An Introduction to Equity Derivatives -- Contents -- Foreword -- Preface -- Addendum: A Path to Economic Renaissance -- PART I BUILDING BLOCKS -- 1 Interest Rate -- 1-1 Measuring Time -- 1-2 Interest Rate -- 1-2.1 Gross Interest Rate -- 1-2.2 Compounding. Compound Interest Rate -- 1-2.3 Conversion Formula -- 1-2.4 Annualization -- 1-3 Discounting -- 1-3.1 Present Value -- 1-3.2 Discount Rate and Required Return -- 1-4 Problems -- 2 Classical Investment Rules -- 2-1 Rate of Return. Time of Return -- 2-1.1 Gross Rate of Return (ROR) -- 2-1.2 Time of Return (TOR) -- 2-2 Net Present Value (NPV) -- 2-3 Internal Rate of Return (IRR) -- 2-4 Other Investment Rules -- 2-5 Further Reading -- 2-6 Problems -- 3 Fixed Income -- 3-1 Financial Markets -- 3-1.1 Securities and Portfolios -- 3-1.2 Value and Price -- 3-1.3 Financial Markets and Short-selling -- 3-1.4 Arbitrage -- 3-1.5 Price of a Portfolio -- 3-2 Bonds -- 3-2.1 Treasury Bonds -- 3-2.2 Zero-Coupon Bonds -- 3-2.3 Bond Markets -- 3-3 Yield -- 3-3.1 Yield to Maturity -- 3-3.2 Yield Curve -- 3-3.3 Approximate Valuation -- 3-4 Zero-Coupon Yield Curve. Arbitrage Price -- 3-4.1 Zero-Coupon Rate Curve -- 3-4.2 Arbitrage Price of a Bond -- 3-4.3 Zero-Coupon Rate Calculation by Inference: the 'Bootstrapping' Method -- 3-5 Further Reading -- 3-6 Problems -- 4 Portfolio Theory -- 4-1 Risk and Return of an Asset -- 4-1.1 Average Return and Volatility -- 4-1.2 Risk-free Asset. Sharpe Ratio -- 4-2 Risk and Return of a Portfolio -- 4-2.1 Portfolio Valuation -- 4-2.2 Return of a Portfolio -- 4-2.3 Volatility of a Portfolio -- 4-3 Gains of Diversification. Portfolio Optimization -- 4-4 Capital Asset Pricing Model -- 4-5 Further Reading -- 4-6 Problems -- PART II FIRST STEPS IN EQUITY DERIVATIVES -- 5 Equity Derivatives -- 5-1 Introduction -- 5-2 Forward Contracts -- 5-2.1 Payoff -- 5-2.2 Arbitrage Price.

5-2.3 Forward Price -- 5-2.4 Impact of Dividends -- 5-2.4.1 Single Cash Dividend -- 5-2.4.2 Single Proportional Dividend -- 5-3 'Plain Vanilla' Options -- 5-3.1 Payoff -- 5-3.2 Option Value -- 5-3.3 Put-Call Parity -- 5-3.4 Option Strategies -- 5-3.4.1 Leverage -- 5-3.4.2 Covered Call -- 5-3.4.3 Straddle -- 5-3.4.4 Butterfly -- 5-4 Further Reading -- 5-5 Problems -- 6 The Binomial Model -- 6-1 One-Step Binomial Model -- 6-1.1 An Example -- 6-1.2 General Formulas -- 6-2 Multi-Step Binomial Trees -- 6-3 Binomial Valuation Algorithm -- 6-4 Further Reading -- 6-5 Problems -- 7 The Lognormal Model -- 7-1 Fair Value -- 7-1.1 Probability Distribution of ST -- 7-1.2 Discount Rate -- 7-2 Closed-Form Formulas for European Options -- 7-3 Monte-Carlo Method -- 7-4 Further Reading -- 7-5 Problems -- 8 Dynamic Hedging -- 8-1 Hedging Option Risks -- 8-1.1 Delta-hedging -- 8-1.2 Other Risk Parameters: the 'Greeks' -- 8-1.3 Hedging the Greeks -- 8-2 The P&L of Delta-hedged Options -- 8-2.1 Gamma -- 8-2.2 Theta -- 8-2.3 Option Trading P&L Proxy -- 8-3 Further Reading -- 8-4 Problems -- PART III ADVANCED MODELS AND TECHNIQUES -- 9 Models for Asset Prices in Continuous Time -- 9-1 Continuously Compounded Interest Rate -- 9-1.1 Fractional Interest Rate -- 9-1.2 Continuous Interest Rate -- 9-2 Introduction to Models for the Behavior of Asset Prices in Continuous Time -- 9-3 Introduction to Stochastic Processes -- 9-3.1 Standard Brownian Motion -- 9-3.2 Generalized Brownian Motion -- 9-3.3 Geometric Brownian Motion -- 9-4 Introduction to Stochastic Calculus -- 9-4.1 Ito Process -- 9-4.2 The Ito-Doeblin Theorem -- 9-4.3 Heuristic Proof of the Ito-Doeblin Theorem -- 9-5 Further Reading -- 9-6 Problems -- 10 The Black-Scholes Model -- 10-1 The Black-Scholes Partial Differential Equation -- 10-1.1 Ito-Doeblin Theorem for the Derivative's Value.

