Implied volatility calculator
Implied volatility is the volatility that makes the Black-Scholes price of an option equal to what it trades for. Enter the option price, the stock price, the strike, the days to expiration, the interest rate and the dividend yield. The calculator solves for the implied volatility and shows the intrinsic and time value, delta, vega and the daily move that volatility implies.
Runs in your browser: nothing you enter is sent anywhere.
How to use it
- Choose call or put and enter the option price.
- Enter the stock price, the strike and the days to expiration.
- Enter the risk-free rate and, for dividend stocks, the dividend yield.
- Read the implied volatility and the Greeks at that volatility.
How it works
The Black-Scholes-Merton price of a call is S e^(−qT) N(d1) − K e^(−rT) N(d2), with d1 = (ln(S/K) + (r − q + σ²/2)T) ÷ (σ√T) and d2 = d1 − σ√T. T is days ÷ 365. The calculator tries volatilities between 0.01% and 1000% and halves the range until the model price matches the market price.
- Intrinsic value: call max(0, S − K), put max(0, K − S)
- Time value = option price − intrinsic value
- Implied daily move = IV ÷ √365
Worked example
A one-year at-the-money call: stock 100, strike 100, 365 days, rate 5%, no dividend. The textbook Black-Scholes value at 20% volatility is 10.4506. The option trades at 10.45:
- Implied volatility ≈ 20 % (19.998%).
- Intrinsic value 0, time value 10.45.
- Delta 0.6368, vega 0.3752: one more point of volatility adds about 0.38 to the price.
- Implied daily move 1.05 %.
The put with the same inputs at 5.5735 also gives 20%, as put-call parity says it should.
Tips
- Compare IV with the stock’s historical volatility to judge whether options look expensive or cheap.
- IV usually differs by strike and expiry (the volatility smile and term structure); compare like with like.
- Deep in-the-money and very short options have little time value, so a small price error moves the IV a lot.
Frequently asked questions
How is implied volatility calculated?
There is no closed formula. The calculator searches for the volatility σ at which the Black-Scholes-Merton price equals the option price you enter. The price rises steadily with σ, so a bisection search always finds the single answer when one exists.
What does an implied volatility of 20% mean?
The market prices the option as if the stock's yearly returns had a standard deviation of about 20%. Divided by √365, that is about 1.05% per day, the move shown as the implied daily move.
Why does the calculator say no volatility fits?
An option cannot cost less than its no-arbitrage floor (for a call, stock price minus the discounted strike) or more than the stock itself. Prices outside those bounds usually come from a typo, a stale quote or a wide bid-ask spread.
Should I use the bid, the ask or the mid price?
Usually the mid price between bid and ask. Using the bid gives a lower IV and the ask a higher one, which is a quick way to see how wide the spread is in volatility terms.
Does it work for American options?
The model is for European options. For calls on stocks without dividends the two are worth the same, so the result is fine; for puts and dividend stocks it is a close approximation.