How options work
Drag the sliders. Every number here is worked out live in your browser with the Black-Scholes model: no market data, no picks, no advice. Just the mechanics, so the next options chain you open makes sense.
A right, not an obligation (for the buyer)
A call is the right to buy shares at a fixed price (the strike). A standard contract usually covers 100 shares. American-style options can be exercised through expiry; European-style options only at expiry. A put is the right to sell. The buyer pays a premium for that right; the seller collects it and takes on the obligation.
You pay $166.20 for the right to buy 100 shares at $105 at expiry in 30 days in this European-style model. You make money if the stock finishes above $106.66. The most you can lose is what you paid.
- Premium / share
- $1.66
- Per contract
- $166.20
- Breakeven
- $106.66
- Max profit
- Unlimited
- Max loss
- −$166.20
Stock at $100 · 30 days to expiry · implied volatility 30%. The chart shows profit or loss per contract (100 shares) on expiry day.
How time decay changes near expiry
With other inputs unchanged, long options often lose time value as expiry approaches. Decay tends to accelerate near expiry for at-the-money options, but the pattern depends on the contract. These charts show calls. Drag toward expiry.
- Price now / contract
- $444.06
- Theta / day
- −$5.19
- Next 7 days
- −$38
- Time value left
- $444
A call on a $100 stock, implied volatility 30%, nothing else changing. The x-axis counts calendar days down to expiry.
Volatility is the price of uncertainty
Implied volatility (IV) is how much movement the market is pricing in. Higher IV widens the range of likely outcomes, so an out-of-the-money option has a better shot and costs more. IV can rise before earnings and fall after the announcement; neither change is guaranteed.
- $110 call / contract
- $65.52
- Chance above $110
- 13%
- Typical 30-day move
- ±$8.60
- Range (≈68%)
- $91–$109
The curve is a risk-neutral model distribution for a hypothetical $100 stock in 30 days, using the IV you choose. The shaded area is the model probability of finishing above $110. No market data is used; this is not a forecast.
Five dials that describe an option
The Greeks measure how an option's price reacts to one thing changing while everything else stays still. Pick one and compare a short-dated, a one-month and a three-month option on the same $100 strike.
Delta
How much the option price moves when the stock moves $1. A 0.50-delta call gains about $0.50 a share, or $50 a contract, on a $1 rise. It is sometimes used as a rough model-based proxy for finishing in the money, not as real-world odds or the probability of a profit.
On the chart: Near expiry the 7-day line snaps toward 0 or 1: there is little time left for the stock to cross the strike.
Strike $100 · implied volatility 30% · the x-axis is the stock price. Values per share.
Put it together: the options calculator
Build a covered call, a spread, a straddle or an iron condor. See max profit and loss, breakevens, the whole position's Greeks, and where the P&L comes from when price, time and volatility change.
What the charts don't shout
Buyers can lose 100%, fast
An option that is out of the money at expiry has no intrinsic value. The premium is the whole bet, and time decay can reduce its value even when the stock barely moves.
Selling a naked call has no ceiling
If the stock keeps rising, so does the loss. Brokers restrict it for a reason.
You can be assigned early
US stock options can be exercised any day. A short option, especially one in the money before a dividend, can turn into shares overnight.
Real prices have a spread
This page uses theoretical prices, not executable quotes. You buy nearer the ask and sell nearer the bid; on thinly traded contracts the gap costs a lot.
The model is a model
Black-Scholes assumes smooth moves and one constant volatility. Real stocks gap on news, and implied volatility differs by strike (the skew).
Common questions
What is the difference between a call and a put?
A standard stock-option contract usually covers 100 shares. A call gives the right to buy at the strike; a put gives the right to sell. American-style options allow exercise before expiry; European-style options only at expiry. Buyers pay a premium for that right, and sellers collect it and take on the obligation.
Why do options lose value over time?
Part of the premium is time value: the chance the option becomes more valuable before expiry. Time decay often accelerates near expiry for at-the-money options, with other inputs unchanged. The pattern depends on the contract; some European puts can have positive theta.
What is implied volatility?
How much movement the market is pricing into an option. Higher implied volatility means a wider range of likely prices and a more expensive option. It often rises before earnings and drops right after, which is called an IV crush.
What does delta mean in options?
Delta is how much the option price moves when the stock moves $1. A 0.50-delta call gains about $0.50 a share on a $1 rise. Delta is sometimes used as a rough model-based proxy for finishing in the money; it is not a forecast or the probability of earning a profit.
Can you lose more than you invest with options?
Buying a call or put, the most you can lose is the premium you paid. Selling options is different: a naked short call has no limit on its loss, and a short put can lose up to the strike price times 100 if the stock goes to zero.
Prices on this page are theoretical: Black-Scholes, European exercise, no dividends, a 4% risk-free rate, calendar days. Educational only, not investment advice or a recommendation to trade. Before trading options, read the OCC's Characteristics and Risks of Standardized Options. AlgoThesis is a publisher, not an adviser; see the disclaimer.