Delta
Delta measures how much an option's price moves when the stock moves one dollar. Learn to read delta, what the number really means, and how traders use it.
Delta tells you how much an option's price moves when the stock moves one dollar. If a call has a delta of 0.50, then for every $1 the stock climbs, the call gains about $0.50.
That is the whole idea. Delta is the speedometer of an option: it tells you how fast your option's price reacts to the stock. Let me make it concrete.
The Towing Analogy
Picture your option tied to the stock by a rope. Delta is how tight that rope is.
A delta of 1.00 is a rigid steel bar. The stock moves $1, your option moves the full $1, right along with it. A delta of 0.50 is a loose bungee cord: the stock moves $1, but your option only gets tugged $0.50. A delta of 0.05 is a long, slack rope. The stock moves $1 and your option barely twitches, gaining a nickel.
The tighter the connection, the more your option behaves like the stock itself.
The Numbers You Will See
Delta runs on a simple scale.
Calls have a delta from 0 to 1.00. A call deep in the money (stock well above the strike) has a delta near 1.00, moving almost like the stock. A call far out of the money has a delta near 0, barely reacting. A call right at the money sits around 0.50.
Puts have a delta from 0 to negative 1.00. The minus sign just means a put gains when the stock falls. A put with delta negative 0.40 gains $0.40 when the stock drops $1.
There is one more handy trick. Multiply delta by 100 and you get a rough chance the option finishes in the money. A delta of 0.30 means the market is pricing in roughly a 30% chance that option ends up worth something at expiration.
Watch Delta in Action
Apple is trading at $200. You own one call with a strike of $200 and a delta of 0.50.
Apple rises $1 to $201. Your call gains about $0.50 a share. Across the 100 shares one contract controls, that is about $50.
Apple rises $4 to $204. Your call gains roughly $2 a share, or about $200. Notice "roughly," because as the stock climbs, delta itself creeps up. That change in delta is a separate Greek called gamma.
Apple falls $1 to $199. Your call loses about $0.50 a share. Delta works in both directions.
- Delta is how much an option moves for a $1 move in the stock.
- Calls run 0 to 1.00; puts run 0 to negative 1.00.
- At-the-money options sit near 0.50; deep-in-the-money near 1.00.
- Delta times 100 is a rough chance of finishing in the money.
Pop Quiz
Three quick questions to see what stuck. Pick an answer and the explanation shows up right away.
A call has a delta of 0.60. The stock rises $1. About how much does the call gain per share?
Delta is the per-dollar move. A delta of 0.60 means about $0.60 of gain for each $1 the stock rises.
Why do puts have a negative delta?
The minus sign just points the other way. A put rises when the stock drops, so its delta is negative.
An at-the-money option usually has a delta near what value?
At the money is a coin flip, so delta sits near 0.50: about half the stock's move, and roughly a 50% chance of finishing in the money.
Bottom Line
Delta is the first Greek worth knowing because it answers the most basic question: if the stock moves, how much does my option move? A high delta means your option tracks the stock closely. A low delta means it barely responds.
Read it as a speed dial and a rough probability at the same time, and you already understand most of what delta is telling you.
Keep going: gamma measures how fast delta itself changes. Theta measures what time does to your option, and vega measures what volatility does.