Default one-year ATM call at 10
Call, spot 100, strike 100, 1% rate, 365 days, price 10. Cheaper than the 30% Black-Scholes value of 12.368.
- Implied volatility
- 23.97%
Implied volatility
Back out Black-Scholes implied volatility for a European vanilla call or put from the observed option price.
Enter call or put, spot, strike, the risk-free rate, days to expiry, and the market price. The solver finds the annualized volatility that matches that price. Figures are theoretical and for information only.
Results
- Implied volatility (%)
- —
How implied volatility is solved
Implied volatility is the annualized σ that makes the Black-Scholes vanilla price equal the price you observed. There is no closed form, so the calculator searches.
Find σ such that BS(σ) = V
- V — observed vanilla call or put price
- BS(σ) — the same European vanilla formula used on the option calculator, with days / 365 as time
- Search: start at 30%, double until the model is above V, then bisect until the prices agree to about 0.001
The printed volatility is rounded to two decimals. The price must be strictly above intrinsic value. If raising σ stops changing the model price, the page reports that it is unable to determine a volatility.
Worked examples
These cases invert the same vanilla formula and rounding as the calculator. The middle example is a round-trip with the default Black-Scholes price on the options page.
Round-trip at 12.368
Same market inputs as above, but price 12.368 — the vanilla calculator’s default call. The solver recovers 30%.
- Implied volatility
- 30.00%
90-day ATM call at 5
Call, spot 100, strike 100, 1% rate, 90 days, price 5. A shorter dated option needs less vol than a 10-price one-year call to justify that premium.
- Implied volatility
- 24.66%
Related calculators on this site
Implied vol inverts the vanilla formula. Price the option first, convert a tenor, or drop the vol into a long-call payoff chart.
Implied volatility FAQ
The solver searches for the annualized volatility that makes the Black-Scholes vanilla price match the option price you entered. It doubles an initial 30% guess until the model is rich enough, then bisects until the prices agree to about 0.001. The result is rounded to two decimals.
The price must sit above intrinsic value (spot minus strike for a call, strike minus spot for a put). If the quoted price is at or below intrinsic, or so high that raising volatility no longer increases the model price, the search stops.
Yes. It inverts the same European vanilla Black-Scholes implementation used on the vanilla / binary options calculator, including a 365-day year. Binaries, American exercise, and FX two-rate pricing are not inverted here. For an FX pair, price with the Garman-Kohlhagen calculator instead.
Yes. The number is a percent per year, the same unit the vanilla option calculator expects. Convert it to daily or weekly with the volatility converter if you need another tenor.
At 30% vol the Black-Scholes ATM call with these defaults is 12.368, not 10. A 10 price is cheaper, so implied vol comes out lower: 23.97%. Typing 12.368 recovers 30.00%.
Yes. Choose Put and enter the put price. The solver prices the put side of the same vanilla formula. Intrinsic value for a put is strike minus spot.
Disclaimer: the contents of this website are for informational purposes only and do not constitute any investment recommendation. The visitor acts at his own risk.