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

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, calculus, statistics and numerical analysis that are used to build the quantitative methods used.

Financial analysts, investment professionals, risk-management professionals, and graduate students will find applicable information throughout the book, and gain from the self-study exercises and the refresher course on key mathematical topics. Equipped with tips and information, The Mathematics of Financial Models

• Provides practical methodologies based on mathematical quantitative analysis to help analysts, investment and risk-management professionals better navigate client issues
• Contains interactive tools that demonstrate the power of analysis and modeling
• Helps financial professionals become more familiar with the challenges across a range of industries
• Includes a mathematics refresher course and plenty of exercises to get readers up to speed

The Mathematics of Financial Models is an in-depth guide that helps readers break through common client financial problems and emerge with clearer strategies for solving issues in the future.

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

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