Delta: how option price moves with stock

Delta, the sensitivity dial

Delta is the first and most important Greek. It answers one question: when the underlying stock moves $1, how much does this option's price move? If a call has a delta of 0.50, the call price gains about $0.50 when the stock gains $1, and loses about $0.50 when the stock drops $1. If the call has a delta of 0.20, it only gains $0.20 on a $1 move. Same stock, very different options. Delta is the dial that translates stock moves into option moves.

Calls have positive deltas, between 0 and +1. Puts have negative deltas, between 0 and -1. The sign tells you direction: calls win when the stock rises (positive delta), puts win when it falls (negative delta). The magnitude tells you speed: a 0.80-delta call almost tracks the stock one-for-one. A 0.10-delta call barely budges. Same logic for puts on the negative side.

Delta is not static. It changes as the stock moves and as time passes — that's gamma's job, which we'll cover in a later lesson. For now, picture delta as the slope of a curve. The curve shows option price on the vertical axis and stock price on the horizontal. Where the curve is steep, delta is big. Where it's flat, delta is small. Deep in-the-money calls sit on the steep right side of the curve (delta near +1). Deep out-of-the-money calls sit on the flat left side (delta near 0).

One more practical note. Delta depends on three things: how far the option is in or out of the money, how much time is left until expiry, and current implied volatility. As any of those shift, delta shifts. A 0.30-delta call today might be a 0.50-delta call tomorrow if the stock rallies into the strike. A 0.50-delta call with two months to expiry might quietly drift toward 0.40 if it stays OTM as time passes. Delta is alive, not static. We'll spend the next lesson on a powerful shortcut delta gives you — and the lesson after that on the Greek that measures delta's own changes.

Recap: delta = $-change in option per $1 change in stock. Calls 0 to +1, puts 0 to -1. Magnitude = sensitivity, sign = direction.