Practitioner course in derivatives
Option Greeks
The sensitivities that options traders manage: delta, gamma, vega, theta and rho, how they behave across strikes and time, delta and gamma hedging, the link between gamma and theta, and hedging a book in simulation.
An option’s price moves with the underlying, with volatility and with time, and the option Greeks measure each of those sensitivities. For anyone who holds or hedges options, they are the working language of risk. This course explains each one and then puts them to use in hedging simulations.
How does delta hedging work?
Delta is how much the option’s price changes for a small move in the underlying. Holding the opposite amount of the underlying cancels that exposure for small moves. Because delta itself changes as the price moves, the hedge must be adjusted, and the cost of those adjustments depends on gamma and on how much the market actually moves. You will simulate it and measure the result.
What does it mean to be long gamma?
A long gamma position gains when the underlying moves sharply in either direction, and pays for that through time decay. Whether it makes money overall depends on whether realised volatility turns out higher than the implied volatility paid for the option. That trade-off is central to how options desks think about risk.
Who is this course for?
Options traders, risk analysts and quant developers who work with derivatives books. It counts toward the Certificate in Derivatives Pricing.
What you will be able to do
- Compute the main Greeks analytically and numerically.
- Explain how the Greeks change with strike, time and volatility.
- Simulate delta hedging and measure the hedging error.
- Explain the gamma-theta trade-off and profit from realised versus implied volatility.
- Hedge the delta, gamma and vega of a small options book.
Syllabus, module by module
Delta
Sensitivity to the underlying, its shape across strikes, and delta hedging.
Gamma
Convexity, gamma near expiry and the cost of rehedging.
Theta
Time decay and its relation to gamma in the Black-Scholes equation.
Vega and rho
Sensitivity to volatility and interest rates, and term structure effects.
Hedging in practice
Discrete rehedging, transaction costs and hedging error.
Realised versus implied
Why a delta-hedged option earns the difference between realised and implied volatility.
Managing a book
Aggregating Greeks, scenario grids and hedging with several options.
How the certificate is earned
An assessed project: you simulate delta and delta-gamma hedging of an options position under different volatility paths, and submit the code with a report on the results. On a pass you receive the Course certificate in Option Greeks, issued by the Institute with a verification code. Read how certification works.
Before you start
The material of The Black-Scholes Model, and working Python.
This course counts toward
Questions applicants ask
What are the option Greeks?
Measures of how an option’s price changes with its inputs: delta for the underlying price, gamma for changes in delta, vega for volatility, theta for the passage of time and rho for interest rates.
Why do gamma and theta usually have opposite signs?
In the Black-Scholes equation, a delta-hedged option position that gains from large moves through positive gamma must lose value over time through theta, and the reverse. The course derives the relationship and shows it in simulation.