Derivative Pricing: A Problem-Based Primer (Chapman and Hall/CRC Financial Mathematics Series)

Description

The proliferation of financial derivatives over the past decades, options in particular, has underscored the increasing importance of derivative pricing literacy among students, researchers, and practitioners. Derivative Pricing: A Problem-Based Primer demystifies the essential derivative pricing theory by adopting a mathematically rigorous yet widely accessible pedagogical approach that will appeal to a wide variety of audience. Abandoning the traditional "black-box" approach or theorists’ "pedantic" approach, this textbook provides readers with a solid understanding of the fundamental mechanism of derivative pricing methodologies and their underlying theory through a diversity of illustrative examples. The abundance of exercises and problems makes the book well-suited as a text for advanced undergraduates, beginning graduates as well as a reference for professionals and researchers who need a thorough understanding of not only "how," but also "why" derivative pricing works. It is especially ideal for students who need to prepare for the derivatives portion of the Society of Actuaries Investment and Financial Markets Exam. Features Lucid explanations of the theory and assumptions behind various derivative pricing models. Emphasis on intuitions, mnemonics as well as common fallacies. Interspersed with illustrative examples and end-of-chapter problems that aid a deep understanding of concepts in derivative pricing. Mathematical derivations, while not eschewed, are made maximally accessible. A solutions manual is available for qualified instructors. The Author Ambrose Lo is currently Assistant Professor of Actuarial Science at the Department of Statistics and Actuarial Science at the University of Iowa. He received his Ph.D. in Actuarial Science from the University of Hong Kong in 2014, with dependence structures, risk measures, and optimal reinsurance being his research interests. He is a Fellow of the Society of Actuaries (FSA) and a Chartered Enterprise Risk Analyst (CERA). His research papers have been published in top-tier actuarial journals, such as ASTIN Bulletin: The Journal of the International Actuarial Association, Insurance: Mathematics and Economics, and Scandinavian Actuarial Journal. Cover Half Title Title Page Copyright Page Table of Contents List of Figures List of Tables Preface Symbols I: Conceptual Foundation on Derivatives 1: An Introduction to Forwards and Options 1.1 Forwards 1.2 Options 1.2.1 Call Options 1.2.2 Put Options 1.3 Classification of Derivatives 1.4 Problems 2: Forwards and Futures 2.1 Alternative Ways to Buy a Stock 2.2 Prepaid Forwards 2.2.1 Nondividend-paying Stocks 2.2.2 Dividend-paying Stocks 2.3 Forwards 2.3.1 Forward Prices 2.3.2 Cash-and-Carry Arbitrage 2.3.3 Digression: Market Frictions 2.4 Futures 2.4.1 Differences between Futures and Forwards 2.4.2 Marking to Market 2.5 Problems 3: Option Strategies 3.1 Basic Insurance Strategies 3.1.1 Insuring a Long Position: Floors 3.1.2 Insuring a Short Position: Caps 3.1.3 Selling Insurance 3.1.4 A Simple but Useful Observation: Parallel Payoffs, Identical Profit 3.2 Put-call Parity 3.2.1 Synthetic Forwards 3.2.2 The Put-call Parity Equation 3.3 Spreads and Collars 3.3.1 Spreads 3.3.2 Collars 3.4 Volatility Speculation 3.4.1 Straddles 3.4.2 Strangles 3.4.3 Butterfly Spreads 3.5 Problems II: Pricing and Hedging of Derivatives 4: Binomial Option Pricing Models 4.1 One-period Binomial Trees 4.1.1 Pricing by Replication 4.1.2 Risk-neutral Pricing 4.1.3 Constructing a Binomial Tree 4.2 Multi-period Binomial Trees 4.3 American Options 4.4 Options on Other Assets 4.4.1 Case Study 1: Currency Options 4.4.2 Case Study 2: Options on Futures 4.5 Epilogue: Pricing by Real Probabilities of Stock Price Movements 4.6 Problems 5: Mathematical Foundations of the Black-Scholes Framework 5.1 A Lognormal Model of Stock Prices 5.2 Lognormal-Based Probabilistic Quantities 5.3 Problems 6: The Black-Scholes Formula 6.1 Black-Scholes Formula for Stocks Paying Continuous Proportional Dividends 6.2 Applying the Black-Scholes Formula to Other Underlying Assets 6.2.1 Case study 1: Stocks paying non-random, discrete dividends 6.2.2 Case Study 2: Currency options 6.2.3 Case Study 3: Futures options 6.3 Option Greeks 6.3.1 Option Delta 6.3.2 Option Gamma 6.3.3 Option Greeks of a Portfolio 6.3.4 Option Elasticity 6.4 Problems 7: Option Greeks and Risk Management 7.1 Delta-hedging 7.2 Hedging Multiple Greeks 7.3 Delta-Gamma-Theta Approximation 7.4 Problems 8: Exotic Options 8.1 Gap Options 8.1.1 Introduction 8.1.2 All-or-Nothing Options 8.1.3 Pricing and Hedging Gap Options 8.2 Exchange Options 8.2.1 Introduction 8.2.2 Pricing Exchange Options 8.2.3 Pricing Maximum and Minimum Contingent Claims 8.3 Compound Options 8.4 Asian Options 8.4.1 Introduction 8.4.2 Pricing Asian Options 8.5 Lookback Options 8.6 Shout Options 8.7 Barrier Options 8.8 Other Exotic Options 8.8.1 Chooser Options 8.8.2 Forward Start Options 8.9 Problems III: Epilogue 9: General Properties of Option Prices 9.1 Put-Call Parity and Duality 9.1.1 Generalized Parity 9.1.2 Currency Put-call Duality 9.2 Upper and Lower Bounds on Option Prices 9.3 Comparing Options with Respect to Contract Characteristics 9.3.1 Strike Price 9.3.2 Maturity 9.4 Early Exercise Decisions for American Options 9.4.1 Proof 1: A Proof Based on No-arbitrage Bounds 9.4.2 Proof 2: A Cost-benefit Dissection Proof 9.4.3 Early Exercise Criterion for American Puts 9.5 Problems Appendix A: Standard Normal Distribution Table Appendix B: Solutions to Odd-Numbered End-of-Chapter Problems B.1 Chapter 1 B.2 Chapter 2 B.3 Chapter 3 B.4 Chapter 4 B.5 Chapter 5 B.6 Chapter 6 B.7 Chapter 7 B.8 Chapter 8 B.9 Chapter 9 Bibliography Index