Basic Black-Scholes: Option Pricing and Trading

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1 Basic Black-Scholes: Option Pricing and Trading BSc (HONS 1 st Timothy Falcon Crack Class), PGDipCom, MCom, PhD (MIT), IMC

2 Contents Preface Tables Figures ix xi xiii 1 Introduction to Options Hedging, Speculation, and Arbitrage " Forwards, Futures, and Options Introductory Option Examples Buying a Protective Put Introduction to Transactions Costs (T-Costs) Buying a Speculative Call 13 2 Mathematics, Statistics, and Finance Prerequisites Logarithms and Exponentials Logarithms Exponentials Inverse Properties Normality and Lognormality Normal Distribution Lognormal Distribution Inverse and Other Properties Z-Score and Cumulative Standard Normal Expected Values Conditional Expected Values Rates of Return Statistical/Distributional Arguments Continuously Compounded Returns Pricing Forwards/Futures with Continuous Dividends Other Prerequisites Equilibrium versus No-Arbitrage Percent Binomial Coefficients Timothy Falcon Crack V All Rights Reserved Worldwide

3 2.5.4 Ex-Dividend Process 36 3 Option Pricing Foundations Factors Affecting Option Prices Payoffs and Payoff Diagrams Directionally Correct Call Options: Restrictions Demonstration and. Discussion of Call Restrictions Put Options: Restrictions Demonstration and Discussion of Put Restrictions Put-Call Parity Synthetic Instruments and Arbitrage Leverage and Insurance Plotting Put-Call Parity American-Style Put-Call Parity Put-Call Parity "Regrets" Decompositions Put-Call Parity Intrinsic Value Decomposition 65 4 Risk-Neutral Option Pricing \ The Simple Answer: Traditional Methods Fail... /: Replication The Formula ; Risk-Neutral Pricing Review First Method (Merton [1973]) Second Method (Cox and Ross [1976]) Third Method (Harrison and Kreps [1979]) The Complex Answer: Non-Traditional Methods 77 5 Numerical Option Pricing: Monte Carlo Do I Need to Know This? Monte Carlo Methods : Monte Carlo in Science Monte Carlo for Options Overview of the Method Generating Stock Price Paths Monte Carlo Put Option Example Variance Reduction Drift and Dividends 88 6 Numerical Option Pricing: Lattice/Binomial Do I Need to Know This? Lattice Pricing I: One-Step Model Lattice Pricing II: J-Step Model...» Choosing u and d and Deducing IT* Binomial Valuation Example Timothy Falcon Crack Vi All Rights Reserved Worldwide

4 6.4 Lattice Pricing III: American Options Adjusting for Dividends 99 7 Partial Differential Equations Do I Need to Know This? PDEs Where Do Financial PDEs Come From? Transforming the PDE PDE Solution by Finite Differences PDE Interpretation: Greeks Analytical Option Pricing: Black-Scholes Black-Scholes Assumptions Ill A Note on Concavity and Geometric Averages Black-Scholes Derivation Black-Scholes Interpretations and Intuition Interpretation I: Recipe for Replication Interpretation II: DCF, Cost/Benefit Interpretation III: Binomial Limit.. \ Interpretation IV: Stock-Numeraire...'' Interpretation V: Digital (Binary) Options Interpretation VI: Conditional Payoffs Interpretation VII: PDE Solution Interpretation VIII: See figure Approximations to Black-Scholes Louis Jean Baptiste Alphonse Bachelier (1900) Immediate Extensions Index: Merton (1973) Futures: Black (1976b) FX: Garman and Kohlhagen (1983) and Grabbe (1983) Application: The Adequation Formula for FX Option Parity Black-Scholes Implementation Method I: Estimate Historical a Method II: Infer Market Forecast a Synthetic Options: Greeks Delta Hedging Delta-Gamma (and Theta) Hedging Beyond Black-Scholes American-Style Options Approximate Analytical Pricing Exact Analytical Pricing Some New Formulae Arithmetic Brownian Motion Power Option I: Crack (1997) : Timothy Falcon Crack VU All Rights Reserved Worldwide

5 9.2.3 Power Option II: Crack (1997, 2008) Forward on an At-the-Money Option: Crack-Maines (Crack [1997]) Summary of Option Pricing Methods I: Plain Vanilla versus Exotic Options Other Data-Generating Processes Jump Risk, Replication, and Risk-Neutral Pricing Stochastic Volatility Summary of Option Pricing Methods II: Discrete versus Continuous Models Trading Institutional Details Options Specifications Exchanges, Regulatory Bodies, and Securities Brokers T-Costs Black-Scholes Assumptions and Violations ' The Spreadsheet Tools Trading Experiences and Lessons Stylized Facts Information Sources Other Trading Tips and Tools Orders and Executions Market Views and Opinions The Deathly Slow Crawl Trading Tools: Greeks Spread Positions and Other Strategies 199 A HP Source Code 203 A.I HP17B/HP19B Black-Scholes 203 A.2 HP12C Black-Scholes A.3 HP17B/HP19B Binomial Pricing 209 A.4 An HP17B/HP19B Warning 210 References for Further Research 211 Abbreviations, Acronyms, and Symbols 217 Alphabets and Numerical Equivalences 218 Index Timothy Falcon Crack Vlll All Rights Reserved Worldwide

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