What is Implied Volatility?
Implied Volatility (IV) is the market's forward-looking estimate of annualised price volatility embedded in an option's price. It is solved by inverting the Black-Scholes formula: given a known option price, you back-solve for the volatility that produces that price. IV is expressed as an annualised percentage and is the single most important variable in options pricing: it determines the extrinsic (time) value. When IV is high, options are expensive; when low, they are cheap. IV typically spikes before earnings announcements and collapses after, a phenomenon known as IV crush. The IV Rank (IVR) and IV Percentile compare current IV to its historical range.
Formula
Solve for σ in: C = S×N(d₁) − K×e^(−rT)×N(d₂)
Method: Newton-Raphson iteration (numerical, no closed form)
σ_(n+1) = σ_n − (BS(σ_n) − Market Price) / Vega(σ_n)
Start with σ = 0.20 as initial guess
Converges in 5-10 iterations typically
Calculator
How to Use
- 1Enter the option's market price: Use the mid-price (bid + ask) / 2 from a live option chain.
- 2Enter the other BS inputs: Stock price, strike, days to expiry, and risk-free rate.
- 3Choose call or put: The calculator will solve for the IV that makes the BS price equal the market price.
- 4Interpret: IV > 30% is generally considered elevated. Compare to the stock's 30-day historical volatility (HV30) for a vol premium/discount assessment.
Worked Example
Example: Call option priced at $5.20
Market Price
$5.20
S
$150
K
$150
DTE
30
Rate
5%
The Newton-Raphson solver finds the σ that makes BS(150, 150, T, 0.05, σ) = $5.20. The result is approximately 27.5% IV. If the stock's 30-day historical volatility is 22%, the option is pricing in a ~5.5pp vol premium, suggesting sellers may have an edge.