An option's premium can double while the stock sits still. It can also fall on the morning the stock finally moves your way. The calls and puts article treats that premium as a number you look up. This one takes it apart.
The Number You Get by Running the Model Backwards
An option pricing model needs five inputs: the stock price, the strike, the time left, an interest rate, and how much the stock is expected to move. Four of those you can look up. The fifth is written down nowhere.
So the market runs the model backwards. The premium is already on the screen. Start from that price and solve for the movement figure that would produce it. That answer is the implied volatility, quoted as an annual percentage.
There is no formula for the reverse direction, so a computer guesses, prices the option, compares, adjusts, and repeats until the two agree.
That makes implied volatility a price in different units, not a forecast. An option quoted at 45% implied volatility is like a bond quoted at a 6% yield. Both exist so contracts with different strikes and dates can be compared.
Vega: What One Point of Volatility Costs
Vega is how much the premium moves when implied volatility moves one percentage point. An option with a vega of 0.08 gains about eight cents per share, or $8 on a 100 share contract, when implied volatility goes from 30 to 31. It loses the same going down.
Delta and Gamma, the two Greeks the dynamic hedging article works through, answer questions about the stock's price. Vega asks about the price of movement itself. It is also the odd one out: vega is not actually a Greek letter.
Two patterns matter. Vega is largest for options struck near where the stock trades now, and shrinks as the strike moves far above or below. An option with months left has more vega than one expiring Friday. A change in expected movement is worth most when the outcome is genuinely open.
Whoever owns the option gains when implied volatility rises. Whoever sold it loses.
Why the Number Climbs Into an Earnings Date
A scheduled earnings report packs a lot of uncertainty into one moment. Nobody sells an option covering that moment at the price they would take in a quiet week. Premiums rise in the days beforehand, and implied volatility rises with them.
The instant the numbers are public, the uncertainty is spent. Implied volatility drops hard, often most of the way back within minutes of the open. Traders call it the volatility crush.
The crush is not the market correcting a mistake. The high number before the report is the honest price of an unknown, and the low number after is the honest price of a known.
A Trade That Is Right and Still Loses Money
Nimbus Freight is an invented company, and every figure below is invented with it.
Nimbus trades at $60 and reports earnings tomorrow morning. A call struck at $60, expiring in 11 days, costs $3.10 per share, or $310 for one contract. Its implied volatility is 75% and its vega is about $0.04 per share, so $4 per contract per point.
The report is good. The stock opens at $61.50, up 2.5%. Implied volatility falls to 35%, because the event everyone was pricing has happened. The call is worth about $2.28, or $228.
You were right about the direction and you lost $82, a quarter of what you paid.
Here is where it went. The 40 point fall in implied volatility, at roughly $4 a point, works against you by about $160. The $1.50 rise in the stock hands back around $79, and a day of time value expired on top. Direction was one of three forces on the premium, and the smallest.
Implied Has Tended to Run Above What Arrives
Once you can read implied volatility, a test suggests itself. Write down what an option is quoting, wait for the period to pass, then measure what the stock did.
Run that test on index options over long stretches and the implied figure has tended to land above the realized one. Researchers call the gap the variance risk premium, and it is documented across decades and asset classes. The volatility and beta article notes the pattern. The reason is the useful part.
The reason is insurance. Most buyers of index options want protection against a fall, and most sellers take that risk on for cash. A seller prices in a margin above what they expect to pay out, the way an insurer charges more than the average claim. That margin pushes implied above realized.
Two cautions. It is a tendency over many periods, not a fact about the option in front of you. And the stretches where it reverses hold enormous moves, so a seller's losses arrive all at once.
The Smile That Showed Up in 1987
Black-Scholes assumes a stock has one volatility, so every option on it should imply the same number. Plot implied volatility against strike price and you should get a flat line.
You do not. On index options the line slopes down: out of the money puts, which pay off in a crash, imply higher volatility than calls above the current price. That tilt is called skew. In currencies both ends sit above the middle, and that curve is the smile the name comes from.
The timing tells you something. Before October 1987, implied volatilities on index options ran roughly flat across strikes, which is what the model predicts. After the crash the skew appeared and it has never gone away. Mark Rubinstein documented the shift in 1994.
Read that as a verdict on the model. Buyers pay more for crash protection than a bell curve says it is worth, because real returns have fatter tails. Traders still use Black-Scholes as a translator between price and volatility, not as a description of how stocks behave. The smile is that correction, applied by hand.
Reading a Number That Has No Absolute Scale
So "implied volatility is 45%" tells you almost nothing by itself. Forty five is quiet for a small biotech and alarming for a water utility. The comparison that carries information is against the same option's own past.
Two measures do that job. IV rank places today's reading between the past year's highest and lowest on a 0 to 100 scale, so 80 sits four fifths of the way up that range. IV percentile counts the share of days in the past year with a lower reading. They can disagree sharply: one violent spike sets the year's high and drags every later rank down, while percentile ignores how far the spike went and just counts days.
Two other comparisons help. Implied against the stock's own realized volatility says whether options price more movement than the stock has delivered. Implied against the calendar says whether a scheduled event is doing the lifting. If earnings land next week, the number is high for a reason that expires in eight days.
None of it tells you what to do. It tells you what you are paying for, which is the step most people skip.
