پارسی   English   العربیه

The Mathematics of Financial Models: Solving Real-World Problems with Quantitative Methods


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

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.

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