# Basic Black-Scholes: Option Pricing and Trading [6 ed.] 1991155433, 9781991155436

##### Dr. Crack studied PhD-level option pricing at MIT and Harvard Business School, taught undergrad and MBA option pricing a

341 59 2MB

English Pages 290 Year 2022

Contents
Preface
List of Tables
List of Figures
1 Introduction to Options
1.1 Hedging, Speculation, and Arbitrage
1.2 Forwards, Futures, and Options
1.3 Introductory Option Examples
1.3.2 Introduction to Transaction Costs (T-Costs)
2 Mathematics, Statistics, and Finance Prerequisites
2.1 Logarithms and Exponentials
2.1.1 Logarithms
2.1.2 Exponentials
2.1.3 Inverse Properties
2.2 Normality and Lognormality
2.2.1 Normal Distribution
2.2.2 Lognormal Distribution
2.2.3 Inverse and Other Properties
2.2.4 Z-Score and CumulativeStandard Normal
2.3 Expected Values
2.3.1 Conditional Expected Values
2.4 Rates of Return
2.4.1 Statistical/Distributional Arguments
2.4.2 Continuously Compounded Returns
2.4.3 Pricing Forwards/Futures with Continuous Dividends
2.5 Other Prerequisites
2.5.1 Equilibrium versus No-Arbitrage
2.5.2 Percent
2.5.3 Binomial Coefficients
2.5.4 Dividend Payment and the Dividend Timeline
3 Option Pricing Foundations
3.1 Factors Affecting Option Prices
3.2 Payoffs and Payoff Diagrams
3.3 Directionally Correct
3.4 Call Options: Restrictions
3.4.1 Demonstration and Discussion of Call Restrictions
3.5 Put Options: Restrictions
3.5.1 Demonstration and Discussion of Put Restrictions
3.6 Put-Call Parity
3.6.1 Synthetic Instruments and Arbitrage
3.6.2 Leverage and Insurance
3.6.3 Plotting Put-Call Parity
3.6.4 American-Style Put-Call Parity
3.6.5 Put-Call Parity “Regrets” Decompositions
3.6.6 Put-Call Parity Intrinsic Value Decomposition
4 Risk-Neutral Option Pricing
4.2 Replication
4.3 The Formula
4.4 Risk-Neutral Pricing Review
4.4.1 First Method (Merton, 1973)
4.4.2 Second Method (Cox and Ross, 1976)
4.4.3 Third Method (Harrison and Kreps, 1979)
5 Numerical Option Pricing: Monte Carlo
5.1 Do I Need to Know This?
5.2 MonteCarlo Methods
5.3 Monte Carlo in Science
5.4 Monte Carlo for Options
5.4.1 Overview of the Method
5.4.2 Generating Stock Price Paths
5.4.3 Monte Carlo Put OptionExample
5.4.4 Variance Reduction
5.4.5 Drift and Dividends
6 Numerical Option Pricing: Lattice/Binomial
6.1 Do I Need to Know This?
6.2 Lattice Pricing I: One-Step Model
6.3 Lattice Pricing II: J-Step Model
6.3.1 Choosing u and d—and Deducing π*
6.3.2 Binomial Valuation Example
6.4 Lattice Pricing III: American Options
7 Partial Differential Equations
7.1 Do I Need to Know This?
7.2 PDEs 101
7.3 Where Do Financial PDEs ComeFrom?
7.4 Transforming the PDE
7.5 PDE Solution by Finite Differences
7.6 PDE Interpretation: Greeks 101
8 Analytical Option Pricing: Black-Scholes
8.1 Black-Scholes A ssumptions
8.1.1 A Note on Concavity and Geometric Averages
8.2 Black-Scholes Derivation
8.3 Black-Scholes Interpretations andIntuition
8.3.1 Interpretation I: Recipe for Replication
8.3.2 Interpretation II: DCF1 Cost/Denefit
8.3.3 Interpretation III: Dinomial Limit
8.3.4 Interpretation IV: Stock-Numeraire
8.3.5 Interpretation V: Digital (Binary) Options
8.3.6 Interpretation VI: Conditional Payoffs
8.3.7 Interpretation VII: PDE Solution
8.3.8 Interpretation VIII: See Figure3.3
8.4 Approximations to Black-Scholes
8.4.1 Louis Jean-Daptiste Alphonse Dachelier(1900)
8.5 Immediate Extensions
8.5.1 Index: Merton (1973)
8.5.2 Futures: Black (1976b)
8.5.3 FX: Garman and Kohlhagen (1983) andGrabbe (1983)
8.6 Application: The Adequation Formulafor FX Option Parity
8.7 Black-Scholes Implementation
8.7.1 Method I: Estimate Historical σ
8.7.2 Method II: Infer Market Forecast σ
8.8 Synthetic Options: Greeks 102
8.8.1 Delta Hedging
8.8.2 Delta-Gamma (and Theta) Hedging
9 Beyond Black-Scholes
9.1 American-Style Options
9.1.1 Approximate Analytical Pricing
9.1.2 Exact Analytical Pricing
9.2 Some New Formulae
9.2.1 Arithmetic Brownian Motion
9.2.2 Power Option I: Crack (1997,2021)
9.2.3 Power Option II: Crack (1997, 2021)
9.2.4 Forward on an At-the-Money Option: Crack-Maines (Crack, 1997)
9.3 Summary of Option Pricing Methods I: Plain Vanilla versus Exotic Options
9.4 Other Data-Generating Processes
9.4.1 Jump Risk, Replication, and Risk-Neutral Pricing
9.4.2 Stochastic Volatility
9.5 Summary of Option Pricing Methods II: Discrete versus Continuous Models
10.1 Institutional Details
10.1.1 Options Specifications
10.1.2 Exchanges, Regulatory Bodies, and Securities
10.1.3 Brokers
10.1.4 T-Costs
10.1.5 Margin Leverage in Stock Trading
10.2 Black-Scholes Assumptions and Violations
10.3.1 Stylized Facts
10.3.2 Information Sources
10.3.3 Other Trading Tips and Tools
10.3.4 Orders and Executions
10.3.5 Market Views and Opinions
10.3.6 The Deathly Slow Crawl