Delta
Option price sensitivity to stock price
What is Delta?
Delta Delta is the most important options Greek for directional traders. It measures how much an option's price changes for every $1 move in the underlying stock. A call option with a delta of 0.50 will gain approximately $0.50 in value when the underlying rallies $1, and lose $0.50 if it falls $1. Put options have negative delta: a -0.30 delta put loses $0.30 when the stock rises $1 and gains $0.30 when it falls. Delta ranges from 0 to +1.0 for calls and from -1.0 to 0 for puts. Deep in-the-money options have delta near 1.0 (calls) or -1.0 (puts), meaning they behave almost identically to the underlying. At-the-money options have delta near 0.50 / -0.50. Deep out-of-the-money options have delta near 0 because small stock moves barely affect their price. Delta has three useful interpretations beyond raw price sensitivity. First, it approximates the probability the option will finish in-the-money — a 0.30 delta call has roughly a 30% chance of expiring ITM. Traders use this for strike selection: selling 0.16-delta puts targets an ~84% probability of finishing OTM, the standard "low-risk" entry for the wheel strategy or cash-secured puts. Second, delta represents equivalent share exposure for hedging — a 0.50 delta call on one contract is equivalent to 50 shares of stock for delta-hedging purposes. Third, the sum of position deltas across a portfolio gives the portfolio's net directional exposure. Delta is not constant. As the underlying moves, delta itself changes — this rate of change is gamma. Delta is also affected by time decay (theta tends to pull delta toward 0 for OTM options and toward 1 for ITM options as expiration approaches) and by implied volatility shifts. In practice, most professional traders think of strikes in delta terms rather than absolute dollar terms. "Sell the 16-delta put" is a more universal instruction than "sell the $182 put", because the 16-delta strike is roughly consistent across underlyings of different prices.
Complete Definition
Delta is the most important options Greek for directional traders. It measures how much an option's price changes for every $1 move in the underlying stock. A call option with a delta of 0.50 will gain approximately $0.50 in value when the underlying rallies $1, and lose $0.50 if it falls $1. Put options have negative delta: a -0.30 delta put loses $0.30 when the stock rises $1 and gains $0.30 when it falls. Delta ranges from 0 to +1.0 for calls and from -1.0 to 0 for puts. Deep in-the-money options have delta near 1.0 (calls) or -1.0 (puts), meaning they behave almost identically to the underlying. At-the-money options have delta near 0.50 / -0.50. Deep out-of-the-money options have delta near 0 because small stock moves barely affect their price. Delta has three useful interpretations beyond raw price sensitivity. First, it approximates the probability the option will finish in-the-money — a 0.30 delta call has roughly a 30% chance of expiring ITM. Traders use this for strike selection: selling 0.16-delta puts targets an ~84% probability of finishing OTM, the standard "low-risk" entry for the wheel strategy or cash-secured puts. Second, delta represents equivalent share exposure for hedging — a 0.50 delta call on one contract is equivalent to 50 shares of stock for delta-hedging purposes. Third, the sum of position deltas across a portfolio gives the portfolio's net directional exposure. Delta is not constant. As the underlying moves, delta itself changes — this rate of change is gamma. Delta is also affected by time decay (theta tends to pull delta toward 0 for OTM options and toward 1 for ITM options as expiration approaches) and by implied volatility shifts. In practice, most professional traders think of strikes in delta terms rather than absolute dollar terms. "Sell the 16-delta put" is a more universal instruction than "sell the $182 put", because the 16-delta strike is roughly consistent across underlyings of different prices.
Example
A SPY $540 call with 30 DTE typically has ~0.52 delta when SPY is at $540. If SPY rallies to $542, the call gains roughly $1.04. The same call has ~50% probability of finishing in-the-money at expiration.
Formula
Related Terms
Frequently Asked Questions
What does a 0.50 delta mean?
A 0.50 delta call gains $0.50 for every $1 the stock rises. It also has approximately a 50% probability of expiring in-the-money, and is equivalent to 50 shares of stock for delta-hedging purposes.
What's the difference between call delta and put delta?
Call delta is positive (0 to +1). Put delta is negative (-1 to 0). A call gains value when the stock rises; a put gains value when the stock falls. The absolute values are similar for equivalent strikes.
How do I use delta for strike selection?
Selling 0.16-delta puts targets an ~84% win rate. Selling 0.30-delta puts targets ~70% win rate with more premium. Buying 0.50-delta calls gives roughly 50/50 directional exposure with maximum leverage near the strike.
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