What an option is
An option is a contract. It gives you the right, but never the obligation, to buy or sell 100 shares of a stock at a fixed price before a set date. You pay for that right up front; the payment is called the premium. Because you are not obligated to follow through, the most a buyer can lose is the premium paid.
Calls vs. puts
There are only two kinds. A call gives you the right to buy at the strike, so it gains value when the stock rises. A put gives you the right to sell at the strike, so it gains value when the stock falls. Buying a call is a bet the stock goes up; buying a put is a bet it goes down, or insurance on shares you already own.
Strike and moneyness
The strike is the fixed price in the contract. Where the stock sits relative to the strike is its moneyness: a call is in-the-money when the stock is above the strike, at-the-money when they are roughly equal, and out-of-the-money when the stock is below it. Out-of-the-money options are cheaper because they are, for now, worthless at expiry.
What the premium is made of
The premium has two parts. Intrinsic value is what the option would be worth if it expired right now, the in-the-money amount. Extrinsic (time) value is everything on top, the market's price for the chance that it moves further in your favor before expiry. An out-of-the-money option is all time value, which is why it can decay to nothing.
Time and expiration
Every option has an expiration date, and time is not neutral. A little more time means a little more chance of a favorable move, so longer-dated options cost more. Each day that passes bleeds a bit of that time value away, an effect called time decay. It is slow when expiry is far off and brutal in the final weeks, which is the single most important thing a new buyer misunderstands.
The Greeks, in one line each
- Delta (Δ) — how much the option moves per $1 move in the stock. A 0.50 delta call gains about 50¢ if the stock rises $1.
- Gamma (Γ) — how fast delta itself changes. It is highest at-the-money and near expiry, which is why those options feel twitchy.
- Theta (Θ) — the value lost per day to time decay. It works against buyers and for sellers.
- Vega — sensitivity to implied volatility. When the market gets more fearful, vega lifts every option's price.
- Rho (ρ) — sensitivity to interest rates. It matters most for long-dated options and is usually the smallest of the five.
See it move
Drag the sliders. The premium, the Greeks, and the payoff are computed live from your inputs. Watch theta grow as you cut days to expiry, and gamma peak when the strike sits right at the stock price.
Illustrative only. Prices and Greeks are computed with the Black-Scholes model from the inputs above — not live market data, and real options also carry bid-ask spreads, early-exercise, and dividends this simple model ignores. Educational, not investment advice.
A worked example
Take a 30-day at-the-money call: stock at $100, strike $100, implied volatility 30%. The Black-Scholes model prices it like this:
| Premium | $3.60 / share ($360 per contract) |
| Break-even at expiry | $103.60 |
| Delta | 0.534 — moves about 53¢ per $1 stock move |
| Theta | $-0.06 / day — the daily time-decay cost |
| Vega | 0.114 — gain per 1-point rise in implied volatility |
Illustrative, computed with Black-Scholes from the inputs above — not a live quote.
Keep going
Ready to test yourself? Run the options flashcards, look up any term in the glossary, or map out a trade's payoff with the options profit calculator.
Common questions
What is a stock option?
An option is a contract giving you the right, but not the obligation, to buy (a call) or sell (a put) 100 shares of a stock at a fixed price, the strike, before it expires. You pay a premium for that right.
What is the difference between a call and a put?
A call profits when the stock rises above the strike; a put profits when the stock falls below the strike. Buying a call is a bet up, buying a put is a bet down or a hedge.
What are the option Greeks?
The Greeks measure how an option’s price reacts to change: delta to the stock price, gamma to delta itself, theta to the passage of time, vega to implied volatility, and rho to interest rates.
What is time decay?
Time decay, measured by theta, is the value an option loses each day simply because it is closer to expiration. It accelerates as expiry approaches, which is why short-dated options lose value fastest.