# On the market - implied volatility.

On The Market--Implied Volatility

Since, at any one time, there are always many different options trading on the same commodity, an option trader would like to have some way of judging the relative price of each option, not necessarily in dollar terms, but in terms of value.

For example, suppose there are two different call options, A and B, available on the same commodity. Suppose the price of call A is \$100, and the price of call B is \$50. An investor who believes that the price of the commodity will rise can buy either of these calls, and if the commodity price rises sufficiently, he will make a profit. (Depending on the exercise prices and expiration dates involved, both options may not profit by an equal amount. Nevertheless, the purchase of a call will result in a long market position.) How can the investor determine which option is a better value?

One way to approach the problem is by looking at the total dollar outlay. Based on this, call B must be a better investment because it requires an outlay of only \$50 for a long market position, while call A requires an outlay of \$100. But is the initial outlay the only consideration? The investor also has to consider what the return on his investment is likely to be. A common method of gauging the relative prices of options, based on the return on the investment, is to look at the option's implied volatility.

Suppose we are using a theoretical pricing model such as the Black-Scholes model to evaluate an option. In order to use the model we need to feed several inputs into the model: exercise price, time to expiration, underlying commodity price, interest rates, and volatility. Having done this, we can generate a theoretical value for the option. Suppose that we have evaluated call option A, which is trading for \$100, and, based on our inputs into the model, we find that the option has a theoretical value of \$125. How can we account for the fact that we think the option is worth \$125, while the marketplace apparently thinks it is worth only \$100?

One way to answer the question is to assume that everyone in the marketplace is using the same theoretical pricing model we are. If that is true, then the discrepancy between our value of \$125 and the marketplace's value of \$100 must be caused by a difference in one or more of the inputs into the model. Note, however, that the first four inputs, time to expiration, exercise price, underlying commodity price, and interest rates, can be readily observed, so there is unlikely to be a difference of opinion about these inputs. We can therefore conclude that the \$25 difference in the two prices is the result of a different volatility.

If we hold all other inputs constant, and change only the volatility input, we will find that there is some volatility which will yield a theoretical value identical to the price of the option in the marketplace. Suppose we do this and find that at a volatility of 23 percent, the theoretical value of call A is exactly \$100.

We say that at a price of \$100 call A has an implied volatility of 23 percent. In other words, the implied volatility is the volatility we would have to feed into a theoretical pricing model in order to generate a theoretical value exactly identical to the price of the option in the marketplace.

Since there are many options trading on the same commodity, we can calculate the implied volatility for every option, and then compare these numbers to decide which options are cheapest and which options are most expensive in theoretical terms. For example, suppose we calculate the implied volatility for call B, which is trading at \$50, and find that its implied volatility is 26 percent. Initially it appeared that call B was cheaper than call A because of its lower dollar price. But in terms of what we expect to get back on our investment, call A is actually cheaper because its implied volatility of 23 percent is three percentage points lower than the implied volatility of call B.

Does this mean that the purchase of call A will result in a profit while the purchase of call B will result in a loss? We can't answer that question because we don't know what the future volatility of the commodity will actually be. If the future volatility turns out to be 30 percent, the purchase of either option will, in theory, result in a profit. If the future volatility turns out to be 20 percent, the purchase of either option will, in theory, result in a loss. Nevertheless, in the long run we will do better purchasing call A rather than call B either because our profit is likely to be greater when we are right, or our loss is likely to be less when we are wrong. By purchasing the option with the lowest implied volatility, or selling the option with the highest implied volatility, we are making the most of our investment opportunities.

Experienced option traders learn to rely on an option's implied volatility, rather than its dollar price, as a better reflection of the option's price in the marketplace. They know that intelligent investing is not only a question of today's cash outlay, but also of tomorrow's payback.

Shelly Natenberg, president, Professional Option Consultants.
No portion of this article can be reproduced without the express written permission from the copyright holder.