Price Volatility

Every volatility figure is the answer to a question that includes several parameters, and the figure is reported without them. Anyone comparing volatility across markets, periods, or sources is implicitly assuming those parameters match, and they routinely do not.

The period

Over what span the variation is measured. A short window captures recent conditions and responds sharply to them; a long window smooths and lags. Neither is right, and they answer different questions.

The interval

How frequently the price is sampled. Variation measured between daily observations and between monthly ones are different quantities, and the relationship between them is not a simple conversion.

The method

How variation is quantified. Different statistical treatments weight extreme movements differently, and a market’s figure can shift substantially with the method alone.

The price series

Which prices are measured. A benchmark, a cash quotation, an index, and an assessed series can all be described as "the price" and will have different volatility.

Continuity of the series

Where a series is stitched together from successive contracts, the joins introduce movements that are artefacts of the stitching rather than of the market — a particular hazard for agricultural series spanning harvests.

The last point is specific to commodities and easy to miss. A continuous price series for a commodity with delivery periods is a construction: each contract expires and the series must move to the next. That transition is a change in what is being measured, and unless handled deliberately it appears in the data as a price movement that no one experienced.

Volatility is used so routinely as a proxy for risk that the two words are frequently treated as interchangeable. They are not, and the difference is not academic. Volatility is a measure of variation in a series. Risk is the possibility of an outcome a party cares about — and which outcomes a party cares about depends entirely on the party.

The clearest way to see the gap is to notice that volatility counts favourable movement as fully as unfavourable movement, while no party regards a windfall as a risk. A producer’s risk is that prices fall; a processor’s risk is that they rise. The same market, with one volatility figure, presents opposite risks to the two of them, and the figure describes neither. It is symmetric by construction, and risk almost never is.

• Volatility is symmetric; risk is directional and specific to a party’s position
• A stable price can be catastrophic — a price stable below a producer’s cost of production carries low volatility and severe risk
• A party’s exposure depends on their volume, timing, costs, and contracts, none of which appears in a price series
• Volatility says nothing about the level, and a party is exposed to levels rather than to variation
• Risks that matter most in agriculture — crop failure, rejection at a border, a buyer defaulting — do not appear in price series at all

The third and fifth points together explain why price volatility is a poor summary of an agricultural party’s situation. The exposures that determine whether a farming or trading business survives are mostly not price variation, and the one that is depends on facts about the business that the price series has never heard of.

Historical volatility describes prices that occurred. Implied volatility is a different object: a figure derived from the prices of options, representing the variation those prices embed given a pricing model. Because it is derived from instruments referring to a future period, it is frequently described as the market’s forecast of volatility, and this description is loose in ways that matter.

An implied figure is a statement about current option prices, read through a model. It depends on the model chosen, and a different model applied to identical option prices gives a different implied figure. It also embeds whatever else those prices contain — the cost of the parties supplying the options bearing risk, the balance of supply and demand for the options themselves, and the market’s conditions at that moment. Calling the result a forecast attributes to expectation a figure that is substantially about the option market’s own mechanics.

Neither kind of volatility predicts. Historical volatility describes what happened, and periods of high variation are followed by periods of high variation often enough to be noticeable and not reliably enough to be depended on. Implied volatility describes what option prices currently embed, which is a fact about prices now. Neither is a statement about what a price will do, and both are routinely read as though they were.