Implied volatility

Implied volatility is the volatility input that makes a pricing model return the price at which an option actually trades. It is not observed directly: it is backed out of the premium. Quoted as an annualised percentage, it is the market’s price for future movement, not a forecast of it.

How it works

Take the option’s market price, the spot or forward, the strike, maturity, rates and dividends, then solve for the volatility that makes a model such as Black-Scholes (or Black-76 on futures) match the premium. Every other input is known, so volatility becomes the unit in which options are quoted and compared. Desks trade “vol”, not dollars: quoting in vol makes options on different strikes and maturities comparable, even when their premiums differ widely. Each strike and maturity carries its own implied volatility, which produces the skew and the term structure.

Example

Hypothetical: an index trades at 100 and the one-month at-the-money option implies 20%. The implied one-standard-deviation move over one month is 100 × 20% × √(1/12), roughly 5.8 points. On a daily basis, 20% divided by √252 (about 16) gives a move of about 1.25% per day.

On the desk

Traders compare implied volatility with the realised volatility they expect to capture through delta hedging. The level alone says little: the same 20% can be rich before a quiet month and cheap ahead of an earnings release or a central bank meeting.