Based on your assumption of 32 volatility in the stock over the next year, you calculate the value ofthe 45 level calls and puts to be $10.44 and $3, respectively. The second column presents a situation in which the market prices of these options are $8.94 for the calls and $1.44 for the puts, resulting in an implied volatility of 22. Thus, by your assessment, the calls are undervalued by $1.50 and the puts are undervalued by $1.56. By contrast, the third column represents market prices for the calls at $1.68 more than you think. that they are worth and market prices for the puts at $1.69 overpriced, reflecting an implied volatility of 42.
Understanding the differences between implied and forecast volatility is critical for the serious options investor or trader. This knowledge is the basis for selecting the most appropriate option position to implement. For any market expectation that you might have (such as bullish, bearish, or neutral), there will be several strategies available to exploit that expectation with limited risk. In evaluating these alternatives, you will find a strategy that involves purchasing options more appealing if those options appear to be underpriced, just as a strategy for selling options would be more appealing if the options appeared to be overpriced. Similarly, you would not want to use these strategies under conditions where underpriced options were being sold or overpriced options needed to be purchased.
Volatility's Impact on the Pricing Model
We discussed the relationship of volatility to the value ofan option in general terms. In so doing, we have learned the following:
1. Volatility is a significant factor in pricing an option.
2. Theoretical pricing through the use of pricing models is sensitive to small changes in volatility inputs.
3. Increased volatility translates to higher option prices, with the reverse being true for decreased volatility.
That said, a rigorous examination ofthe detailed mathematics of the various pricing models is beyond the scope of this blog. In the judgment of the authors, this knowledge is unnecessary for gaining useful mastery of the concepts involved. Needless to say, some familiarity with these models is useful. We will now turn our attention to the following issues:
1. How pricing models account for price movement in the underlying issue
2. How volatility is expressed and what that expression represents
3. How the models use that information to establish an option's theoretical price
Read More: The Importance of Implied Volatility
