Trading Real Options Using Model Prices
The problems associated with applying a theoretical option valuation model to the real world have obviously not prevented virtually every serious option trader from doing just that. But they use th...Trading Real Options Using Model Prices
The problems associated with applying a theoretical option valuation model to the real world have obviously not prevented virtually every serious option trader from doing just that. But they use the model in ways that are more consistent with the second wise man’s approach than with the model's theoretical underpinnings.
Few investors use the model mainly for finding mispriced options that can be arbitraged against the underlying stock. A major reason for this is that no one feels confident they know the true volatility. Estimating volatility from a sample of past prices is a routine exercise, but you can't be sure the future will be exactly like the past. Based on historical volatility, for example, the price change that occurred on October 19, 1987 was essentially impossible.
Option traders normally pay more attention to the implied volatility that sets the model option value equal to the market price. This is easy to compute and, in principle, gives a direct reading of the market's volatility estimate. But it has the disadvantage that you have to assume the market ispricing the option according to the model, which rules out using implied volatility to detect mispricing.
Another problem is that, because volatility is the one input to the model that can't be directly observed, implied volatility actually serves as a free parameter. It impounds expected volatility and everything else that affects option supply and demand but is not in the model. If a change in the tax law makes writing options less attractive, for instance, the price effect will show up in implied volatility. Any time the market prices options differently from a liven model, for any season, the implied volatility derived from that model is not going to be the market's true volatility estimate.
Generally, implied volatilities differ across strike prices in a regular way, even though it is logically inconsistent for a stock to have more than one volatility. Out-of-the-money options typically have higher implied volatilities than at and in-the-money options, puts are often priced on different volatilities than calls, and the patterns vary from time to time. This is evidence that the market does not price options strictly according to the model, or at least not according to the particular model that produces the differing implied volatilities.
Traders don’t care much about these problems. In fact, they seldom think about the technical details of the computerized models they use, or even about whether they are pricing European or American options. Instead, they tend to take whatever theoretical model happens to be available on the computer and treat the implied volatility it produces for a particular option as a kind of index of how the option is currently being priced in the market relative to other options and relative to how it was priced at other times.展开 |
|
转播
