What is a good delta for buying calls?

There is no single good number. A higher-delta call, deeper in the money, costs more and moves more like the stock. A lower-delta call is cheaper and needs a bigger move to pay off. Pick the delta that matches how far and how fast you expect the stock to move, and size the position by its share equivalent.

Why did my option's delta change overnight?

Delta shifts when the stock price moves, when time passes and when implied volatility changes. An option that is near the money and close to expiration is the most sensitive, so a small move or one more day gone can push its delta a long way toward 0 or toward 1.

Is a 0.50 delta the same as at the money?

Roughly. A call with a strike near the current stock price usually has a delta close to 0.50, and the matching put close to -0.50. Interest rates, dividends and time to expiration can move it a little either side, so treat 0.50 as a guide to where the money line is.

Option Delta: What It Means for Calls, Puts and Your Position

Treat a 0.40-delta call as 40 shares of stock. Size it that way, set its stop that way and add it to the rest of your book that way, and many of the surprises in owning options go away. The number sits in the delta column of the option chain, one per strike, and it changes every time the stock ticks.

Reading the number

A call’s delta runs from 0 to 1. A put’s runs from 0 to -1. The sign gives the direction. Calls gain when the stock rises, puts when it falls.

Deep in-the-money options have deltas near 1 or -1 and move almost dollar for dollar with the stock. Far out-of-the-money ones sit near zero and barely react to a $1 move. At the money, it’s near 0.50.

Delta moves: gamma

Delta holds only for small moves. A call’s delta climbs toward 1 as the stock rises. It shrinks toward 0 as the stock falls. That rate of change is gamma. A 0.40-delta call might be a 0.50-delta call after a $2 rally, so the second dollar of the move pays more than the first. Time does the same work. As expiration gets close, options near the strike swing between very low and very high deltas on small moves, and options far from the strike drift toward zero or one.

Implied volatility moves delta too. Higher volatility pulls deltas toward the middle, because a far strike becomes more reachable, and lower volatility pushes them out toward the edges. The guide to implied vs historical volatility covers where those volatility figures come from.

Position delta

Add up the deltas of everything you hold on one stock, each multiplied by 100 shares a contract, and you get the position delta: the number of shares the whole position acts like for a small move.

One 0.40-delta call: about 40 shares long.
One -0.30-delta put: about 30 shares short.
100 shares plus one short 0.40-delta call: about 60 shares long.

That last line is a covered call. Selling the call trims the position’s exposure from 100 shares to about 60 for small moves, which is why a covered call gains less than the shares on a rally. Position delta is also the cleanest way to size option trades against an account, because it translates contracts into the share exposure you’d take with stock. The guide on how much money to trade options works through sizing on a small account.

Where it shows on the option chain

Most chains let you add a delta column next to bid, ask and implied volatility, and some show it by default, usually quoted per share as a decimal such as 0.40 or -0.30, though a few platforms multiply it by 100 and print 40 or -30, which means the same thing. The figure comes from a pricing model that uses the stock price, strike, time to expiration, interest rates and implied volatility, so two platforms can show slightly different deltas for the same option.

What people get wrong

Many traders read delta as the probability the option finishes in the money. It’s a rough approximation at best, and the two numbers can drift apart, especially on long-dated options and when volatility is high, so a 0.30-delta call gives you a loose sense that the market sees the strike as less likely than not to be reached, which is useful for comparing strikes and too loose to plan a trade around.

Another mistake is treating delta as fixed. A position that started as 40 shares long can become 80 shares long after a rally without you trading anything. A third is forgetting the sign on puts and adding a -0.30 put to a 0.40 call as if both were long exposure; the pair is about 10 shares long.

Gamma is the rate at which delta changes. Theta is the daily loss of time value. Vega is sensitivity to implied volatility. Together these are the Greeks, all printed on the same chain. Moneyness describes where a strike sits against the stock price. More options topics sit under the options desk.