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Delta: Sensitivity to Price

intermediate7 min read

How much the option moves when the stock moves — and its hidden second life as a probability.

DeltaHow much an option moves per ₹1 move in the underlying. is the most important Greek: it tells you *how much an optionThe right, not the obligation, to buy or sell at a set price.’s price moves when the underlying moves ₹1*. A deltaHow much an option moves per ₹1 move in the underlying. of 0.5 means the optionThe right, not the obligation, to buy or sell at a set price. gains ~₹0.50 for every ₹1 rise in the stock. CallsThe right to buy the underlying at a set price — a bullish bet. have positive delta (0 to +1); putsThe right to sell the underlying at a set price — a bearish bet. have negative delta (0 to −1).

DeltaHow much an option moves per ₹1 move in the underlying. secretly wears two hats at once, and seeing both is the “aha.” First, it’s your price sensitivity — your effective exposure to the underlying (a 0.5-deltaHow much an option moves per ₹1 move in the underlying. optionThe right, not the obligation, to buy or sell at a set price. behaves like holding half a shareA unit of ownership in a company.). Second — and this stuns most beginners — delta is roughly the **probability the optionThe right, not the obligation, to buy or sell at a set price. finishes in-the-money**. A 0.30-delta OTMWhere an option’s strike sits relative to the current price. callThe right to buy the underlying at a set price — a bullish bet. is the market saying “about a 30% chance this pays off.” These two readings are deeply connected: an option likely to finish ITMWhere an option’s strike sits relative to the current price. (high probability) also tracks the stock closely (high sensitivity). So one number tells you both how much you’ll make per move and how likely you are to win. That’s why traders live by delta.
ExampleA ₹1,000 callThe right, not the obligation, to buy or sell at a set price. with deltaHow much an option moves per ₹1 move in the underlying. 0.5: the stock rises ₹10, the optionThe right, not the obligation, to buy or sell at a set price. gains ~₹5. That same 0.5 deltaHow much an option moves per ₹1 move in the underlying. also says ~50% odds of finishing ITMWhere an option’s strike sits relative to the current price. (it’s ATMWhere an option’s strike sits relative to the current price.). Buy a far-OTMAn option with no intrinsic value yet. callThe right to buy the underlying at a set price — a bullish bet. with delta 0.10 and it barely moves ₹1 for a ₹10 stock jump — and the market is pricing only ~10% odds it ever pays off.
Key takeawayDeltaHow much an option moves per ₹1 move in the underlying. = how much the optionThe right, not the obligation, to buy or sell at a set price. moves per ₹1 move in the underlying (callsThe right to buy the underlying at a set price — a bullish bet. +, putsThe right to sell the underlying at a set price — a bearish bet. −), and it doubles as the rough *probability of finishing ITMWhere an option’s strike sits relative to the current price.*. One number gives you both your directional exposure and your odds of winning — deep-ITMWhere an option’s strike sits relative to the current price. ≈ 1, ATM ≈ 0.5, far-OTMAn option with no intrinsic value yet. ≈ 0.
FAQs
Why does an ATM option have a delta around 0.5?

Because at the money it’s a near coin-flip whether it finishes ITM or OTM (~50% probability), and it captures about half of each ₹1 stock move. As the option goes deeper ITM, delta rises toward 1 (it tracks the stock fully and is very likely to pay off); as it goes OTM, delta falls toward 0.

Related glossary terms
DeltaOption GreeksGammaMoneyness (ITM/ATM/OTM)