Learn 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, 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.

Learn how quantitative models can help fight client problemshead-onBefore financial problems can be solved, they need to be fullyunderstood. Since in-depth quantitative modeling techniques are apowerful tool to understanding the drivers associated withfinancial problems, one would need a solid grasp of thesetechniques before being able to unlock their full potential of themethods used. In The Mathematics of Financial Models, theauthor presents real world solutions to the everyday problemsfacing financial professionals. With interactive tools such asspreadsheets for valuation, pricing, and modeling, this resourcecombines highly mathematical quantitative analysis with usefulpractical methodologies to create an essential guide for investmentand risk-management professionals facing modeling issues ininsurance, derivatives valuation, and pension benefits, amongothers. In addition to this, this resource also provides therelevant tools like matrices, calculus, statistics and numericalanalysis that are used to build the quantitative methods used.Financial analysts, investment professionals, risk-managementprofessionals, and graduate students will find applicableinformation throughout the book, and gain from the self-studyexercises and the refresher course on key mathematical topics.Equipped with tips and information, The Mathematics of FinancialModels* Provides practical methodologies based on mathematicalquantitative analysis to help analysts, investment andrisk-management professionals better navigate client issues* Contains interactive tools that demonstrate the power ofanalysis and modeling* Helps financial professionals become more familiar with thechallenges across a range of industries* Includes a mathematics refresher course and plenty of exercisesto get readers up to speedThe Mathematics of Financial Models is an in-depth guidethat helps readers break through common client financial problemsand emerge with clearer strategies for solving issues in thefuture.

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