1. The term structure of volatility: there is no single implied, there is a curve

Derivatives 7: Volatility as an asset

Level 3 left you with a comfortable, false idea: that an underlying has an implied volatility. It does not. It has as many as there are listed expiries, and the differences between them are not calculation noise or model imprecision. They are the message.

Every expiry is a different market

An option expiring on Friday and another on the same underlying expiring nine months out are not competing for the same buyer. Someone wanting to hedge Thursday's earnings will not settle for a December expiry. A fund selling premium to finance its portfolio does not touch the weeklies. Every maturity has its own supply and its own demand, and consequently its own price.

Take an index's option chain on a quiet day and note the implied of the at-the-money option at each expiry. You get a series: around 12 at one week, 13 and a half at one month, 15 at three months, 16 and a half at six, 18 at one year. That is the term structure of volatility. Together with the skew across strikes it forms the two axes of the surface you already know, and of the two this one reads like a calendar.

Why the curve rises under normal conditions

First the intuitive explanation has to be dismantled, because it is the wrong one: it does not rise because a longer maturity accumulates more risk. Implied volatility is quoted annualized, so it compares rates, not amounts. An 18 at one year and a 12 at one week do not say the asset will move more over the year; they say the rate priced in for the next twelve months is higher than the one priced in for the next seven days. The underlying reasons are these three:

• Volatility is mean-reverting. It does not behave like a price, which can go anywhere and stay there. It tends to come back to a central zone. In calm conditions, the short expiry anchors on what is being observed today and the long one anchors on the long-run average, which is higher. In a scare, exactly the opposite happens.
• There is uncertainty about the uncertainty itself. A week has no room for a change of regime; a year has room for three. Whoever prices a distant expiry is not only estimating how much the asset will move, but how much that estimate can change along the way, and that second component is charged for too.
• Selling long maturities ties up capital. The seller of a one-year option carries margin, possible top-ups and the impossibility of recycling that money. It is the volatility risk premium of level 3, stretched over time: the greater the commitment, the greater the mark-up demanded.

The inverted curve: a problem with an expiry date

In scares the curve turns over. The one-month expiry shoots up to 33 while the one-year barely reaches 22. The reading is not that the market has turned pessimistic in general, but something far more specific: the problem is perceived as intense, immediate and resolved before the year is out. It is the same signal an inverted yield curve sends and it means the same thing.

The degree of inversion measures urgency. Three points of difference between the month and the year is tension; fifteen is panic with a date on it. And a warning many people skip: an inverted curve is not a buy or sell signal on the underlying. It is a statement about how risk is distributed over time, not about direction.

The step: dated events do not draw smooth curves

If the term structure were a genuine curve, it would be smooth. It is not. When there is an event with a known date, whether earnings, a rate meeting, a court ruling or a vote, the implied jumps between the last expiry that does not contain it and the first one that does.

A stock reporting earnings on Wednesday the 12th may have the Friday the 7th expiry trading at 30 and the Friday the 14th one at 48, seven calendar days apart. That step is neither an error nor an opportunity: it is proof that the curve is not a curve, but independent markets sorted by date. And it unwinds within hours. The morning after the release, the expiry of the 14th may be at 26.

How to read an option chain properly

• Look at implieds, not premiums. A more expensive premium may be so because of maturity, strike or dividends. The implied is the only thing comparable across different expiries.
• Compare the same point of the strike curve. If you look at the 100 strike in one expiry and at the same one in another, you are mixing maturity with skew, because that strike is not at the same effective distance from the price in the two cases. You compare at-the-money with at-the-money, or one delta with the same delta.
• Note the days remaining, not the name of the month. Two monthly expiries can be 28 days apart or 35, and that alone distorts the comparison.
• Check the spread and open interest before believing a number. An implied backed out of the price of an option nobody trades is arithmetic on a price that does not exist.
• Locate the events in the calendar. Almost every odd step has a name and a day, and looking it up takes a minute.

Real case: sterling, June 2016

The British referendum of June 23, 2016 is the textbook example: it had a date in the calendar months in advance. In the preceding weeks, the implied on sterling options against the dollar with expiries containing that night shot up past its levels from the 2008 crisis, while the long expiries barely moved. The curve was inverted and with a brutal step around a single date.

On June 24 sterling fell around 8% against the dollar, its largest single-session collapse in several decades. And here comes the lesson: the short implied caved in that very day. Realized volatility had just been enormous, but there was no longer anything to pay for what was going to happen, because it had happened. Anyone who bought short-dated volatility the night before and got the direction completely right could close out with less money than they had put in.

This is education about how these prices form, not a recommendation to trade them.