The Greeks measure how an option's price responds to each input.
| Greek | Measures change in option price for | Typical sign for a long call | Typical sign for a long put |
|---|---|---|---|
| Delta | A $1 rise in the share price | 0 to +1 | -1 to 0 |
| Gamma | (Change in delta for a $1 rise in the share) | Positive | Positive |
| Theta | One day passing | Negative | Negative |
| Vega | A one-point rise in implied volatility | Positive | Positive |
| Rho | A one-point rise in interest rates | Positive | Negative |
An at-the-money option has a delta near 0.50 (minus 0.50 for a put). Deep in-the-money calls approach 1 and behave like shares; far out-of-the-money calls approach 0. Three uses: the expected price change, the share-equivalent exposure (10 contracts with a delta of 0.40 behave like 400 shares), and a rough guide to the probability of finishing in the money.
Delta is not constant. Gamma is highest for at-the-money options close to expiry, where a small share move swings the option between worthless and valuable. Option buyers are long gamma: their delta grows as the trade goes their way and shrinks as it goes against them. Sellers are short gamma and face the reverse.
Time value decays every day, slowly at first and fastest in the final weeks for at-the-money options. Theta is the rent a buyer pays for gamma and the income a seller receives for bearing it.
Longer-dated and at-the-money options have the most vega. Buying options is a long volatility position; selling is short volatility.
Usually the least important Greek for short-dated equity options; it matters for LEAPS.
A call is priced at $4.00 with delta 0.55, gamma 0.04, theta minus 0.03 and vega 0.12.
A trader who is short 10 of these calls has a delta of minus 550 shares and buys 550 shares to be delta-neutral. As the share moves, delta changes (gamma), so the hedge must be rebalanced. Market makers hedge this way and earn the bid-ask spread instead of betting on direction. When many traders buy short-dated calls, dealers who sold them must buy shares as the price rises, which can amplify the move (a gamma squeeze).
Add the Greeks of every leg, multiplied by the number of contracts and by 100. A position can be delta-neutral and still exposed to gamma, theta and vega.
A trader is short an at-the-money straddle with theta of +$0.10 a day and gamma of -0.08. If the stock does not move, she earns $0.10 a share overnight. If it moves $2, the gamma loss is about 0.5 x 0.08 x 2^2 = $0.16, more than the day's theta. The break-even daily move is the square root of (2 x 0.10 / 0.08), about $1.58. Short-option sellers are betting that actual moves will be smaller than this; buyers that they will be larger.
A trader is long 10 calls with a delta of 0.60 and short 300 shares. Position delta = 10 x 100 x 0.60 minus 300 = +300 shares. The position still gains if the stock rises, by about $300 for each $1.
An option with vega of 0.15 is bought the day before earnings when implied volatility is 55%. After the release, implied volatility drops to 40%. The vega loss is about 15 x 0.15 = $2.25 a share, which can outweigh a gain from the share price moving the right way.
Combining long and short options offsets Greeks. A bull call spread has less vega and less theta than the long call alone, because the short call cancels part of each. That is why spreads are less sensitive to volatility crushes, and also why their upside is capped.
Delta also changes with volatility (vanna) and with time (charm). Close to expiry, charm can swing an option's delta sharply overnight. Market makers manage these through the day; individual traders mainly need to know that hedges built on today's delta drift.
An at-the-money option a day from expiry can move from almost worthless to several dollars on a small move. That is the source of both the appeal and the danger of very short-dated options (Module 10).
For one live option, record the price and all five Greeks. Predict its price for a $2 rise in the share, for three days passing and for a three-point fall in IV. Check against the chain over the following days.
Educational content only; not investment, tax or legal advice. Companies, tickers and figures are illustrative examples, not recommendations. Rules, rates and limits change, so check current details with the regulator, exchange or tax authority before relying on them. Worked examples are not forecasts. Written by Elizabeta Dimoska. RiskStock is not a registered dealer or adviser.