Using Volatility and Price Changes in Options Trading Strategies

Why might a trader want to estimate daily or weekly price changes from an annual volatility? Volatility is one input into a theoretical pricing model that cannot be directly observed. Yet many option strategies, if they are to be successful, require a reasonable assessment of volatility. Therefore, an option trader needs some method of determining whether his expectations about volatility are being realized in the marketplace.

volatility-price-changesUnlike directional strategies, whose success or failure can be immediately observed from current prices, there is no such thing as a current volatility. A trader must usually determine for himself whether he is using a reasonable volatility input into the theoretical pricing model.

Let’s say, we estimated that for a $45 stock with an annual volatility of 37 percent, a one standard deviation price change is approximately $1.04. Suppose that over five days we observe the following daily settlement price changes:

+$0.98, –$0.65, –$0.70, +$0.25, –$0.85

Are these price changes consistent with 37 percent volatility?

We expect to see a price change of more than $1.04 (one standard deviation) about one day in three. Over five days, we would expect to see at least one day, and perhaps two days, with a price change greater than one standard deviation. Yet, during this five-day period, we did not see a price change greater than $1.04 even once. What conclusions can be drawn from this? One thing seems clear: these five price changes do not appear to be consistent with 37 percent volatility.

Before making any decisions, we ought to consider any unusual conditions that might be affecting the observed price changes. Perhaps this was a holiday week, and as such, it did not reflect normal market activity. If this is our conclusion, then 37 percent may still be a reasonable volatility estimate. On the other hand, if we can see no logical reason for the market being less volatile than predicted by 37 percent volatility, then we may simply be using the wrong volatility. If we come to this conclusion, perhaps we ought to consider using a lower volatility that is more consistent with the observed price changes.

If we continue to use a volatility that is not consistent with the actual price changes, then we have the wrong volatility. If we have the wrong volatility, we have the wrong probabilities. And if we have the wrong probabilities, we are generating incorrect theoretical values, thereby defeating the purpose of using a theoretical pricing model in the first place.

Admittedly, five days is a very small number of price changes, and it is unlikely that a trader will rely heavily on such a small sample. If we flip a coin five times and it comes up heads each time, we may not be able to draw any definitive conclusions. But if we flip the coin 50 times and it comes up heads every time, now we might conclude that there is something wrong with the coin. In the same way, most traders prefer to see larger price samplings, perhaps 20 days, or 50 days, or 100 days, before drawing any dramatic conclusions about volatility.

Exactly what volatility is associated with the five price changes in the foregoing example? Without doing some rather involved arithmetic, it is difficult to say. (The answer is actually 27.8 percent.) However, if a trader has some idea of the price changes he expects, he can easily see that the changes over the five-day period are not consistent with 37 percent volatility.