🌊 Implied volatility: what the option price expects

🎯 In 30 seconds: Volatility measures how much a price swings. Historical volatility is what the stock actually did. Implied volatility (IV) is the swing size baked into today's option prices, the market's estimate of what comes next. Higher IV means more expensive options. IV often jumps before known events like earnings and collapses right after, which is called IV crush. You can pick the right direction and still lose money if you overpaid for volatility.

Volatility in plain numbers

Volatility is the standard deviation of a stock's returns, expressed as a yearly (annualized) percentage. A stock with 30% volatility has, roughly, a one-standard-deviation range of plus or minus 30% over a year. In a normal-shaped world, about two years out of three would land inside that range.

Real stock returns are not perfectly normal. Big moves happen more often than the bell curve says. Treat these ranges as a scale for comparing options, not a promise.

Historical volatility: what already happened

Historical volatility (HV), also called realized volatility, is calculated from past prices:

1. Take daily returns over a window, often 20 or 30 trading days.
2. Compute their standard deviation.
3. Annualize by multiplying by the square root of 252, the approximate number of trading days in a year. The square root of 252 is about 15.87.

Worked example. Hypothetical: Company X's daily returns over the last 20 days have a standard deviation of 1.6%. HV = 1.6% x 15.87 = about 25.4%.

Traders use 16 instead of 15.87 for quick math. The OIC calls this the Rule of 16: divide annualized volatility by 16 to get a typical daily move. At 32% volatility, 32 / 16 = 2% a day.

Implied volatility: what the market is paying for

An option pricing model takes five main inputs: stock price, strike, time, interest rate and volatility. The first four are known. Volatility is not. Implied volatility is the volatility number that, plugged into the model, gives today's market price of the option. It is "implied" because you solve for it backwards from the price.

So IV is not a forecast someone published. It is a price, expressed in volatility units. When buyers want options badly, prices go up and IV goes up. The OIC puts it simply: higher implied volatility means higher option prices, for calls and puts alike.

Only options have implied volatility. Each strike and expiration has its own IV, which is why your options chain shows an IV column. See Reading an options chain.

Turning IV into an expected move

IV gives a quick estimate of the one-standard-deviation move by expiration:

expected move = stock price x IV x square root of (days to expiration / 365)

Worked example. Company X at $100, IV 32%, 30 days to expiration: $100 x 0.32 x square root of (30/365) = $100 x 0.32 x 0.287 = about $9.17. The options are priced for a typical move of roughly $9 either way over the month.

A second shortcut: the price of the at-the-money straddle (one ATM call plus one ATM put, same expiration) is close to the move the market expects by expiration. In the earnings example below, the $100 straddle costs $4.45 + $4.38 = $8.83, so the market is pricing a move of about 8.8% through earnings.

IV vs HV: is the market paying up?

Comparing implied with historical volatility tells you whether options are pricing bigger or smaller swings than the stock has recently delivered.

• IV 40%, HV 25%: options are priced for much bigger moves than recent history. Often there is a known event ahead, such as earnings, a court ruling or a product decision.
• IV 20%, HV 30%: options are priced for calmer days than the stock has been having.

Neither is automatically a buy or sell signal. The market may know something is coming. But it tells you what you are paying for.

IV rank and IV percentile

Is 35% IV high? For a sleepy utility, very. For a small biotech company, maybe not. Two measures compare a stock's IV with its own past year.

IV rank = (current IV - 52-week low IV) / (52-week high IV - 52-week low IV) x 100.

IV percentile = the share of trading days in the past year when IV was below today's level.

Worked example. Hypothetical: Company X's IV is 40% today. Over the past year it ranged from 20% to 60%, and it closed below 40% on 200 of 252 trading days.

The two disagree because one huge spike to 60% stretches the rank's range. The percentile says today's IV is higher than on most days of the year. Look at both.

The VIX: the market's fear gauge

The Cboe Volatility Index (VIX) applies the same idea to the whole S&P 500. Cboe calculates it from the prices of S&P 500 index (SPX) puts and calls across many strikes, weighted to give a constant 30-day measure of expected volatility, expressed as an annualized percentage.

Reading it: a VIX of 16 means SPX options are priced for about 16% annualized volatility. By the Rule of 16, that is roughly 1% a day. A VIX of 32 implies roughly 2% a day. The VIX tends to jump when stocks fall sharply, because demand for protective puts rises.

You cannot buy the VIX itself. There are VIX futures and options and related ETPs, which behave differently from the index. They are covered briefly in Index options. Compare its moves with the S&P 500 itself on the index dashboard.

IV crush: a worked earnings example

Before earnings, nobody knows the number, so options get expensive: IV rises. The morning after, the uncertainty is gone, and IV falls sharply even if the stock moved. That fall is IV crush.

Hypothetical, priced with Black-Scholes. Company X is at $100 the afternoon before earnings. You buy one $100 call expiring in 7 days. IV is 80%, so the call costs $4.45, or $445. The next morning, after the report, IV drops to 35%. Six days remain.

The stock rose 4%, you were right, and you made $8. The call's $4.00 of new intrinsic value was almost entirely offset by the time value that vanished with the IV drop. To make real money, the stock needed to beat the move the market had already priced: about 8.8%, the straddle price.

The vega math matches: before earnings this call had vega of about 0.055, so a 45-point IV drop is worth roughly 45 x 0.055 = $2.48 per share at the start. The exact repricing differs a little because vega itself shrinks as IV falls. See The Greeks.

Volatility skew

If the model's assumptions were perfect, every strike in one expiration would show the same IV. They do not. The pattern of IV across strikes is called skew.

For stocks and stock indexes the usual shape is a smirk: out-of-the-money puts have higher IV than at-the-money options. Investors pay up for crash protection, and sharp drops tend to come faster than sharp rallies. The OIC links the prominence of skew to the 1987 crash. Some stocks where traders fear a sudden jump up, such as takeover targets, can show the opposite, with higher IV on calls. A smile, higher IV on both wings, shows up when big moves either way are expected.

Skew matters in practice. A protective put five strikes below the stock costs more volatility than the call five strikes above it. That shapes the cost of collars and spreads.

Try it

Pick a stock from the earnings calendar that reports in the next two weeks. The day before the report, write down the price of the at-the-money straddle in the first expiration after earnings, the ATM IV, and the implied move as a percent of the stock price. The day after, record the actual move and the new ATM IV. Did the stock beat the implied move? How many points did IV fall? Repeat for five companies in your trading journal before you consider trading an earnings event.

Sources

• Options Industry Council (OIC): Volatility and the Greeks
• OIC: Understanding the Rule of 16 in plain terms
• OIC: The crush is real
• OIC: Volatility skew and options, an overview
• Cboe: VIX Volatility Index
• Stanford GSB: de Silva, So and Smith, Losing is Optional: Retail Option Trading and Expected Announcement Volatility