Implied volatility
Capital MarketsThe volatility figure that makes an option pricing model reproduce the price at which the option actually trades.
Also written: implied vol, implied volatilities
An option pricing model needs six inputs: the underlying price, the strike, the time to expiry, the risk free rate, expected dividends and volatility. Five of those are observable and uncontroversial. Volatility is not, because it is a statement about the future.
So the market inverts the problem. Take the traded price as given and solve for the volatility figure that would produce it. That figure is the implied volatility, and it is best thought of as the price of the option restated in a unit that can be compared across strikes, maturities and companies. Two people who agree on nothing else can look at a volatility quote and agree on whether an option is expensive.
It is not a forecast. What the market charges to carry uncertainty includes a risk premium, so the implied figure differs persistently from the volatility that later gets realised. A candidate who describes implied volatility as the market's expectation of future volatility is making the error that sounds most informed, and any options trader will correct it.
The practical use in banking is convertibles. The call embedded in a convertible can be measured against listed options on the same shares. A convertible implying lower volatility than the listed market is cheap to a buyer who can hedge the equity and credit away, and new issues are frequently priced to leave that gap open, because arbitrage funds are the buyers who close it.
Worked example
Two options on the same share, same expiry, different strikes. One trades at €2.60, the other at €0.40, so the euro prices tell you nothing about which is dearer.
Converted into implied volatility they can be compared directly, and the strike below the market usually implies the higher figure, because investors pay up for downside protection. That pattern is the skew, and it is itself evidence that the constant volatility assumption inside the model is not true.
Do the same for the option inside a convertible. If it implies less volatility than the listed options do, the convertible is the cheaper way to buy the same optionality.