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.
Table of Contents
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
