Finance
Option Calculator
Enter the stock price, strike, expiry, rate, and volatility to price European options and review the Greeks instantly.
Parameters
Option Prices
$2.49
$2.08
Greeks
| Call | Put | |
|---|---|---|
| Delta (Δ) | 0.5400 | -0.4600 |
| Gamma (Γ) | 0.0692 | |
| Theta (Θ) /day | -0.0450 | -0.0313 |
| Vega (ν) /1%σ | 0.1138 | |
| Rho (ρ) /1%r | 0.0423 | -0.0395 |
Intermediate values
d₁
0.1003
d₂
0.0430
N(d₁)
0.5400
N(d₂)
0.5172
Need a change for Option Calculator?
About this calculator
Method, formulas, and limits.What this does
Uses the Black-Scholes model to compute the theoretical fair value of European call and put options. The calculator also breaks down intrinsic value and time value, and returns the full set of option Greeks (delta, gamma, theta, vega, rho) so you can understand how price, time, volatility, and interest rates each affect the option.
Who it is for
Options traders, finance students, and portfolio managers who need a quick Black-Scholes price check. Also useful for anyone learning how option pricing and the Greeks work before trading real contracts.
How it works
The calculator applies the closed-form Black-Scholes formula: C = S·N(d₁) − K·e^(−rT)·N(d₂) for calls, and P = K·e^(−rT)·N(−d₂) − S·N(−d₁) for puts. It derives d₁ and d₂ from the spot price, strike, time to expiry, risk-free rate, and volatility, then evaluates the standard normal CDF. Greeks are computed analytically from the same inputs.
Limitations
The Black-Scholes model assumes European-style exercise (no early exercise), constant volatility, constant interest rates, no dividends, and log-normal price distribution. It does not account for transaction costs, bid-ask spreads, or liquidity. For American options or dividend-paying stocks, the result is an approximation.
Key calculations
- d₁
- d₁ = [ ln(S/K) + (r + σ²/2)·T ] / (σ·√T)
- d₂
- d₂ = d₁ − σ·√T
- Call price
- C = S·N(d₁) − K·e^(−rT)·N(d₂)
- Put price
- P = K·e^(−rT)·N(−d₂) − S·N(−d₁)
- Delta
- Call delta = N(d₁), Put delta = N(d₁) − 1
- Gamma
- γ = n(d₁) / (S·σ·√T), same for calls and puts
- Theta
- Daily decay of option value. Negative for long positions.
- Vega
- Price change per 1% change in implied volatility.
Reference ranges
- Typical Input Ranges
- Most equity options have 10-90 days to expiry, 10-40% implied volatility, and spot prices near the strike. ATM options are the most sensitive to volatility changes.
- Moneyness
- Calls are ITM when S > K and puts when S < K. ATM options (S ≈ K) have the highest time value, gamma, and vega.
- Time Decay
- Theta is most negative in the final 30 days before expiry. Options lose roughly one-third of their time value in the last month.
How to use it
- 1.Enter stock priceType the current market price of the underlying asset.
- 2.Set strike priceEnter the option's exercise price.
- 3.Set time to expiryEnter the number of days (or years) until the option expires.
- 4.Enter rate and volatilityAdd the annual risk-free rate and the implied volatility as percentages.
- 5.Review resultsThe calculator instantly shows call and put prices, intrinsic/time value, and all Greeks.
The Black-Scholes model is a mathematical formula that estimates the fair value of European-style options. It was published in 1973 by Fischer Black and Myron Scholes and is the most widely used option pricing model in finance. The formula takes the stock price, strike price, time to expiry, risk-free rate, and volatility as inputs, and returns a theoretical price for both calls and puts.
A call option gives the holder the right (but not the obligation) to buy the underlying asset at the strike price before expiry. A put option gives the holder the right to sell the underlying asset at the strike price. When the stock price rises, calls gain value and puts lose value; the opposite happens when the stock price falls.
The Greeks measure how an option's price responds to changes in its inputs. Delta measures sensitivity to the stock price. Gamma measures the rate of change of delta. Theta measures daily time decay. Vega measures sensitivity to volatility. Rho measures sensitivity to interest rates. Together they give traders a complete picture of option risk.
Intrinsic value is the amount by which an option is in the money — for a call it is max(S − K, 0), for a put max(K − S, 0). Time value is the difference between the option's total price and its intrinsic value; it represents the premium paid for the possibility that the option will become more valuable before expiry. As expiry approaches, time value decays toward zero.
The Black-Scholes formula is derived for European-style options that can only be exercised at expiry. American options allow early exercise, which requires more complex models such as binomial trees or Monte Carlo simulations. For most liquid index and ETF options, the European assumption produces a close approximation to actual market prices.
For liquid, near-the-money European options, the Black-Scholes price is usually close to the market price. However, real markets exhibit volatility smiles, skew, and jumps that the model cannot capture. The result should be treated as a baseline fair-value estimate; traders compare it with the actual bid-ask to assess whether an option appears rich or cheap.
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