Reading delta across deep in-, at-, and out-of-the-money

Question

Three calls on the same stock have deltas of $0.95$ (deep in the money), $0.50$ (at the money), and $0.05$ (deep out of the money).

Explain the pattern. Which one's hedge needs the most attention as the stock moves, and why?

Accepted Answer

Delta as a function of stock price traces an S-shaped curve that rises from 0 (far out of the money) to 1 (far in the money). The three options sit at three points on that curve: - Deep in the money (\Delta \approx 0.95). The call is almost certain to be exercised, so it behaves like the stock itself, nearly one share per option. Its delta barely changes as the stock wiggles (low gamma). - Deep out of the money (\Delta \approx 0.05). Almost certain to expire worthless, so it barely responds to the stock, like holding almost nothing. Also low gamma. - At the money (\Delta \approx 0.50). Genuin…

Reading delta across deep in-, at-, and out-of-the-money

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