TABLE of CONTENTS Preface Chapter 1: Theory of Arbitrage Pricing: Equity Markets 1.1 A Basic One Period Model 1.2 Defining the No-Arbitrage Condition 1.2.1 Identifying an Arbitrage Portfolio 1.2.2 Law of One Price 1.3 Pricing by Replication 1.3.1 Three Special Contingent Cash Flows 1.4 Stochastic Discount Factors 1.4.1 SDF and Risk Neutral Probability 1.5 Concluding Remarks 1.6 Questions and Problems 1.7 Appendix 1.7.1 Complete Market 1.7.2 Incomplete Market 1.7.3 Incomplete Market and Arbitrage Bounds 1.7.4 The No-Arbitrage Condition: Geometric Exposition Chapter 2: Arbitrage Pricing Applications: Equity Markets 2.1 Market Structure and the Risk-Free Rate 2.2 One Period Binomial Model 2.3 Valuing Two Propositions 2.4 Forwards: A First Look 2.4.1 Forward Contract on a Security 2.4.2 Forward Contract on the Exchange Rate 2.5 Swaps: A First Look 2.5.1 Currency Swaps 2.5.2 Equity (Asset) Swaps 2.6 General Valuation 2.6.1 The Risk-free Rate of Interest Implicit in the Market 2.6.2 The Two Propositions 2.6.3 Forwards 2.6.4 Swaps 2.7 Concluding Remarks 2.8 Questions and Problems Chapter 3: Pricing by Arbitrage: Debt Markets 3.1 Setting the Framework 3.2 Arbitrage in the Debt Market 3.2.1 Distinct Features of the Debt Market 3.2.2 Defining the No-Arbitrage Condition 3.3 Discount Factors 3.4 Rates, Discount Factors, and Continuous Compounding 3.4.1 Continuous Compounding 3.5 Concluding Remarks 3.6 Questions and Problems 3.7 Appendix 3.7.1 No-Arbitrage Condition in the Bond Market Chapter 4: Fundamentals of Options 4.1 Extending the Simple Model 4.2 Two Types of Options 4.3 Trading Strategies 4.3.1 Portfolios of Calls and Puts with the Same Maturity Date 4.4 Payoff Diagrams and Relative Pricing 4.4.1 Pricing Bounds Obtained by Relative Pricing Results 4.4.2 Put-Call Parity 4.5 From Payoffs to Portfolios 4.6 Concluding Remarks 4.7 Questions and Problems 4.8 Appendix 4.8.1 Explanation of Stripay 4.8.2 Procedural Issues Chapter 5: Risk Neutral Probability and SDF 5.1 Infinite vs. Finite States 5.2 SDF for an Infinite Omega 5.3 Risk Neutral Probability and SDF 5.4 A First Look at Stock Prices 5.5 The Distribution of the Rate of Return 5.6 Paths of the Price Process 5.7 Specifying a Risk Neutral Probability 5.8 Lognormal Distributions and SDF 5.9 The Stochastic Discount Factor Function 5.10 Concluding Remarks 5.11 Questions and Problems Chapter 6: Valuation of European Options 6.1 Valuing a Call Option 6.2 Valuing a Put Option 6.3 Combinations across Time 6.4 Dividends and Option Pricing 6.5 Volatility and Implied Volatility 6.5.1 Estimating Volatility from Historical Data 6.5.2 Implied Volatility 6.6 Concluding Remarks 6.7 Questions and Problems 6.8 Appendix 6.8.1 Estimating Implied Volatility Using Trial and Error Chapter 7: Sensitivity Measures 7.1 The Theta Measure 7.2 The Delta Measure 7.3 The Gamma Measure 7.4 The Vega Measure 7.5 The rho Measure 7.6 Concluding Remarks 7.7 Questions and Problems 7.8 Appendix 7.8.1 Derivation of Sensitivity Measures 7.8.2 Sensitivity of Other Options 7.8.3 Signs of the Sensitivities Chapter 8: Hedging with the Greeks 8.1 Hedging: the General Philosophy 8.2 Delta Hedging 8.2.1 Solving for a Delta Neutral Portfolio 8.3 Delta Neutral Portfolios and the Defintion of Delta 8.4 General Hedging 8.5 Optimizing Hedged Portfolios 8.6 Concluding Remarks 8.7 Questions and Problems Chapter 9: The Term Structure its Estimation & Smoothing 9.1 The Term Structure of Interest Rates 9.1.1 Zero Coupon, Spot and Yield Curves 9.2 Smoothing of the Term Structure 