Delta & Theta — the Two That Matter First

Delta

Delta = how much the option's price moves per $1 of stock move (0.50 ≈ 50¢ per $1) — AND roughly the probability of expiring ITM. Calls: 0 to 1. Puts: 0 to −1. Delta is your EXPOSURE dial: 5 contracts at 0.40 delta ≈ 200 shares of directional exposure (5 × 100 × 0.40). Portfolio delta is the honest size of an options position.

Theta

Theta = value lost per day from time decay (−$0.05 = the option bleeds 5¢/day, all else equal). Theta accelerates into expiration and is largest for ATM options. Buyers PAY theta daily; sellers COLLECT it. The buyer's real bet: the stock must move MORE than theta eats — direction alone is not enough.

The breakeven implication

Combined: an ATM call with 0.50 delta and −0.08 theta needs the stock to rise ~2¢/day just to stay flat. Over a week that is ~15¢ of required drift. This is why "the stock went up but my call lost money" happens — the move was smaller than the decay. Every options trade should be checked against theta: is my expected move bigger than the daily tax × days held?

Sources

• Options Greeks: Delta & ThetaCBOE education
• Option Volatility & PricingSheldon Natenberg