Everything Changes over Time, Including Volatility

Volatilities change over time, just as prices do. The SV of a market and the IVs of its associated options react to the same news and market developments as does the price of the asset, but they do not necessarily react in the same way or to the same extent. When SV and IVs diverge considerably, as for instance they sometimes do before an important supply/demand report is issued, we can listen for the sound of opportunity knocking.

In such a case, the IVs of the options may rise well above the underlying market’s SV and we can look around for cautious ways to sell this excess volatility,which will be represented in the market by relatively high option prices.Conversely, when SV is depressed and the IVs of the options are even more depressed, it’s generally profitable to look at buying some selection of longer-term options, which, given the low volatilities, will tend very strongly to be underpriced to some degree.

If we trade only in assets, we are completely dependent on the movement of the asset’s price for our profit. This is not the case when trading options,whether by themselves or in combination with their underlying assets.Trades are commonplace that reap a tasty profit solely from changes in IV,even when the price of the asset does nothing or moves in slightly the wrong direction over a period of time.

Further, when we use options in our trading, we can on many occasions enlist the most inexorable force in the universe on our side. That force is time, and it is a very powerful ally indeed.One enormously pleasant thing about volatilities, SV especially, and especially in futures markets, is that they tend to persist within a measurable range for long periods of time, and during these periods they tend even more strongly to revert to the mean semiregularly.

When a market’s SV has varied from 8% to 14% consistently for years, under a variety of market conditions, through euphoria and calamity, the trader who observes SV approaching either end of the range can, much more often than not, construct a trade having a high positive expectation.Figures 3.6 through 3.10 illustrate the persistence of SV ranges in five widely different futures markets from 1998 into 2002.

For these examples,I chose the 60-day SV of the nearest contract, but it doesn’t make a whole lot of difference what term of volatility we examine. Figure 3.11 is the 120-day SV for Swiss franc futures, and you’ll notice a clear degree of symmetry between that figure and its 60-day cousin, Figure 3.10.Implied Volatility and Delta:The study of volatility doesn’t only suggest possible trading strategies and potentially advantageous situations.

We’re interested in figuring the expectation of trades we might enter, are we not? Absolutely we are, and the notion of volatility provides us with a couple of ways to do this. The more complex way is to perform a series of calculations using the various formulae of whichever model we may be using. The simpler way is just to use a couple of the results of these calculations, which are almost universally available from the same folks from whom we obtain SVs (if we don’t calculate them ourselves, of course).

To find an approximate probability of an asset’s price moving from A to B over a known period of time, we can first apply the measure called delta.In the simple lognormal pricing model, the delta of the X-strike call option turns out to be a decently close approximation of the probability of the future price of an asset being at or above X when the option expires. Suppose that the price of an asset is 50, and that the actual price of a 90-day, 60-strike call option is 1.00. If we calculate this option’s 90-day IV, along the way we obtain the delta of the option as a free bonus.

If the delta of the option turns out to be 0.20, then we can say that the rough probability of the asset’s price being above 60 in 90 days’ time is equal to 0.20. Stated another way, the asset price 90 days from now can be expected to be below 60 in about 80 cases out of 100.Delta has another practical use. By its definition in the model, it is the measure of how much an option’s price can be expected to change if the price of the underlying asset changes by one unit.

In the preceding example,if the price of the asset would move from 50 to 51 tomorrow, the model would predict the price of the 60-strike call to move to 1.20. If the asset price moved down to 49, this option’s delta indicates we would expect the price of the call to fall to 0.80.If you’re wondering about the delta of the underlying asset itself, it’s always 1.00, and this is perfectly sensible. Every time the price of an asset moves one unit, it moves exactly one unit, whereas the price of any of its options will only move a fraction of one unit (with rare exceptions).