Derivative pricing: a Problem-based primer

Ambrose Lo

doi:10.1201/9781315301235

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 . 　 List of Figures List of Tables Preface Symbols I Introductory Derivatives: Fundamental Concepts 1. An Introduction to Forwards and Options Forwards Options Call Options Put Options Classification of Derivatives Problems 2. Forwards and Futures Alternative Ways to Buy a Stock Prepaid Forwards on Stocks Nondividend-paying Stocks Dividend-paying Stocks Forwards on Stocks Forward Price Cash-and-carry Arbitrage Digression: Market Frictions Futures Differences between Futures and Forwards Marking to Market Problems 3.Option Strategies Basic Insurance Strategies Insuring a Long Position: Floors Insuring a Short Position: Caps Selling Insurance A Simple but Useful Observation: Parallel Payoffs, Identical Profit Put-call Parity Synthetic Forwards The Put-call Parity Equation Spreads and Collars Spreads Collars Volatility Speculation Straddles Strangles Buttery Spreads Problems II Advanced Derivatives: Pricing and Hedging 4. Binomial Option Pricing Models One-period Binomial Trees Pricing by Replication Risk-neutral Pricing Constructing a Binomial Tree Multi-period Binomial Trees American Options Options on Other Assets Currency Options Options on Futures Epilogue: Pricing by True Probabilities Problems 5. Mathematical Foundations of the BS Framework A Lognormal Model of Stock Prices Lognormal Probability Calculations Estimating the Parameters of a Lognormal Stock Price Model Problems 6. The Black-Scholes Formula BS Formula for Stocks Paying Continuous Dividends Applying the Black-Scholes Formula to Other Assets Option Greeks Option Delta Option Gamma Key Learning Items in Interpreting Option Greeks Option Greeks of a Portfolio Option Elasticity Implied Volatility Problems 7. Option Greeks and Risk Management Delta-hedging and Holding Profits Hedging Multiple Greeks Delta-Gamma-Theta Approximation Problems 8. Exotic Options All-or-Nothing Options Cash-or-nothing Options Asset-or-nothing Options Option Greeks of All-or-nothing Options Gap Options Introduction Pricing and Hedging Gap Options Exchange Options Introduction Pricing Exchange Options Pricing Maximum and Minimum Options Compound Options Asian Options Introduction Pricing Asian Options Lookback Options Barrier Options Other Exotic Options Chooser Options Forward Start Options Problems III Epilogue 9. General Properties of Option Prices Put-Call Parity and Duality Generalized Parity Currency Put-call Duality Upper and Lower Bounds on Option Prices Comparing Options Strike Price Maturity Early Exercise Decision for American Options Proof : A Proof Based on No-arbitrage Bounds Proof : A Cost-benefit Dissection Proof Early Exercise Criterion for American puts Problems Appendix A Solutions to End-of-Chapter Problems Bibliography Index 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 .

Derivative pricing: a Problem-based primer

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