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# chapter4/3 data quality and models

Chapter 4

#### Data Quality and Models

It is important to note all models are based on the premise that historical volatility represents future volatility, and that volatility will remain constant over the term of the option. However, past performance does not guarantee future results. Stocks often experience periods of unusual activity. As a result, it may not make sense to measure historical volatility over the same time period when pricing an option. If a stock has traded between 40 and 45 dollars for one year, then jumps to \$55 over the course of 2 weeks, does it make sense to use historical volatility based on a year's worth of pricing data to determine the theoretical price of an option that expires in one month? This question cannot be answered with certainty, unless of course, you can predict the future.

The computation of implied volatility requires accurate pricing which is not always available. There are three significant quoted prices for an option: the bid price, the ask price, and, if the option has traded, the last price. Options are derivative products, their prices are derived from the price of the underlying security, therefore, option prices change as the price of the underlying security changes, even if they do not trade. If a stock price is changing frequently and the option is not trading, then the last price of the option is of little use when computing the implied volatility. A common approach to computing implied volatility is to take the midpoint of the bid price and the ask price of the option, since these prices are updated even in the absence of trading.

The bid and ask can be a relatively large percentage of the stock, particularly for lower priced stocks. This can have a significant impact on the accuracy of the implied volatility computation. For example, an at the money option on an active \$3 stock typically trades with a 5 cent bid and ask spread. If the bid price is 10 cents and the ask price is 15 cents, the bid and ask differ by a whopping 33%. The implied volatility will be significantly different if 10 cents is used versus 15 cents. Even taking the mid point of the bid and ask has a wide margin of error.

The computation of theoretical prices and implied volatility are subject to a wider range of error when there is little or no volume in the underlying stock or the options. These errors can be compounded when option prices are very low, as is typical with very short term or out of the money options. The accuracy of theoretical computations is also adversely effected by large spreads, which are typical of long term, out of the money options.

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