Implied Volatility: Meaning, Pricing and IV Crush

Implied volatility (IV) is the annualized volatility that makes an option-pricing model match a chosen premium. It describes the uncertainty reflected in that price under the model’s assumptions—not a prediction of whether the stock will rise or fall. Historical volatility measures variability in returns over a past period; IV is inferred from an option price and need not match the volatility realized later. 1

Inferring volatility from a premium

A pricing model normally takes volatility as an input and calculates an option’s value. Finding IV reverses that process: hold the underlying price, strike, remaining time, interest rate, dividends and exercise terms fixed, then find the volatility that reproduces the selected premium. For model value $V$ :

V(\sigma_{\mathrm{IV}})=\text{Observed option price}

The answer depends on the model and its assumptions, not just the premium. 2

Consider a European call with a $750 underlying price, a $775 strike and 45 days remaining. Using a 4% continuously compounded annual interest rate, a 1% continuous dividend yield and $T=45/365.25$ years, Black–Scholes–Merton gives:

Annualized volatility	Call value per share
15%	$7.28
20%	$12.03
25%	$16.99

A premium near $12.03 therefore implies about 20% IV with these inputs. The table changes volatility alone; a different underlying price or remaining term would change the comparison.

Using the bid, midpoint or ask can produce different IVs. A solution exists only when the selected premium is attainable under the model. And when an option’s value barely responds to volatility, small differences in price, rounding or quote timing can cause large differences in inferred IV.

Interpreting the annualized percentage

An IV of 20% does not mean a stock should move 20% before the option expires. Annualization puts different time horizons on a common scale. In a constant-volatility model, annual volatility $\sigma$ over $T$ years gives a log-return standard deviation of:

\sigma\sqrt{T}

For 20% annual volatility over 45 days:

0.20\sqrt{45/365.25}\approx0.0702

That is about 7.02%. For relatively small returns, multiplying by the starting stock price gives an approximate dollar standard-deviation scale: about $52.65 at $750. This measures dispersion, not a required move or a price target. It is neither a hard boundary on outcomes nor a guaranteed real-world probability interval. 3

How can an IV drop outweigh a stock-price rise after earnings?

A call can lose value even when the stock rises. Before earnings, its premium may reflect substantial uncertainty about the announcement. Afterward, IV may fall sharply as that uncertainty clears. This IV crush can remove more value than the stock’s rise adds, although it does not happen after every announcement. OIC’s earnings discussion explains this interaction.

A worked example: stock up, call value down

Take one hypothetical European call with a $100 strike and a 100-share multiplier. Use Black–Scholes with a 4% continuously compounded annual interest rate, no dividends and calendar days divided by 365.25. Ignore transaction costs. The following are model valuations, not market quotes:

State	Underlying	Days left	Annual IV	Model call value per share
Initial reference	$100	30	80%	$9.2767
One day later, other inputs unchanged	$100	29	80%	$9.1192
One day later, underlying rises	$103	29	80%	$10.8482
One day later, underlying rises and IV falls	$103	29	30%	$5.3280

Without the IV drop, the later call value would exceed the initial value. With IV at 30%, it is only about $5.33 per share. The stock rose 3%, yet the call’s model value fell by about $394.87 per 100-share contract. This change uses unrounded model values; the table’s prices are rounded.

The final call value includes $3.00 of intrinsic value per share—the $103 stock price minus the $100 strike—and about $2.3280 of extrinsic value. Initially, at a $100 stock price, the call had no intrinsic value. Moving into the money did not make up for the drop in extrinsic value.

Which part came from volatility?

In the table’s order, one day’s passage reduces the contract’s value by about $15.75. The rise from $100 to $103 then adds about $172.90. Finally, cutting IV from 80% to 30% removes about $552.02. Each step changes one input while holding the others fixed.

Change that order and the individual contributions can differ; only the total repricing between the same starting and ending assumptions stays the same. The IV decline is 50 percentage points, not a 50% proportional reduction. For such a large move, reprice the option rather than multiply its starting vega by the entire change. Vega estimates sensitivity to a one-percentage-point change near the current inputs.

Is that my realized loss?

No. This is a decline between two theoretical values. A realized result uses actual entry and exit premiums, quantity, the contract multiplier and costs. A purchase at a premium other than $9.2767 would have a different starting point. The 100-share multiplier matches this calculator’s convention, but contract specifications can differ by product and market. Being in the money is not the same as being profitable relative to the premium paid.

How can I explore it in this calculator?

Compare separate valuations using the example’s stock price, time, IV, rate and dividend inputs, and keep the initial theoretical premium separately for the subtraction. Changing IV recalculates the calculator’s opening premium; it does not preserve an earlier purchase price. The same is true of editing Entry price, which means the opening underlying price, not the option premium.

The model uses whole days, so this example compares daily valuation states rather than intraday changes around an announcement. See methodology for the calculator’s pricing and baseline rules.

Falling IV can reduce a short option’s liability, but an adverse stock move can outweigh that benefit. It does not make selling options before earnings reliably profitable or limit the seller’s risk to the premium received.

Skew and term structure

An underlying does not necessarily have one IV for every option. Across strikes, a volatility smile has higher IV on both sides of a central region; a skew is more pronounced on one side. Equity-index options often have higher IV at lower strikes, reflecting the pricing of sharp declines and demand for downside protection. 3

Differences across expirations form the volatility term structure. An approaching announcement can account for more of a short-dated option’s remaining uncertainty than a longer-dated option’s. Its effect on annualized IV can therefore be larger for the shorter contract, and different expirations need not move together.

For European calls and puts with the same strike and expiration, put-call parity links prices to the underlying and financing terms. Prices satisfying that relationship imply the same IV when consistent model inputs are used. Bid-ask spreads, stale quotes and different dividend assumptions can create differences in displayed IV. American early-exercise rights require separate treatment; European parity does not apply unchanged. 4

Vega and position exposure

Vega estimates how much an option’s value changes for a one-percentage-point IV change, holding other inputs fixed. At 20% IV, vega of $1.04 per share means a rise to 21% adds approximately $1.04 per share, or $104 for one purchased 100-share contract. A short position has the opposite exposure. 5

Vega changes with volatility, time and moneyness, so this is a local estimate, not a fixed conversion rate. In a spread, long and short vegas can partly offset a common IV change without protecting against different changes at different strikes. The calculator applies one shared IV to all legs; it does not independently vary each leg’s volatility.