How is implied volatility calculated?

There is no closed-form inverse, so IV is found numerically. This calculator uses bisection: it tries a volatility, computes the Black-Scholes price, and narrows the search range between 0.1% and 500% until the model price matches the market price to within 0.00001.

Why does my calculated IV differ from the broker's?

Brokers may use a different interest rate, account for dividends, use the futures price instead of spot, or quote IV against the last traded price versus mid. Small input differences move IV. Use the same spot, strike, days and rate the broker uses to reconcile.

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Q: What is implied volatility?

Implied volatility (IV) is the annualised volatility that, when plugged into the Black-Scholes formula, makes the model price equal the option's actual market price. It reflects the market's expectation of future movement, not the option's past behaviour.

Back out the IV of an NSE call or put from its market price — Black-Scholes solved by bisection, in INR.

Your option

Type

Option market price (₹ per unit)

₹

Spot price (₹)

₹

Strike price (₹)

₹

Days to expiry

Risk-free rate (% annualised) — verify current rate

Result

Implied volatility (annualised)

—

Enter values and press Calculate

Model price at solved IV—

Intrinsic value—

Time value—

Bisection iterations—

How it's calculated

Implied volatility has no closed-form formula — you cannot rearrange Black-Scholes to give σ directly. Instead it is found numerically by bisection:

The Black-Scholes price of a European option is computed for a trial volatility: d₁ = [ln(S/K) + (r + σ²/2)·t] / (σ·√t), d₂ = d₁ − σ·√t, where t = days/365 and r is the risk-free rate. A call is worth S·N(d₁) − K·e^−rt·N(d₂); a put is K·e^−rt·N(−d₂) − S·N(−d₁).
Bracket the answer: we know the true IV lies between 0.1% and 500%. Because the Black-Scholes price rises monotonically with volatility, bisection is guaranteed to converge.
Halve the interval ~100 times: compute the model price at the midpoint volatility; if it is above the market price, search the lower half, otherwise the upper half. We stop when the price gap is under 0.00001. The surviving volatility is the implied volatility, shown as a percentage.

The risk-free rate is a user input (defaulting to an editable 6.5% — verify the current Indian rate). This model uses spot and assumes no dividends; brokers sometimes use the futures price, which shifts IV slightly. Read the IV explainer for how to interpret the result.

FAQ

What is implied volatility?

IV is the volatility that makes the Black-Scholes model price equal the option's market price. It is the market's forward-looking estimate of how much the underlying will move.

How is it calculated here?

By bisection on the Black-Scholes price between 0.1% and 500% volatility, iterating until the model price matches the market price to within 0.00001.

Why might it differ from my broker?

Different rate, dividends, futures-vs-spot, or last-price-vs-mid all move IV. Match the broker's inputs to reconcile. Compare against live IV on the option chain.

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