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 sigma that, when plugged into the Black-Scholes formula, reproduces the observed market price of an option. It is not a forecast of future volatility. It is a price — the market's consensus on how much the underlying will move, plus a risk premium.
Historical volatility (HV) looks backward: the annualised standard deviation of past daily returns. Implied volatility looks forward: what the market is pricing in for future moves. They measure different things. HV tells you where volatility has been. IV tells you where the market thinks it is going — with a systematic upward bias called the volatility risk premium.
There is no closed-form solution for IV. You solve for it numerically. Take a European call priced at $1.875, with S = $21, K = $20, r = 10%, T = 0.25 years. Try sigma = 20% — Black-Scholes gives $1.76, too low. Try sigma = 30% — gives $2.10, too high. Iterate (Newton-Raphson or bisection) until you find sigma = 23.5%. That is the implied volatility.
Dollar option prices change whenever the stock moves, time passes, or rates shift — even if the market's volatility expectation is unchanged. IV isolates the volatility component. A trader who says "this option is trading at 25 vol" is making a statement about the market's pricing of uncertainty, independent of the current stock price. This makes IV comparable across strikes, maturities, and underlyings.
IV systematically exceeds realised volatility by 2–4 percentage points on average. This is not a mispricing. It is compensation — option sellers demand a premium for bearing the risk that realised volatility spikes above expectations. Short-volatility strategies harvest this premium, but they carry tail risk: when markets crash, realised volatility can far exceed implied.
No. Implied volatility is the number that makes the Black-Scholes model match the observed option price. It reflects market consensus plus a risk premium, not a forecast. IV can be high because the market correctly anticipates an event (earnings, central bank meeting), not because options are mispriced.
Because option sellers demand compensation for bearing the risk of unexpected volatility spikes. This difference is called the volatility risk premium. On average, IV exceeds realised vol by 2 to 4 percentage points. Short-volatility strategies profit from this gap, but suffer large losses when volatility spikes beyond what was priced in.
The VIX measures the 30-day implied volatility of S&P 500 options. It is calculated from a strip of out-of-the-money puts and calls, making it model-free (it does not depend on Black-Scholes). A VIX of 20 means the market implies 20% annualised volatility for the next 30 days. It is often called the fear index, but it measures option prices, not fear directly.
FinLingo covers volatility in Level 3 — 6 units from historical vs implied to the VIX. Level 1 is free.
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