Implied Volatility

Option pricing models map inputs to a value: underlying price, strike, time to expiration, risk-free rate, carry or dividend yield, and volatility. Every input except volatility is observable. Reversing the model therefore means holding the observables fixed and searching for the single volatility figure that reproduces the traded premium.

No closed-form inversion of the Black-Scholes-Merton formula for volatility exists, so the number is found numerically. A solver guesses a volatility, prices the option, compares the result with the market quote, and adjusts. Convergence is reliable because an option's value rises monotonically with volatility for both calls and puts: vega is positive, so a higher volatility guess always produces a higher model value. That one-to-one relationship guarantees a unique solution for any premium lying between the option's intrinsic value and its theoretical upper bound.

Black-Scholes-Merton assumes a single constant volatility for the underlying, which implies that every option on that underlying should return the same implied figure. Markets contradict this. Implied volatility varies systematically with strike, generally rising for deep out-of-the-money puts on equity indices, and it also varies with time to expiration. Plotting the two dimensions together produces the volatility surface.

The shape carries information rather than noise. A steep downside skew signals that participants are paying up for crash protection and that the market prices a left-tailed distribution rather than a symmetric lognormal one. Term structure is usually upward sloping in calm conditions and inverts during stress, when near-dated uncertainty dominates. Traders quote and hedge from the surface, treating the model as a translation device between price and volatility rather than as a literal description of the world.

On dealing desks, options are frequently quoted in volatility points rather than currency premiums, with the model converting the agreed volatility into a cash price at execution. This convention exists because volatility is the dimension participants disagree about; the remaining inputs are common knowledge. Volatility indices extend the idea to the index level by aggregating implied volatilities from a strip of listed options into a single annualised figure for expected near-term movement.

The empirical regularity worth knowing is that implied volatility tends to sit above subsequently realised volatility, particularly for index options. Sellers of options are effectively insurers and demand compensation for bearing tail risk, producing what is called the variance risk premium. Implied volatility also spikes ahead of scheduled events such as earnings releases and collapses once the outcome is known, even when the underlying price barely moves.

Three skills matter at Level I. First, reason about direction: because vega is positive, an increase in implied volatility raises the value of long calls and long puts alike, and hurts short option positions. Questions often test this by describing a volatility change and asking about position value rather than about the underlying's price.

Second, connect implied volatility to strategy selection. A trader who believes actual volatility will exceed the level embedded in premiums buys volatility through structures such as a long straddle or strangle; a trader who considers options expensive relative to expected movement sells them and accepts convexity risk. Third, recognise the limits. Implied volatility is model-dependent, so a figure extracted with the wrong dividend assumption, the wrong rate, or a European formula applied to an American option is contaminated by that error rather than being a clean market expectation.