# Delta and in/at/out of the money

The delta of a call option curve goes from 0 to 1. Would it be correct to say that: - at the beginning of the curve (when the slope is nearly horizontal), the call option is far out of the money or deep in the money (not sensitive to stock price changes) - at the end of the curve (when the slope is very steep), the call option is at the money (very sensitive to stock price changes) - somewhere along the middle of the curve, the call option is slightly in the money or slighty out of the money. Thanks.

it is at the money where the slope starts moving outwards at 45 degrees. Left extreme - delta = 0, far out the money extreme right -> delta = 1, far in the money. 0…+1 …/ … / ---------/ out…at… in this is for a long option.

cpk, i dont agree. the call option value is most sensitive to price changes when it hovers aroudn the strike price (i.e. at the money). when it is far far in the money, a small change in stock value wont affect the call value much. so the right extreme of the graph (where the call option value changes the most per unit of stock price change) should be at the money no?

it is at the money when stock price = exercise price. level I stuff… delta = change in option price / change in stock price in the 45 degree part => both stock and option price change by the same amount… so delta = 1 at the exercise price - a small price change in stock will cause a big price change in the option… bcos it is exactly AT the money - so delta will be the highest.

the show NY Wrote: ------------------------------------------------------- > cpk, > > i dont agree. the call option value is most > sensitive to price changes when it hovers aroudn > the strike price (i.e. at the money). when it is > far far in the money, a small change in stock > value wont affect the call value much. > > so the right extreme of the graph (where the call > option value changes the most per unit of stock > price change) should be at the money no? The curriculum states gamma is greatest at the strike price. For a call, delta approaches +1 as it gets deeper in the money. For a put, delta approaches -1 when it is deep in the money.

bp-- what I have written is correct isn’t it?

CP in the first post: extreme right -> delta = 1, far in the money. this is correct, delta 1 option value most sensitive to spot price when option deep in the money in second post: at the exercise price - a small price change in stock will cause a big price change in the option… bcos it is exactly AT the money - so delta will be the highest. option atm has delta around 0.5 when option deep otm or itm delta is not very sensitive to spot changes gamma is highest with spot around strike, small change in spot will cause big change in delta

Definition for a call option which is in the money would be strike price below the market price. Let’s say for a call option deep in the money where Stock = \$10 and strike (X) = \$5. Thus the option should be priced close to \$5 to prevent arbitrage. When stock moves up by \$1 to \$11 the option price should move up by \$1 also to bring the total cost of conversion to be ~\$11. Thus delta =1

call delta: 0~1 (deep out to deep in) put delta: -1~0 (deep out to deep in) when at the money, call delta is +0.5 and put delta is -0.5

edit: nevermind