What is an option worth?
The option calculator prices calls and puts with several models, shows all the Greeks (how strongly the price reacts to the underlying, time, volatility and interest rates) and works through strategies made of several options up to expiry.
Free during the beta, no ads and no subscription. Once you sign in, this page opens the tool.
How it works
An option is the right to buy (call) or sell (put) an underlying such as a stock at a fixed price (the strike). Its value depends on the price, the strike, the time to expiry, the interest rate and above all on volatility, that is, how much the price is likely to swing until expiry.
Portfolio Lab uses the formulas of Black, Scholes and Merton and binomial trees that move the price up or down in many small steps. Trees also price American options, which can be exercised at any time. On top come barriers, digitals, Asian and lookback options and a volatility smile.
The Greeks show the risk: delta is the change in value when the price rises by 1, theta the loss in value per day, vega the change per point of volatility. For strategies such as spreads or the iron condor, the chart shows profit and loss across prices, today and at expiry.
What a result looks like
Sample dataMade-up sample data, no real prices and no recommendation. Calculated with the same methods as the tool itself.
Inputs in this example
Locked: you can't change the inputs in the preview.
Run your own numbers with a free account Your own inputs, real data and every setting.
Create accountPrice
Volatility 20.00% · forward 101.5071
| Model | Price | Deviation |
|---|---|---|
| Black-Scholes-Merton · main price | 6.3613 | – |
| Cox-Ross-Rubinstein | 6.3585 | -0.0028 |
| Jarrow-Rudd | 6.3638 | +0.0025 |
| Leisen-Reimer | 6.3613 | 0.0000 |
With 500 steps the three binomial trees land within fractions of a cent of the closed-form price: Leisen-Reimer hits it almost exactly, Cox-Ross-Rubinstein and Jarrow-Rudd oscillate around it.
Greeks
First order in closed form (Black-Scholes), second order via central differences.
| Metric | Value |
|---|---|
| Delta Change in value per unit of price | 0.5701 |
| Gamma Change in delta per unit of price | 0.02781 |
| Vega per volatility point | 0.2774 |
| Theta per calendar day | -0.0194 |
| Rho per percentage point of interest rate | 0.2525 |
| Rho dividend per percentage point of dividend yield or foreign rate | -0.2843 |
| Vanna Change in delta per volatility point | -0.00069 |
| Volga Change in vega per volatility point | 0.00009 |
| Charm Change in delta per day | -0.00019 |
| Speed Change in gamma per unit of price | -0.000623 |
| Lambda Leverage: change in value in % per 1% price change | 8.96 |
Profile across the price
Option value across prices of the underlying: today, halfway to expiry and one week before expiry; dashed, the payoff at expiry.
Strategy: Iron condor
Four legs with 91 days to expiry: put 85 bought, put 92 and call 108 sold, call 115 bought. Profitable as long as the price stays between the short strikes.
| Leg | Price | Delta | Vega | Theta |
|---|---|---|---|---|
| +1 Put 85 | 0.1666 | -0.0399 | 0.0429 | -0.0044 |
| −1 Put 92 | 0.9405 | 0.1686 | -0.1257 | 0.0123 |
| −1 Call 108 | 1.4868 | -0.2592 | -0.1617 | 0.0198 |
| +1 Call 115 | 0.4604 | 0.1012 | 0.0884 | -0.0105 |
| Total | -1.8002 | -0.0293 | -0.1561 | 0.0172 |
Truncated to the price range shown: “unlimited” means profit or loss keeps growing beyond the edge.
Assumptions: Fixed sample values without market data: volatility 20% for all strikes (no smile), continuous interest rate 3%, no dividend, prices per share. Short legs have a negative quantity.
Frequently asked questions
What is the difference between a call and a put?
A call gains when the price rises above the strike, a put when it falls below. The buyer pays a premium and cannot lose more than that premium. The seller receives the premium and carries the risk.
What does the Black-Scholes model calculate?
The fair price of a European option from price, strike, maturity, interest rate, dividend and volatility. It assumes the price moves randomly with constant volatility. In practice, volatility differs by strike (the smile).
What are the Greeks?
Measures of how strongly the option price reacts to changes: delta (price), gamma (change in delta), vega (volatility), theta (time) and rho (interest rate). The calculator also shows vanna, volga, charm, speed and lambda, the leverage.
Why do you need binomial trees?
There is no simple formula for American options, which may be exercised before expiry. The tree checks at every node whether exercising pays off. For European options it converges to the Black-Scholes price.
Do I need market data for this?
No. You enter price, strike, maturity, interest rate and volatility yourself. With an account you can also load the smile for US options from real option chains.
Learn more in the knowledge base
Run it with your own portfolios
Create an account, confirm your email and use this tool with real prices and your own ETFs.
- Price
- Free during the beta
- Data
- Prices, interest rates, inflation and factors from public sources
- Privacy
- Servers in the EU, no ads, statistics without cookies
- Devices
- Computer and phone, everything saved in your account