Volatility: Theory vs. Reality
In Tuesday’s (August 3) commentary I showed the following table:
| # of Days | Volatility | Model Multiplier | Actual Multiplier |
|---|---|---|---|
| 1 | .89% | 1.00 | 1.00 |
| 4 | 1.62% | 2.00 | 1.82 |
| 9 | 2.3% | 3.00 | 2.58 |
| 16 | 2.9% | 4.00 | 3.29 |
| 25 | 3.58% | 5.00 | 4.00 |
| 36 | 4.2% | 6.00 | 4.75 |
| 49 | 4.9% | 7.00 | 5.54 |
| 64 | 5.57% | 8.00 | 6.26 |
| 81 | 6.26 | 9.00 | 7.03 |
| 100 | 6.84% | 10.00 | 7.68 |
If you plot the Model Multipliers and the Actual Multipliers you get the following chart:
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| Figure 1. Model and Actual Multipliers
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Note that the Actual Multipliers grow more slowly than the Model Multipliers. The fact that the volatilities do not grow as fast as they should under the model tells you that the S&P has a tendency to reverse, and not to trend as much as it should under the model. Because it trends less, the S&P will, for instance, have less of a chance of being 20% from its current price than the model thinks, which will affect option values.
For this market, the model option values, which depend on the underlying market behaving as it “should” under the model, are too high. To get a firmer intuitive grip on this, consider out-of-the-money (OOTM) option: Because the S&P tends to trend less and reverse more than the model assumes, the OOTMs have less of a chance of expiring in-the-money than the model thinks. So even at “fair” prices, the OOTMs are overpriced.
The table above is one you should create for any underlying whose options you trade. It will tell you if the underlying has a tendency to trend more than the model thinks (in which case the multipliers will be greater than the Model Multipliers), less the model thinks (as above), or just as much as the model thinks (if the Actual Multipliers are about equal to the Model Multipliers). This information will tell you if the model prices overestimate, underestimate or properly estimate the true values of the underlying’s options.