Delta indicates the change in option price as the underlying asset price changes. For example, if a stock option has a delta value of 0.65, meaning that if the underlying stock increases in price by $1 per share, the option on it will rise by $0.65 per share, all else being equal.

Mathematically, Delta is the first derivative of the value of the option with respect to the underlying asset's price, it is often explained as the rate of change the option price movement has in relation to the underlying asset’s price change. Delta value moves as the underlying asset price moves. Delta is often used in hedging strategies and is also referred to as a hedge ratio.

Delta values can be positive or negative depending on the type of option. For example, the delta for a call option always ranges from 0 to 1 because as the underlying asset increases in price, call options increase in price. Put option deltas always range from -1 to 0 because as the underlying security increases, the value of put options decreases.

Call option delta behavior depends on whether the option is "in-the-money" (currently profitable), "at-the-money" (its strike price currently equals the underlying stock's price) or "out-of-the-money" (not currently profitable). In-the-money call options get closer to 1 as their expiration approaches. At-the-money call options typically have a delta of 0.5, and the delta of out-of-the-money call options approaches 0 as expiration nears. The deeper in-the-money the call option, the closer the delta will be to 1, and the more the option will behave like the underlying asset.

Similarly, put option delta behaviors also depend on whether the option is "in-the-money," "at-the-money" or "out-of-the-money" and are the opposite of call options. In-the-money put options get closer to -1 as expiration approaches. At-the-money put options typically have a delta of -0.5, and the delta of out-of-the-money put options approaches 0 as expiration approaches. The deeper in-the-money the put option, the closer the delta will be to -1.

To put it simple,

- In effect, at delta values of -1.00 and 1.00, the option behaves like the underlying asset in terms of price changes.
- Delta is used when determining the likelihood of an option being in-the-money at expiration.