Implied Volatility Calculator (Solve IV from an Option Price)
Back out the implied volatility from an option's market price with the Black-Scholes model: enter the underlying, strike, expiry, rate, dividend yield and the call or put price to get IV, the model price at that IV, vega (how much price per IV point), the expected one-standard-deviation move to expiry, a comparison with realised volatility, and the IV needed to justify a different price.
How it works
find σ such that BS(S, K, T, r, q, σ) = market price (bisection on σ ∈ [0.05%, 500%]) · d₁ = [ln(S/K) + (r − q + σ²/2)T] ÷ σ√T, d₂ = d₁ − σ√T · call = S e^(−qT) N(d₁) − K e^(−rT) N(d₂) · vega = S e^(−qT) φ(d₁) √T · 1σ move = S σ √T
An option price contains one unknown that no data feed prints directly: the volatility the market is assuming. Every other Black-Scholes input is observable, so the model can be run backwards, searching for the volatility that reproduces the traded price — which is what implied volatility is, and why it is the language options traders quote in rather than dollars. It translates into an expected size of move, a probability of finishing in the money, and a comparison with how much the underlying has actually been moving; the gap between implied and realised is the premium sellers charge for bearing surprises, and its history for a given name tells whether today's options are expensive or cheap.
Worked example
A 45-day call struck at $105 on a $100 stock trading at $2.35, with a 4.5% rate and 1.2% dividend yield, implies a volatility of about 29.7%. That means a one-standard-deviation move of about ±$10.40 by expiry (≈ $1.87 a day), a 31% risk-neutral chance of finishing in the money, and a vega of about $0.13 per IV point; against 22% realised volatility the option is priced almost 8 points rich — a fat variance premium, typical ahead of an event.
Frequently asked questions
Why do different strikes give different IVs?
Because the market does not believe in a lognormal world: downside puts trade at higher IV (skew) and far strikes at higher IV than at-the-money (smile), pricing crashes and fat tails. IV is therefore quoted per strike and expiry — the whole surface, not one number.
Can I use this for American options?
Approximately, for calls on non-dividend stocks (never optimally exercised early) and for options far from early-exercise territory. For deep in-the-money puts or high-dividend names the American premium biases the IV upward; use a binomial model for those.
Related calculators
Educational finance mathematics. Models such as Black-Scholes, parametric VaR and lognormal Monte Carlo rest on simplifying assumptions (constant volatility, normal returns, no fat tails) that real markets violate. Nothing here is investment advice — consult a licensed professional for decisions about your money.