The Greeks as a position dashboard

Delta: the first directional read

Delta estimates the option-price change for a small $1 move in the underlying, with other model inputs held steady. A call with 0.55 delta might gain about $0.55 per share after a $1 stock rise. A put delta is usually negative, reflecting its inverse relationship with the underlying price.

For a standard contract, multiply quoted delta by 100 shares and the number of contracts. Ten calls with 0.55 delta carry roughly 550 share-equivalents of directional exposure at that moment.

Gamma: how fast the steering changes

Gamma estimates the change in delta after a $1 move in the underlying. If a call has 0.50 delta and 0.04 gamma, a $1 rise might move delta toward 0.54 under a simple local approximation. Gamma makes directional exposure dynamic.

Gamma is often concentrated near the money and can become large in short-dated options. Long options generally carry positive gamma. Short options generally carry negative gamma, so an adverse move can increase directional exposure as the market travels.

Theta and vega: the clock and the volatility dial

Theta estimates the change in option value associated with one day passing, with other inputs held steady. Long options usually have negative theta. Short options usually have positive theta. The path is curved, and short-dated at-the-money extrinsic value can decay quickly.

Vega estimates the option-price change for a one percentage-point move in implied volatility. A vega of 0.12 suggests roughly $0.12 per share of value change after implied volatility moves from 25% to 26%, under the model's local approximation. Longer-dated options often carry larger vega.

A two-Greek example

Suppose one long call has 0.50 delta, 0.04 gamma, -0.06 theta, and 0.15 vega. With a 100-share multiplier, the position begins near 50 share-equivalents, loses about $6 from one day of modelled time decay, and gains about $15 if implied volatility rises one point.

If the stock rises $2, a first-pass delta estimate suggests a $100 gain. Gamma indicates that delta increases during the move, so the curved-price estimate adds roughly $8. These are model approximations and the live quote can reflect simultaneous changes in volatility, rates, dividends, and supply and demand.

Read Greeks at the position level

A vertical spread has two deltas, gammas, thetas, and vegas. The combined position responds to the net values. A covered call also includes 100 shares of stock, which contribute about +100 delta and no option gamma, theta, or vega.

Use Greeks to describe current exposure, size stress scenarios, and spot concentration around strikes. Refresh the analysis as the market moves. The calculator and historical attribution views make the interactions visible across price and time.

• Check net delta for directional size.
• Check gamma for the speed of delta change.
• Check theta for the daily cost or carry estimate.
• Check vega for exposure to a change in implied volatility.
• Stress several inputs together because markets enjoy multitasking.