Grizzly Bulls

Implied Volatility Calculator

Solve the annual volatility that makes a European Black-Scholes-Merton option value match the premium you enter.

Option and market assumptions

Enter the option premium per share, not the full contract value. A quoted $2.50 option premium means 2.50 here.
Enter 1 to 3,650 whole calendar days. The model converts this to years using days ÷ 365.
Enter the continuously compounded annual rate used by the pricing model.
Enter a continuous annual dividend-yield assumption. Discrete dividend dates and amounts are not modeled.

Solved implied volatility

19.9985%Annual implied volatility
$10.4500Model value / share at solved volatility
$10.4500Entered market premium / share
$0.0000Model minus entered premium

Inspect theoretical value and Greeks at this solved volatility. The shared model assumptions and solved volatility carry forward; contract size stays a separate Pricing & Greeks input. Compare this solved IV with prior observations. Only the solved IV carries forward; the historical sample stays separate. Estimate target-price probabilities with this solved IV. Stock price, time, solved volatility, rate, and dividend yield carry forward; target prices stay separate. Build a strategy around this option contract and solved IV. Option type, stock price, strike, time, solved volatility, rate, and dividend yield carry forward. The entered market premium and solver results stay here; long/short side, strategy premium, quantity, and contract size stay for you to choose.

Price bounds for these assumptions

Before solving volatility, the calculator checks the entered premium against the European Black-Scholes-Merton bounds implied by the entered stock price, strike, rate, dividend yield, and time to expiration.

BoundValue / share
Lower model bound$4.8771
Entered premium$10.4500
Upper model bound$100.0000

How the solver works

The calculator uses the same Black-Scholes-Merton pricing engine as the Options Pricing & Greeks Calculator. Instead of taking volatility as an input, it repeatedly reprices the option with a bounded bisection search until the modeled value matches the premium you entered.

Call lower bound = max(S e−qT − K e−rT, 0)
Call upper bound = S e−qT
Put lower bound = max(K e−rT − S e−qT, 0)
Put upper bound = K e−rT

S is stock price, K is strike, T is calendar days divided by 365, r is the continuously compounded annual risk-free rate, and q is the continuous annual dividend yield. A premium at the lower bound maps to 0% model volatility. The numerical search is capped at 500% annual volatility and fails closed when the entered premium would require a higher value.

What implied volatility does and does not mean

Implied volatility is the volatility input that makes this pricing model match one entered premium. It is not a direct forecast of the stock's realized volatility, a probability of profit, or a statement that the option is cheap or expensive.

This calculator uses a European-style Black-Scholes-Merton model with constant volatility, rates, and continuous dividend yield. Listed U.S. equity options are generally American-style, so early exercise, discrete dividends, borrow conditions, volatility skew and term structure, bid-ask spreads, and other contract or market effects can make a broker or exchange-displayed implied volatility differ from this result.

The tool does not fetch an option chain, quote, stock price, interest rate, dividend schedule, or contract specification. It does not recommend a strike, expiration, strategy, or trade. Use the Options Profit/Loss Calculatorfor single-leg expiration P&L from an entered premium.

Pricing-model references