Basic BlackScholes: Option Pricing and Trading


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1 Basic BlackScholes: 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 (TCosts) 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 ZScore 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 NoArbitrage Percent Binomial Coefficients Timothy Falcon Crack V All Rights Reserved Worldwide
3 2.5.4 ExDividend 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 PutCall Parity Synthetic Instruments and Arbitrage Leverage and Insurance Plotting PutCall Parity AmericanStyle PutCall Parity PutCall Parity "Regrets" Decompositions PutCall Parity Intrinsic Value Decomposition 65 4 RiskNeutral Option Pricing \ The Simple Answer: Traditional Methods Fail... /: Replication The Formula ; RiskNeutral Pricing Review First Method (Merton [1973]) Second Method (Cox and Ross [1976]) Third Method (Harrison and Kreps [1979]) The Complex Answer: NonTraditional 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: OneStep Model Lattice Pricing II: JStep 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: BlackScholes BlackScholes Assumptions Ill A Note on Concavity and Geometric Averages BlackScholes Derivation BlackScholes Interpretations and Intuition Interpretation I: Recipe for Replication Interpretation II: DCF, Cost/Benefit Interpretation III: Binomial Limit.. \ Interpretation IV: StockNumeraire...'' Interpretation V: Digital (Binary) Options Interpretation VI: Conditional Payoffs Interpretation VII: PDE Solution Interpretation VIII: See figure Approximations to BlackScholes 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 BlackScholes Implementation Method I: Estimate Historical a Method II: Infer Market Forecast a Synthetic Options: Greeks Delta Hedging DeltaGamma (and Theta) Hedging Beyond BlackScholes AmericanStyle 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 AttheMoney Option: CrackMaines (Crack [1997]) Summary of Option Pricing Methods I: Plain Vanilla versus Exotic Options Other DataGenerating Processes Jump Risk, Replication, and RiskNeutral Pricing Stochastic Volatility Summary of Option Pricing Methods II: Discrete versus Continuous Models Trading Institutional Details Options Specifications Exchanges, Regulatory Bodies, and Securities Brokers TCosts BlackScholes 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 BlackScholes 203 A.2 HP12C BlackScholes 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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