This new book gives extremely clear explanations of Black-Scholes option pricing theory, and discusses direct applications of the theory to option trading. The presentation does not go far beyond basic Black-Scholes for three reasons:
- First, a novice need not go far beyond Black-Scholes to make money in the options markets
- Second, all high-level option pricing theory is simply an extension of Black-Scholes
- Third, there already exist many books that look far beyond Black-Scholes without first laying the firm foundation given here
The trading advice does not go far beyond elementary call and put positions because more complex trades are simply
combinations of these. The appendix includes Black-Scholes option pricing code for the HP17B, HP19B, and HP12C. An accompanying spreadsheet can be downloaded that allows the user to forecast transactions costs for option positions using simple models.
1. Introduction to Options
1.1 Hedging, Speculation, and Arbitrage
1.2 Forwards, Futures, and Options
1.3 Introductory Option Examples
1.3.1 Buying a Protective Put
1.3.2 Introduction to Transaction Costs (T-Costs)
1.3.3 Buying a Speculative Call
2. Maths, Stats, 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 Cumulative Standard 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 Coeffcients
2.5.4 Ex-Dividend Process
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
4.1 The Simple Answer: Traditional Methods Fail
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])
4.5 The Complex Answer: Non-Traditional Methods
5. Numerical Option Pricing: Monte Carlo
5.1 Do I Need to Know This?
5.2 Monte Carlo 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 Option Example
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 Modell
6.3 Lattice Pricing II: J-Step Model
6.3.1 Choosing u and d|and Deducing 1/€
6.3.2 Binomial Valuation Example
6.4 Lattice Pricing III: American Options
6.5 Adjusting for Dividends
7. Partial Di®erential Equations
7.1 Do I Need to Know This?
7.2 PDEs 101
7.3 Where do Financial PDEs come from?
7.4 Transforming the PDE
7.5 PDE Solution by Finite Differences
7.6 PDE Interpretation: Greeks
8. Analytical Option Pricing: Black-Scholes
8.1 Black-Scholes Assumptions
8.1.1 A Note on Concavity and Geometric Averages
8.2 Black-Scholes Derivation
8.3 Black-Scholes Interpretations and Intuition
8.3.1 Interpretation I: Recipe for Replication
8.3.2 Interpretation II: DCF, Cost/Benefit
8.3.3 Interpretation III: Binomial 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 Figure 3.3
8.4 Approximations to Black-Scholes
8.4.1 Louis Jean Baptiste Alphonse Bachelier (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) and Grabbe (1983)
8.6 Application: The Adequation Formula for FX Option Parity .
8.7 Black-Scholes Implementation
8.7.1 Method I: Estimate Historical 3/4
8.7.2 Method II: Infer Market Forecast 3/4
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 Pricing179
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)
9.2.3 Power Option II: Crack (1997)
9.2.4 Forward on an At-the-money Option:
Crack-Maines (in 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. Trading
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
10.2 Black-Scholes Assumptions and Violations
10.3 The Spreadsheet Tool
10.4 Trading Experiences and Lessons
10.4.1 Stylized Facts
10.4.2 Information Sources
10.4.3 Other Trading Tips and Tools
10.4.4 Orders and Executions
10.4.5 Market Views and Opinions
10.4.6 The Deathly Slow Crawl
10.5 The Greeks
10.6 Spread Positions and Other Strategies
A HP Source Code
A.1 HP17B/HP19B Black-Scholes
A.2 HP12C Black-Scholes
A.3 HP17B/HP19B Binomial Pricing
A.4 An HP17B/HP19B Warning
References for Further Research
Index
About Timothy Falcon Crack
Timothy Crack has a PhD from MIT. He has won many teaching awards and has publications in the top academic, practitioner, and teaching journals in finance. He has degrees in Mathematics/Statistics, Finance, and Financial Economics and a diploma in Accounting/Finance.
Dr. Crack taught at the university level for 17 years including four years as a front line teaching assistant for MBA students at MIT. He now heads a quantitative active equity research team at the world's largest institutional money manager.
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