Implied Volatility Calculator
Work backwards from a traded option price to the volatility the market is implying at that strike.
Result
- Option type
- Call
- Premium entered
- ₹470.00
- Intrinsic value ₹0.00
- Time value in the premium
- ₹470.00
- Price at this IV (check)
- ₹470.00
- Should match the premium you entered — this is the solver reporting its own work
- Vega at this IV
- ₹28.26
- What a 1 percentage point change in IV is worth
Black-Scholes prices a European option under constant volatility in a frictionless market. None of those assumptions holds exactly — a real option chain shows a different implied volatility at every strike. Indian INDEX options are European and fit the model; Indian SINGLE-STOCK options are American and can be exercised early, so treat these as a reference value rather than a quote. This is arithmetic on the numbers you entered, not a price, a forecast or advice to trade.
Estimated from the numbers you entered — not a projection of guaranteed returns.
About this calculator
Implied volatility is not observed, it is inferred. There is no volatility input on an exchange screen — there is a price, and IV is the volatility you would have to feed Black-Scholes to get that price back out. This calculator does that inversion, which is why an option is often described as being quoted in volatility rather than in rupees.
Formula
- Find σ such that BlackScholes(S, K, T, σ, r, q) = market premium
- Solved by bisection between 0.01% and 500% volatility
- No closed form exists — the equation cannot be rearranged for σ
Frequently asked questions
Why can implied volatility not be calculated directly?
Because the Black-Scholes equation cannot be rearranged to isolate σ — it appears inside a cumulative normal distribution twice. Every IV number anywhere, including on your broker terminal, is produced by a numerical solver like this one.
Why does the calculator sometimes return nothing?
Because no volatility reproduces the price you entered. The commonest cause is a premium below intrinsic value, which the model cannot produce at any volatility. Check the spot, the strike, and that you have set the call/put flag correctly.
Why does IV differ at every strike?
That is the volatility smile or skew, and it is the market disagreeing with one of the model's assumptions. Black-Scholes assumes a single constant volatility for the underlying; real option prices imply higher volatility for far strikes, particularly downside puts.
Is high IV good for a buyer?
It makes the option expensive, which is bad at the point of purchase and good if IV rises further afterwards. High IV before an event and a collapse after it — IV crush — is a common way for a directionally correct option buyer to still lose money.