Implied Volatility (IV) Solver
Newton-Raphson SolverReverse-calculate market implied volatility from known market call or put option prices down to 1e-6 precision.
📈 Market Parameters
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💡 How Implied Volatility (IV) Is Solved
Because Black-Scholes cannot be inverted algebraically for volatility (σ), IV is solved using a Hybrid Newton-Raphson + Binary Search (Bisection) Root Finder:
1. Newton-Raphson StepUses Vega derivative: σn+1 = σn - [BS(σn) - TargetPrice] / Vega(σn) for fast 3-5 step convergence.
2. Bisection FallbackActivated when Vega is near zero (Deep ITM/OTM) to guarantee 100% convergence down to 1e-6 precision.
Solved Implied VolatilityConverged (4 iterations)
25.42%Annualized Standard Deviation
Target Price$4.50
Theoretical Match$4.500
Pricing Error0.0000%