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
20%
- Method
- Newton-Raphson
- Iterations
- 2
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.
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.