Historical volatility looks backward. Implied volatility looks at the option market and asks a different question: given what people are paying for options right now, how much movement are they expecting? That expectation, expressed as an annualized volatility, is the price options are implying the stock will move, called implied volatility, or IV.
Module 3 showed where the number comes from: hold the stock price, strike, time and rate fixed, and search for the one volatility that makes the pricing model return the option's market price. A higher volatility always means a higher price, so each price lines up with exactly one volatility, and nobody has to announce a forecast; it is sitting inside the price.
The price of an option, in vol terms
Because the mapping is one to one, traders quote options in volatility instead of dollars. A $3.43 call on one stock and a $0.80 call on another, at different strikes and dates, cannot be compared directly. At 30 vol and 22 vol they can. Volatility is the unit that strips out the stock price, the strike and the time left, and leaves only the thing being paid for: how much movement. When a trader says an option is expensive, they mean its implied volatility is high, not its dollar price.
Every option on the chain has its own implied volatility, and they differ by strike and by expiration. Those differences are the subject of later modules. For now, two readings matter.
The 30-day headline
The chain's IV column gives you one number per contract. To talk about a stock's volatility as a whole, the market uses the at-the-money implied volatility at a standard horizon, and 30 days is the convention. ORATS interpolates between the listed expirations so that 30-day IV is always exactly 30 calendar days out, whichever contracts happen to be listed. It is the number quoted when someone says a stock is trading at 25 vol, and it is the one the Terminal puts at the top of every screen. The same method gives 60-day, 90-day and one-year readings, and the way they line up is the term structure, which gets its own lessons later.
IV versus HV
This is the comparison a volatility trader lives by. Put the stock's 30-day implied volatility next to its 20-day historical volatility: what options are charging for the next month against what the stock did over the last one. The two windows cover roughly the same span of trading days.
- IV 30% against HV 20%: options are priced for half again as much movement as the stock has been delivering. Premium is rich relative to recent behavior, which favors sellers of options if the calm continues.
- IV 20% against HV 30%: options are cheaper than the stock's recent movement. The market thinks things will calm down, or it is underpricing what is happening, which favors buyers.
The difference, in volatility points, is the volatility risk premium. On most stocks most of the time it is positive: implied sits a few points above realized, because option sellers demand compensation for the moves they cannot predict. A premium far above its usual size, or a negative one, is where the interesting trades start.
One caution on the arithmetic. Strictly, the premium is today's implied against the volatility the stock goes on to deliver over the option's life, which nobody knows yet. Implied minus the last month's realized is the stand-in you can read today, and it looks backward: a quiet month just ended says little about a busy one ahead. The Terminal prints this backward-looking version as VRP.
The chart below shows why the comparison matters to anyone who owns an option. It buys an at-the-money straddle at one implied volatility, hedges its delta every day, and lets the stock move with a different, realized volatility.
A straddle bought at 30% implied and hedged daily, on a stock realizing 20%: theta paid beats gamma earned. Drag realized up to 40% and the net line ends above zero on most paths. Press New price path a few times to see how much luck there is in one month.
The owner pays implied and collects realized. When the stock moves less than the option priced, theta outruns the gains from re-hedging; when it moves more, the owner comes out ahead. Which one wins is only known after the fact, which is why past realized volatility is a guide to the comparison, not a verdict.
One caution. IV is a forecast and HV is a measurement. A high IV in front of an earnings date is not mispricing; the market knows a move is coming, and HV, which has not seen it yet, cannot.
The maths: building a 30-day number from two expirations
Thirty days out rarely lands on a listed expiration, so the headline is built from the two that straddle it. Drawing a straight line between their vols is close but not quite right. What grows in a straight line with time is variance, the square of volatility: the square-root-of-time rule from Module 3 seen from the other side. So a standard method interpolates total variance, w = v² × days, then converts back: w30 = w1 + (w2 - w1) × (30 - d1) / (d2 - d1) and v30 = √(w30 / 30). Here d1 and d2 are the days to the two expirations, and w1 and w2 their total variances.
A worked example: a 23-day expiration at 32 vol and a 51-day one at 28 vol. In vol points squared times days, w1 = 32² × 23 = 23,552 and w2 = 28² × 51 = 39,984. Thirty days is a quarter of the way from 23 to 51, so w30 = 23,552 + 0.25 × 16,432 = 27,660, and v30 = √(27,660 / 30) = √922 = 30.4. A straight line between the two vols would say 31.0. The gap is small here and grows as the two vols move further apart.
Your turn
Open NVDA in Vol Snapshot and read the 30-day row of IV vs HV by tenor, then open the chain to see where the headline comes from. The one-year reading is on IV Intelligence's Overview tab. The last live question moves to Price Context, whose Volatility panel prints IV 30d, HV 20d and the difference between them as VRP.