Options 101 · Chapter 3
The greeks, one by one
An option's price moves for several reasons at once: the underlying moves, time passes, volatility shifts. The greeks split that mess into separate numbers, each answering one question — if only this changes, how much does my option price change? Learn them one at a time and an option stops being a black box.
Δ Delta — direction
How much the option price moves per $1 move in the underlying. A call with a delta of 0.60 gains about $0.60 when the underlying rises $1. Calls run from 0 to 1, puts from −1 to 0: deep OTM contracts sit near 0, ATM near 0.50, deep ITM near 1. Traders also read delta as a rough probability of finishing in the money, and as the number of shares an option behaves like — a 0.60 delta call acts like 60 shares.
Γ Gamma — curvature
How much delta itself changes per $1 move. Delta is not fixed; gamma is its speed. If delta is 0.60 with gamma 0.04, a $1 rally leaves you with a 0.64 delta — the position gets longer as it wins and shorter as it loses. Gamma peaks at the money and grows sharply as expiry approaches, which is why short-dated ATM options are so twitchy.
Θ Theta — time decay
How much value the option loses per day, all else equal. Theta is normally negative for buyers and positive for sellers: an option is a wasting asset, and every day that passes with nothing happening is money gone. Decay accelerates near expiry — the red curve above — and hits ATM options hardest, since they carry the most time value to lose.
ν Vega — volatility
How much the option price moves per 1 point of implied volatility. Vega is not about which way the market goes, only about how much it is expected to move. With vega at 0.12, a rise in implied volatility from 50% to 55% adds roughly $0.60 to the option. Vega is always positive for buyers, largest at the money, and grows with time to expiry — long-dated options are mostly a volatility bet.
ρ Rho — interest rates
How much the option price moves per 1 point change in interest rates. Higher rates lift calls and weigh on puts, because holding the option instead of the underlying frees up cash that now earns more. For short-dated contracts rho is the one you can usually ignore — it only starts to matter on long-dated options or when rates move violently.
The trade-off: gamma and theta pull in opposite directions. Buying options gives you positive gamma — you profit from movement — but you pay for it with negative theta every single day. Selling options flips it: you collect decay, and a sharp move can hurt badly. Most option strategies are just a chosen point on that spectrum.
The greeks are not independent, and they are not static — they shift with price, time and volatility. Delta and gamma are the two that dominate day to day, and they are also the pair that forces market makers to hedge. Aggregate that hedging across the whole book and you get gamma exposure, which is where the next chapter goes.