Option Delta is the change in the price of
an option for a one point moves in the underlying.
Call options: 0 < Option Delta < 1
Put options: -1 < Option Delta < 0
In-the-money options: Delta Option approaches 1 (call:+1,put:-1)
At-the-money options: Delta is about 0.5 (call:+0.5, put: -0.5)
Out-of-the-money options: Delta Option approaches 0
Call Option Delta can be interpreted as the probability that
the option will finish in the money. An at-the-money option,
which has a delta of approximately 0.5, has roughly a 50/50
chance of ending up in-the-money.
Put Option Delta can be interpreted as -1 times the probability
that the option will finish in the money.
Hedge ratio
Since Delta Option is a measure of how sensitive an option’s
price is to changes in the underlying, it is useful as a hedge
ratio. A futures option with a delta of 0.5 means that the
option price increases 0.5 for every 1 point increase in the
futures price. For small changes in the futures price therefore,
the option behaves like one-half of a futures contract.
Constructing a delta hedge for a long position in 10 calls, each with a delta of 0.5 would require you to sell 5 futures contracts. (The delta of a futures contract is always 1).
Delta Option and Time to expiration
As time passes, the delta of in-the-money options increases and the delta of out-of-the-money options decreases.
Delta Option and Volatility
As volatility falls, the delta of in-the-money options increases and the delta of out-of-the-money options decreases.
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