9.2.1 Smoothing and Continuous Compounding 9.3 Forward Rates 9.3.1 Forward Rate: A Classical Approach 9.3.2 Forward Rate: A Practical Approach 9.4 A Variable Rate Bond 9.5 Concluding Remarks 9.6 Questions and Problems 9.7 Appendix 9.7.1 Theories of the Shape of the Term Structure 9.7.2 Approximating Functions Chapter 10: Forwards, Eurodollars and Futures 10.1 Forward Contracts: A Second Look 10.2 Valuation of Forward Contracts Prior to Maturity 10.3 Forward Price of Assets that Pay Known Cash Flows 10.3.1 Forward Contracts, Prior to Maturity, of Assets that Pay Known Cash Flows 10.3.2 Forward Price of a Stock that Pays A Known Dividend Yield 10.4 Eurodollar Contracts 10.4.1 Forward Rate Agreements (FRA) 10.5 Futures Contracts: A Second Look 10.6 Deterministic Term Structure (DTS) 10.7 Futures Contracts in a DTS Environment 10.8 Concluding Remarks 10.9 Questions and Problems Chapter 11: Swaps: A Second Look 11.1 A Fixed-for-Float Swap 11.1.1 Valuing an Existing Swap 11.2 Currency Swaps 11.3 Commodity and Equity Swaps 11.4 Forwards and Swaps: A Visualization 11.5 Concluding Remarks 11.6 Questions and Problems Chapter 12: American Options 12.1 American Call Options 12.1.1 Arbitrage Bounds 12.1.2 Early Exercise Decision 12.2 American Put Options 12.2.1 Arbitrage Bounds 12.2.2 Early Exercise Decision 12.3 Put Call Parity 12.4 The Effect of Dividends 12.4.1 A Call Option 12.4.2 A Put Option 12.5 Concluding Remarks 12.6 Questions and Problems Chapter 13: The Binomial Model I 13.1 Setting the Premises 13.2 No-Arbitrage and SDF 13.2.1 No-Arbitrage 13.2.2 SDF 13.3 Valuation 13.3.1 Valuation with SDF 13.3.2 Valuation by Replication 13.4 Numerical Valuation 13.4.1 Price Evolution 13.4.2 European Call 13.4.3 European Put 13.4.4 American Options 13.5 Concluding Remarks 13.6 Questions and Problems Chapter 14: The Binomial Model II 14.1 Binomial Model and the Black-Scholes Formula 14.1.1 Binomial vs. Lognormal 14.1.2 Numerical Implementations 14.1.3 The Effect of Dividends 14.2 Risk Neutral Probabilities and Price Processes 14.3 Futures and Forwards: A Symbolic Example 14.4 Brownian Motion 4.5 Concluding Remarks 14.6 Questions and Problems 14.7 Appendix 14.7.1 The Black-Scholes Formula as a Limit of the Binomial Formula Chapter 15: A Second Look at the Black-Scholes Formula 15.1 An Overview 15.2 The Price Process: A Second Look 15.2.1 Stochastic Evolution: The Discrete Case 15.3 Simulation of Stochastic Evolution 15.4 Stochastic Evolution: Toward a continuous Model 15.5 Ito's Lemma 15.5.1 Heuristic Proofs of Ito's Lemma 15.5.2 Examples Utilizing Ito's Lemma 15.6 The Black-Scholes Differential Equation 15.6.1 A Second Derivation 15.7 Reconciliation with Risk-Neutral Valuation 15.8 American vs. European 15.9 Concluding Remarks 15.10 Questions and Problems 15.11 Appendix 15.11.1 A Change Over an Instant 15.11.2 The Limit of a Random Variable 15.11.3 A More Rigorous Insight into Ito's Lemma Chapter 16: Other Types of Options 16.1 American Options, Dividend-paying Stocks and Binomial Models 16.2 Options on Indixes, Foreign Currency and Futures 16.2.1 Stock Index Options 16.2.2 Currency Options 16.2.3 Options on Futures Contracts 16.3 Examples of Exotic Options 16.3.1 Binary (Digital) Options 16.3.2 Combinations of Binary and Plain Vanilla Options 16.3.3 Gap Options 16.3.4 Paylater (cash on delivery) Options 16.4 Interest Rate Derivatives 16.4.1 Black's Model 16.4.2 Black, Derman and Toy Model 16.5 Concluding Remarks 16.6 Questions and Problems Chapter 17: The End or the Beginning References