Traders must consider the existence of volatility skews when making forecasts. If out-of-the-money option strike O is trading at a higher implied volatility than at-the-money option strike A, for example, then as the underlying moves from strike A to strike O, there may be a tendency for the implied volatility of the call and put with strike O, which
is not at the money, to decrease and for the implied volatility of the call and put with strike A, which is now out of the money, to increase.

Consider the forecasting problem being addressed by Barb, an experienced XSP options trader. Assuming an XSP level of 132 and the option prices and market conditions in Table 7-7, Barb must first state her three-part forecast for the XSP level, for the time period, and for the implied volatility of the option she is considering buying.Barb is considering buying an XSP 126 Put with 25 days to expiration because she is bearish on the market and predicts that XSP will decline from 132 to 126 or lower in 10 days.

Barb also believes that implied volatility will remain constant. Her volatility forecast, however,raises a question.What does implied volatility will remain constant mean when there is a volatility skew? What implied volatility level should Barb use when estimating the value of the 126 Put? If XSP declines to 126 in 10 days,as Barb predicts, the 126 Put will have moved from six points out of the money to at the money.

If the level of implied volatility remains constant and the skew does not change, then the implied volatility of the 126 Put will decline from 23.52 to 20.83 percent. Table 7-8 shows the implications of this change.Column 1 shows the initial market conditions: The index level is 132, there are 25 days to expiration, the implied volatility is 23.52 percent, and the price of the 126 Put is 0.95.

Column 2 estimates a price of 2.30 for the 126 Put, assuming an index level of 126, 15 days to expiration, and the implied volatility of the 126 Put unchanged at 23.52 percent. Column 3 estimates a price of 2.00 for the 126 Put, assuming the same conditions as column 2 but with an implied volatility decline to 20.83 percent. This difference means that had Barb bought the put for 0.95, she would make 1.05 per option instead of 1.35 per option.

Whether this difference is sufficient to dissuade Barb from making this trade is a subjective decision that only she can make.Nevertheless, even if Barb is confident of her forecasts for the index level and the time period, the volatility skew could have an impact on her decision.The conclusion from this example is that if other factors remain constant, the existence of implied volatility skew tends to be a disadvantage for buyers of out-of-the-money options.

Other factors, of course, are rarely equal. There could be a change in the overall level of implied volatility, or there could be a change in the slope of the volatility skew. Changes in either or both of these market conditions could produce favorable or unfavorable results for a particular option strategy. Consequently, option traders must consider the overall level of implied volatility and the volatility skew, if any.

Summary Volatility is a measure of price change without regard to direction. Mathematicians, option traders, and the market each view volatility somewhat differently. Mathematically, volatility is the annualized standard
deviation of daily returns. A volatility percentage, such as 35 percent, is an annual standard deviation, which can be converted to another time period by multiplying it by the square root of time.

There are many terms that describe volatility. Historic volatility is a measure of stock-price fluctuations during some defined period in the past. Expected volatility is a trader’s prediction of what volatility will be in the future and is used to calculate theoretical values. Realized volatility is a measure of actual stock-price fluctuations between now and some point in the future and is unknown.

Implied volatility justifies the current market price of an option.Implied volatility is the common denominator of option prices. Just as the price-earnings ratio makes possible comparisons of stock prices over a range of variables such as total earnings and number of shares outstanding, implied volatility facilitates comparisons of options on different underlying instruments and comparisons of the same option at different times.

Theoretical value of options is a statistical concept only. Traders should focus on relative value, not absolute value. The terms overvalued and undervalued describe a relationship between implied volatility and expected volatility. Two traders could differ in their opinion of the relative value of the same option if they had different market forecasts and trading styles.