What is implied volatility?

Implied volatility is the volatility input that makes the Black-Scholes price equal the option's observed market price. It reflects the market's expected movement.

We invert Black-Scholes numerically using Newton-Raphson, falling back to bisection on a [0.01%, 500%] bracket. If no volatility fits, it reports non-convergence.

Why might the solver fail to converge?

If the quoted market price is below intrinsic value or above what's achievable at very high volatility, no valid sigma exists and the tool reports non-convergence rather than a wrong number.

Does implied volatility predict direction?

No — it reflects the magnitude of expected movement (in either direction), not which way the price is expected to go.

Why do different strikes on the same underlying show different implied vol?

This is the volatility smile/skew: the market prices tail risk differently across strikes, so IV is not flat across a chain even though Black-Scholes assumes constant volatility.

How many iterations does it usually take?

Newton-Raphson typically converges in under 10 iterations when vega is well-behaved; the bisection fallback is slower but guaranteed to converge if a solution exists in the search range.

Options

Implied Volatility Calculator

Solve implied volatility from an option's market price using Newton-Raphson with a bisection fallback. Enter spot, strike, expiry, rate and price.

Implied volatility is the volatility figure that makes an option pricing model's theoretical value equal the option's actual market price.

Implied volatility

20%

Method: Newton-Raphson
Iterations: 2

Worked example

A 1-year at-the-money call (spot $100, strike $100, 5% rate) is quoted at $10.45.

Initial guess: sigma = 20%
Newton-Raphson iterations: price converges toward $10.45
Solved implied volatility: 20.00%

A $10.45 market price on these inputs implies almost exactly 20% volatility — consistent with the Black-Scholes price for the same inputs.

How this is calculated

Implied volatility is the σthat makes the Black-Scholes price equal the option's market price. We solve it numerically:

σ ← σ − (BS(σ) − price) ÷ Vega (Newton-Raphson)

If Vega becomes tiny or the step diverges, we fall back to bisection on a [0.01%, 500%] bracket. If no volatility reproduces the price (for example, a price below intrinsic value), the tool reports non-convergence rather than a misleading number.

When to use this calculator

Use this to back out the volatility the market is pricing into an option from its quoted premium. Where the Black-Scholes calculator turns volatility into a price, this runs the same model in reverse.

It is the right tool for judging whether options are rich or cheap. Comparing today's implied volatility with the underlying's recent realised volatility — or with its own IV history — tells you whether you are buying premium at a high or a low.

Options sellers use it to quantify the edge they are being paid for; buyers use it to avoid overpaying just before an anticipated event deflates the premium.

Common mistakes

Entering a stale or crossed market price (e.g. a bid instead of a fair mid), producing a distorted implied volatility.
Assuming implied volatility from one strike applies to the whole chain — skew makes this unreliable near earnings or tail strikes.
Forgetting that IV is annualised — a 20% IV does not mean a 20% move by tomorrow, but over one year.

Frequently asked questions

What is implied volatility?: Implied volatility is the volatility input that makes the Black-Scholes price equal the option's observed market price. It reflects the market's expected movement.
How is it solved?: We invert Black-Scholes numerically using Newton-Raphson, falling back to bisection on a [0.01%, 500%] bracket. If no volatility fits, it reports non-convergence.
Why might the solver fail to converge?: If the quoted market price is below intrinsic value or above what's achievable at very high volatility, no valid sigma exists and the tool reports non-convergence rather than a wrong number.
Does implied volatility predict direction?: No — it reflects the magnitude of expected movement (in either direction), not which way the price is expected to go.
Why do different strikes on the same underlying show different implied vol?: This is the volatility smile/skew: the market prices tail risk differently across strikes, so IV is not flat across a chain even though Black-Scholes assumes constant volatility.
How many iterations does it usually take?: Newton-Raphson typically converges in under 10 iterations when vega is well-behaved; the bisection fallback is slower but guaranteed to converge if a solution exists in the search range.