Delta

Delta measures how much an option's price changes when the underlying moves one point. It is the most important Greek and has three useful interpretations at once.

What the number means

Delta = change in option price / change in underlying

• A call delta ranges from 0 to +1; a put delta from 0 to -1.
• A call with delta 0.60 gains about 0.60 if the stock rises 1.00, and loses about 0.60 if it falls 1.00.

Three readings of delta

1. Rate of change. How fast the premium moves with the underlying (above).
2. Equivalent shares. A 0.60-delta call behaves like holding 60 shares — useful for sizing a position's directional exposure.
3. Rough probability of finishing ITM. A 0.30-delta option is loosely a 30% chance of expiring in the money. Handy intuition, not a precise figure.

A worked example

Own 1 call, delta 0.50, on a stock at 100.
Stock rises to 102 (+2):
  option gains ~ 0.50 x 2 = +1.00 (per share, x100 = +100)

The catch

Delta is not constant — it changes as the underlying moves, as time passes, and as volatility shifts. A delta of 0.50 today can be 0.70 after a rally. The speed at which delta itself changes is the next Greek, gamma — and it is why a position that looks neatly hedged can drift out of balance.