Options course · Lesson 4 of 10
The Greeks tell you how an option price will move.
Each Greek measures how the price of an option changes when one input changes. Together they show how a position reacts to each change.
Five measures of change
The Greeks measure how an option price changes when one input changes and the others stay the same. Each has the name of a Greek letter, except vega. They come from the model, so they are estimates for small changes.
| Greek | What it measures | 100 call | 100 put |
|---|---|---|---|
| Delta | Price change for a $1 rise in the stock | 0.56 | -0.44 |
| Gamma | Change in delta for a $1 rise in the stock | 0.032 | 0.032 |
| Theta | Price change in one day, per contract | -$3.27 | -$2.19 |
| Vega | Price change for 1 point of volatility, per contract | $19.61 | $19.61 |
| Rho | Price change for 1 point of interest rate, per contract | $12.38 | -$12.04 |
Delta
A delta of 0.56 means that the call gains about $0.56 a share if the stock rises $1. For one contract, that is about $56. So for small moves, the contract acts like 56 shares of the stock.
A put has a negative delta, because it gains when the stock falls. A call deep in the money has a delta near 1. A call far out of the money has a delta near 0.
| Strike | Call delta | Put delta |
|---|---|---|
| $90 | 0.84 | -0.16 |
| $95 | 0.71 | -0.29 |
| $100 | 0.56 | -0.44 |
| $105 | 0.40 | -0.60 |
| $110 | 0.27 | -0.73 |
At each strike, the call delta minus the put delta is 1. One share of stock has a delta of 1.
Gamma
Delta does not stay fixed. Gamma tells you how fast it changes. If the stock rises $1, the delta of the 100 call rises by about 0.03.
This is why a $1 rise adds $0.57 to the call, not $0.56. The delta increases during the move. Gamma is largest for options at the money and near expiration. With 7 days left, the gamma of the 100 call is 0.115, against 0.032 with 90 days left.
Theta
Theta is the value that an option loses in one day, if nothing else changes. The 100 call loses about $0.03 a share each day, or $3.27 a contract. The buyer pays this cost, and the seller collects it. Lesson 5 shows how theta grows near expiration.
Vega
Vega is the price change for a 1-point change in implied volatility. If volatility rises from 25% to 26%, the 100 call gains about $0.20 a share, or $19.61 a contract. A call and a put at the same strike have the same vega. Both gain when volatility rises.
Rho
Rho is the price change for a 1-point change in the interest rate. For a 90-day option, it is small. Rho matters more for options with a year or more to expiration.
Greeks for a position
To find the Greeks of a position, add the Greeks of each part. A short option has the opposite sign of a long one. A share of stock has a delta of 1 and no other Greeks.
A covered call is 100 shares plus one short 110 call. Its delta is 1 minus 0.27, which is 0.73 a share. So for small moves, it acts like about 73 shares.
Key points
- Delta is the price change for a $1 move. It also tells you how many shares the option acts like.
- Gamma tells you how fast delta changes. It is largest at the money and near expiration.
- Theta is the daily cost of time for a buyer. Vega shows how much volatility moves the price.
Sources
- Fischer Black and Myron Scholes, The Pricing of Options and Corporate Liabilities, Journal of Political Economy, 1973, for the model that gives every price in this course.