Implied Volatility | Examined Content

IV is the volatility parameter making Black-Scholes match market prices. Higher IV means higher expected price swings—often before events.

The Concept

BS_Price(σ) = Market Price
Solve for σ using Newton-Raphson

How It Works

// Bisection method to find implied volatility
function impliedVolatility(S, K, T, marketPrice, r) {
    let lo = 0.01;   // 1% IV
    let hi = 2.0;     // 200% IV
    
    for (let i = 0; i < 50; i++) {
        const mid = (lo + hi) / 2;
        const price = blackScholesCall(S, K, T, mid, r);
        
        if (price > marketPrice) {
            hi = mid;  // Price too high, lower IV
        } else {
            lo = mid;  // Price too low, raise IV
        }
    }
    return (lo + hi) / 2;
}

// Black-Scholes call price
function blackScholesCall(S, K, T, sigma, r) {
    const d1 = (Math.log(S/K) + (r + sigma*sigma/2)*T) / (sigma*Math.sqrt(T));
    const d2 = d1 - sigma*Math.sqrt(T);
    return S*normalCDF(d1) - K*Math.exp(-r*T)*normalCDF(d2);
}