The Greeks: Delta, Gamma and Theta

Option traders use a set of measurements called "the Greeks" to understand how their position will respond to changes in the underlying price, time, and volatility. Each Greek represents a different risk or sensitivity.

Delta: directional sensitivity

Delta measures how much an option's price will change when the underlying moves by one rupee. A call option with a delta of 0.60 will gain approximately 60 paise if the stock rises by 1 rupee. A put option with a delta of -0.40 will gain 40 paise if the stock falls by 1 rupee. Deeper in-the-money options have deltas closer to 1.0 (for calls) or -1.0 (for puts), because they behave almost like the underlying itself. Out-of-the-money options have deltas close to zero, because they're unlikely to end up profitable.

Gamma: the derivative of delta

Gamma measures how much delta itself will change if the underlying moves. An option with high gamma is sensitive to big moves—as the underlying price changes, the delta of your option changes too, accelerating your gains or losses. This is why options with high gamma can produce large percentage swings on relatively small underlying moves. Options near the money (strikes close to the current price) have the highest gamma; deep in-the-money or out-of-the-money options have low gamma.

Theta: time decay

Theta measures how much an option loses value each day as time passes, all else being equal. A call with a theta of -0.05 loses 5 paise in value every single day, just because one day has passed. This decay accelerates as expiry approaches. For option buyers, theta is an enemy; for option sellers (who receive the premium), theta is a friend—your position becomes more profitable as time passes.

• Delta = sensitivity to price moves in the underlying.
• Gamma = the rate at which delta changes.
• Theta = the daily erosion of time value.
• These Greeks help quantify risk and opportunity in option positions.