The ratio comparing the change in the price of the underlying asset to the corresponding change in the price of a derivative. Sometimes referred to as the "hedge ratio".
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For example, with respect to call options, a delta of 0.7 means that for every $1 the underlying stock increases, the call option will increase by $0.70.
Put option deltas, on the other hand, will be negative, because as the underlying security increases, the value of the option will decrease. So a put option with a delta of -0.7 will decrease by $0.70 for every $1 the underlying increases in price.
As an in-the-money call option nears expiration, it will approach a delta of 1.00, and as an in-the-money put option nears expiration, it will approach a delta of -1.00.
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