Implied Volatility

Options
Updated Apr 2026 • Has calculator

The volatility level implied by an option's market price, derived by reverse-solving the Black-Scholes formula.

What is Implied Vol (IV)?

Implied volatility (IV) is the annualised volatility that, when plugged into the Black-Scholes formula, produces the observed option market price. Unlike historical volatility (which looks backward), IV reflects the market's consensus forecast of future volatility. Higher IV means options are more expensive; lower IV means they are cheaper. The VIX index is the market-wide implied volatility for S&P 500 options.

Formula

Solve σ: BS(σ) = Market Price (Newton-Raphson)

Worked Example

Worked example — S&P 500 index option — illustrative example

Textbook example — Hull (2021)

Step 1  Call price observed: $10.45 (market mid-price)
Step 2  S = $100, K = $100, r = 5%, T = 1 year, type = call
Step 3  Newton-Raphson iteration:
Step 4   Guess σ = 20% → BS call = $10.45 → residual ≈ 0
Step 5  Implied Volatility = 20.00%
Step 6  → The market prices in 20% annualised volatility for this option

Source: Hull, J.C. — Options, Futures, and Other Derivatives, 11th ed., Ch. 20 (2021-01-01)

Calculate Implied Vol (IV)

Observed bid/ask mid-price of the option

Current underlying stock price

Option strike price

Annual risk-free rate

Time to expiration in years

Enter 'call' or 'put'

Implied Volatility

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Not investment advice.

How to Interpret Implied Vol (IV)

< 15
Low IV — calm market, options are cheap
15 – 25
Normal IV — typical large-cap equity range
25 – 45
Elevated IV — uncertainty or earnings approaching
> 45
High IV — market stress or speculative event

📚 Advanced Options — Complete the path

  1. Implied Vol (IV)
  2. Put-Call Parity
  3. Time Value
  4. Rho (Call)
  5. BS Put
Sources
  1. Hull, J.C. — Options, Futures, and Other Derivatives, 11th ed.
  2. CBOE VIX White Paper
  3. Investopedia — Implied Volatility