10-1.2 Riskless Hedged Portfolio -- 10-1.3 Arbitrage Argument -- 10-1.4 Partial Differential Equation -- 10-1.5 Continuous Delta-hedging -- 10-2 The Black-Scholes Formulas for European Vanilla Options -- 10-3 Volatility -- 10-3.1 Historical Volatility -- 10-3.2 Implied Volatility -- 10-4 Further Reading -- 10-5 Problems -- 11 Volatility Trading -- 11-1 Implied and Realized Volatilities -- 11-1.1 Realized Volatility -- 11-1.2 Implied Volatility -- 11-2 Volatility Trading Using Options -- 11-3 Volatility Trading Using Variance Swaps -- 11-3.1 Variance Swap Payoff -- 11-3.2 Variance Swap Market -- 11-3.3 Variance Swap Hedging and Pricing -- 11-4 Further Reading -- 11-5 Problems -- 12 Exotic Derivatives -- 12-1 Single-Asset Exotics -- 12-1.1 Digital Options -- 12-1.2 Asian Options -- 12-1.3 Barrier Options -- 12-1.4 Lookback Options -- 12-1.5 Forward Start Options -- 12-1.6 Cliquet Options -- 12-1.7 Structured Products -- 12-2 Multi-Asset Exotics -- 12-2.1 Spread Options -- 12-2.2 Basket Options -- 12-2.3 Worst-of and Best-of Options -- 12-2.4 Quanto Options -- 12-2.5 Structured Products -- 12-2.6 Dispersion and Correlation Trading -- 12-3 Beyond Black-Scholes -- 12-3.1 Black-Scholes on Multiple Assets -- 12-3.2 Fitting the Smile -- 12-3.2.1 Stochastic Volatility -- 12-3.2.2 Jumps -- 12-3.2.3 Local Volatility -- 12-3.3 Discrete Hedging and Transaction Costs -- 12-3.3.1 Discrete Hedging -- 12-3.3.2 Transaction Costs -- 12-3.4 Correlation Modeling -- 12-4 Further Reading -- 12-5 Problems -- SOLUTIONS -- Problem Solutions -- Chapter 1 -- Chapter 2 -- Chapter 3 -- Chapter 4 -- Chapter 5 -- Chapter 6 -- Chapter 7 -- Chapter 8 -- Chapter 9 -- Chapter 10 -- Chapter 11 -- Chapter 12 -- APPENDICES -- A Probability Review -- A-1 States of Nature. Random Variables. Events -- A-2 Probability. Expectation. Variance -- A-3 Distribution. Normal Distribution.

A-4 Independence. Correlation -- A-5 Probability Formulas -- A-6 Further Reading -- B Calculus Review -- B-1 Functions of Two Variables x and y -- B-2 Taylor Expansions -- C Finance Formulas -- C-1 Rates and Yields -- C-2 Present Value. Arbitrage Price -- C-3 Forward Contracts -- C-4 Options -- C-5 Volatility -- C-6 Stochastic Processes. Stochastic Calculus -- C-7 Greeks etc. -- Index.