associated with the problem. The book explains the concept intuitively so it is very easy for readers to get it. This book is a must–read for anyone new to mathematical modeling in finance and serves as a great complement to any good book on finance and derivatives.
Dr. Pin Chung, FRM, ASA, MAAA, Chief Financial Officer and Chief Investment Officer, R+V International Business Services Limited, Dublin, Ireland
This is a unique work that provides easy–to–follow practical solutions in addition to the underlying theory for solving problems using quantitative methods. A must read for the new practitioner and a great refresher for the experienced practitioner.
Kirk Evans, FSA, MAAA, CFA, FRM, Vice President, Product Development & Pricing and Risk Management, Sammons Retirement Solutions
The actuary or financial quant entering variable annuity risk management faces a bewildering array of new terminology, concepts, and practices. Dr. Ravindran s book provides a comprehensive but compact introduction for new practitioners including clear spreadsheet models for building intuition and practical bench marking.
Daniel D. Heyer, FCAS, CQF, Vice President, Quantitative Risk Management, Nationwide Financial
This book and the accompanying Excel worksheets are a valuable resource for quants and would–be quants.
John Hull, Maple Financial Chair in Derivatives and Risk Management, Joseph L. Rotman School of Management, University of Toronto
Dr. Kannoo Ravindran s book is a welcomed addition to a student s or practitioner s library alike, given the range of topics it covers, the accompanying spreadsheet examples, and all the solid references that can be found at the end of each chapter. The author has done a great job of covering the diverse subject matter, like the chapter on financial guarantees embedded in life insurance products, and the one on hedge strategy effectiveness, and leaving readers with a set of building blocks to help them tackle real risk management problems they would face in the field.
Peter M. Phillips, Managing Director, Aon Benfield Securities, Inc.
Dr. Ravindran has written a valuable book that bridges the all–too–wide gap between theory and practice in mathematical finance. It is useful and should be required reading for students in quantitative finance programs, and yet is immediately accessible to many who work in the field, from front–office users to risk managers, modelers, programmers, and operations staff.
Paul Staneski, Ph.D., Principal, Derivatives Solutions, LLC
CHAPTER 1 Setting the Stage 1
Why Is This Book Different? 2
Road Map of the Book 3
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
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
CHAPTER 4 Simulations 81
Uniform Number Generation 82
Non–Uniform Number Generation 86
Applications of Simulations 93
Variance Reduction Techniques 100
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
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
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
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
CHAPTER 9 Real Options 281
Surrendering a GMAB Rider 282
Adding Servers in a Queue 300
CHAPTER 10 Parting Thoughts 315
About the Author 317
About the Website 319
DR. KANNOO RAVINDRAN consults with corporations on investments, derivatives trading, modeling, and risk management. He also lectures around the world on these topics and runs a private equity fund. Dr. Ravindran pioneered the use of derivatives to manage risks embedded in variable annuity products.