The Greeks

Delta, gamma, theta, vega

~30 min · 6 lessons

What you'll learn

✓Describe each Greek
✓Interpret an options P&L

Lessons

🎛️
The Dashboard of Risk
Four numbers that explain every option move
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Delta: How Stock Moves Become Option Moves
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Gamma: When Delta Itself Starts Sprinting
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Theta and Vega: Time and Fear
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Greeks in the Wild
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Final Boss: Decomposing One Day's P&L
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Sources

All content is drawn from the sources below. We deliberately avoid unverified material.

Options, Futures, and Other Derivatives (John C. Hull)
Pearson · book
Primary textbook reference for definitions and properties of delta, gamma, theta, vega and the first-order P&L decomposition. Used throughout the module for the math framing.
Option Volatility and Pricing (Sheldon Natenberg)
McGraw-Hill · book
Reference for the practitioner-level intuition on delta-hedging, gamma's behavior near expiration and at-the-money, theta acceleration, and vega's term-structure properties.
Options as a Strategic Investment (Lawrence G. McMillan)
Prentice Hall Press · book
Reference for trader-side framing of theta as time decay and the gamma/theta tradeoff for long versus short option positions.
The Pricing of Options and Corporate Liabilities (Black & Scholes, 1973)
Journal of Political Economy · academic
Foundational paper. Referenced as the underlying model from which closed-form Greeks are derived.
https://www.jstor.org/stable/1831029
Theory of Rational Option Pricing (Robert C. Merton, 1973)
Bell Journal of Economics and Management Science · academic
Companion foundational paper to Black-Scholes, extending the framework. Referenced for the theoretical backing of the Greek sensitivities.
https://www.jstor.org/stable/3003143
Cboe VIX White Paper
Cboe Global Markets · institutional
Primary source for the definition of the VIX as the 30-day implied volatility index on S&P 500 options, used to anchor the vega and volatility examples (March 2020, February 2018).
https://cdn.cboe.com/api/global/us_indices/governance/Volatility_Index_Methodology_Cboe_Volatility_Index.pdf
CBOE Options Institute educational materials
Cboe Options Institute · institutional
Reference for plain-English exchange-published explanations of the option Greeks and delta-hedging mechanics.
https://www.cboe.com/education/
Staff Report on Equity and Options Market Structure Conditions in Early 2021
US Securities and Exchange Commission · institutional
Primary regulatory source for the GameStop January 2021 episode, including the role of options market-maker hedging in amplifying the move (gamma squeeze mechanics).
https://www.sec.gov/files/staff-report-equity-options-market-structure-conditions-early-2021.pdf
Cboe VIX Index overview and historical data
Cboe Global Markets · data
Source for the historical VIX levels cited in the module, including the February-March 2020 spike from the high teens to the March 16, 2020 closing peak above 80.
https://www.cboe.com/tradable_products/vix/
Review of the Federal Reserve's Supervision and Regulation of Silicon Valley Bank (Barr Report)
Board of Governors of the Federal Reserve System, April 28, 2023 · institutional
Source for the SVB collapse timeline (March 8 to 10, 2023) used in the applied lesson on vega and gamma in a real equity-crash scenario.
https://www.federalreserve.gov/publications/files/svb-review-20230428.pdf