Delta measures the sensitivity of an option's price to changes in the price of the underlying asset. It ranges from -1 to 1 for puts and calls, respectively.
Delta Formula
The Delta of a call option is calculated as:
Delta = N(d1)
Where:
- N(d1) is the cumulative distribution function of the standard normal distribution.
- d1 = [ln(S/K) + (r + σ²/2)T] / (σ√T)
For a put option, Delta is N(d1) - 1.
Example:
If the Delta of an option is 0.23, it means that for every $1 increase in the price of the underlying asset, the option's price will increase by $0.23. Conversely, if the underlying asset decreases by $1, the option's price will decrease by $0.23.
Behavior of Delta:
- Call Options: Delta tends to increase as the underlying asset price rises and approaches expiration. For deep in-the-money calls, Delta approaches 1. For deep out-of-the-money calls, Delta approaches 0.
- Put Options: Delta tends to decrease (become more negative) as the underlying asset price falls and approaches expiration. For deep in-the-money puts, Delta approaches -1. For deep out-of-the-money puts, Delta approaches 0.