By the FinLingo Team | Capital markets practitioner, front office experience at a major European investment bank. FinLingo covers 342 lessons from bonds to exotic derivatives. About · Last updated:
Implied volatility (IV) is the value of σ that, when plugged into the Black-Scholes formula, reproduces the market price of an option. It is not calculated from historical data. It is not a forecast. It is a translation device — the market's way of expressing how expensive an option is in volatility units rather than dollar terms.
There is no closed-form expression for IV. You solve for it iteratively. Take the market price of a call, the stock price, strike, rate, and time to expiry. Guess a sigma, compute the BSM price, compare to the market price. If too low, increase sigma. If too high, decrease. Newton-Raphson converges in 3–5 iterations because vega (the derivative of price with respect to sigma) is always positive — the function is monotonic.
European call: S = $21, K = $20, r = 10%, T = 0.25 years, market price = $1.875. Try σ = 20%: BSM gives $1.76 (too low). Try σ = 30%: BSM gives $2.10 (too high). Bisect: σ = 25% gives $1.90 (slightly high). Iterate: IV = 23.5%. This is the number traders quote. "This option trades at 23.5 vol."
Dollar prices change whenever the stock moves, time passes, or rates shift — even if the market's view on volatility has not changed. IV strips out all those effects. If a call trades at 25 vol today and 25 vol tomorrow, the market's vol view is unchanged — even if the dollar price moved from $3.40 to $3.25 because the stock dropped. IV is apples-to-apples across strikes, maturities, and underlyings.
IV systematically exceeds subsequent realised volatility by 2–4 percentage points on average. This gap is the volatility risk premium (VRP). Option sellers earn it as compensation for bearing the risk that realised vol spikes above expectations. Short-vol strategies harvest the VRP, but they carry tail risk: in 2008 and 2020, realised vol far exceeded implied, and short-vol positions suffered catastrophic losses.
No. IV is a price, not a prediction. It is the number that forces Black-Scholes to match the observed market price. It reflects supply and demand for options, risk appetite, and hedging flows, not a mathematical forecast of future stock movement. A high IV can be correct (pre-earnings) or overstated (premium for uncertainty).
By iterative numerical methods. There is no closed-form formula for IV. You guess a sigma, compute the BSM price, compare to the market price, and adjust. Newton-Raphson is the most common method, converging in 3 to 5 iterations because vega (the derivative of price with respect to sigma) is always positive, making the function well-behaved.
The systematic tendency for implied volatility to exceed subsequent realised volatility. On average, this gap is 2 to 4 percentage points for equity index options. It exists because option sellers demand compensation for bearing the risk of unexpected volatility spikes. Short-vol strategies harvest this premium, but suffer large losses when realised vol exceeds implied, as in 2008 and 2020.
FinLingo covers implied volatility in Level 3 — 6 units on vol, plus the VIX and vol trading. Level 1 is free.
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