# Option Values and Volatility

Volatility, as will be discussed in detail in Chapter 7, is a measure of stock price fluctuation without regard to direction. The greater the volatility, the higher is an option’s price. Volatility is stated in percentage terms. For example, the past price action of a particular underlying security is said to “trade at 25 percent volatility,” or an
option’s theoretical value is said to be calculated “using 30 percent volatility.”

Figure 3-5B gives an example of how theoretical values of an at the-money 100 Call change as the volatility changes from 0 to 50 percent,assuming a stock price of \$100, a 4 percent interest rate, and no dividends. The upper line demonstrates values at 90 days to expiration,and the lower line shows values at 45 days to expiration. The figure shows that changing volatility is nearly linear for at-the-money options regardless of time to expiration.

Extreme Volatility:Extreme volatility means that option values rise to their limit. The limit of value for a call is the stock price because no rational investor would pay more for a call than for the stock. For a put, the limit of value is the strike price because prices cannot fall below zero. Figure 3-6 shows how prices of at-the-money calls rise when volatility rises to 1,000 percent.

Figures 3-5A and 3-6 both illustrate an at-the-money call but look different because of the range on the x axis. The range of volatility for Figure 3-5 is 0 to 50 percent, and for Figure 3-6 it is 0 to 1,000 percent.Dynamic Markets:The discussion to this point has assumed that only one component of value changes while the rest stay constant. In the real world, of course, more than one component changes at a time.

Many market forecasts do not generally call for a stock to move up or down on the same day while volatility remains unchanged. Rather, stock prices and volatility both can change over a period of several days or weeks, and changes in each of the three factors—stock price, time, and volatility—will affect an option’s price differently. While interest rates do change, the changes are typically small, and the impact on option values is negligible.

Dividend changes typically occur only once each year and are somewhat predictable, although special dividends, dividend suspensions,and deviations from past practices can cause option prices to “adjust” when the news hits the market. The topic of dividends is discussed in Chapter 6. Three-Part Forecasts While stock traders need to focus only on the direction of the stock price, option traders must add two components—a forecast for time a forecast for the level of implied volatility.

Chapter 7 discusses the topic of implied volatility in depth.Back to Table 3-1. If a forecast called for the stock price to rise from \$97 at 90 days to \$101 at 75 days, the 100 Call price might be expected to rise from 4.97 to 6.49. If, however, the stock price rise was expected to take 15 days longer, until 60 days to expiration, then the call would be expected to rise to 5.82, an outcome that is 0.67, or approximately 40 percent, less profitable.

And what if volatility changed? The trading scenarios discussed next examine a forecast with changing volatility.Trading Scenarios:Assume that Joe is anticipating a bullish earnings report from Jumpco,a children’s playground equipment distributor. The report is due in three days, and Joe believes that good news could send the stock price,currently \$67, up 10 percent to \$74 shortly thereafter.

To analyze howmuch he might make if he buys the Jumpco April 75 Call and if his forecast proves accurate, Joe creates Table 3-7. He starts with what he knows, a stock price of \$67, a strike price of 75, interest rates of 4 percent, dividends of 2 percent, and 16 days to April expiration. Seeing that the market price of the call is 50 cents, Joe calculates the implied volatility at 38 percent using the method that will be described in Chapter 7.

Scenario 1 in Table 3-7 forecasts a stock price rise from \$67 to \$74, or approximately 10 percent, in seven days, with volatility staying at 38 percent. Given these assumptions, Joe estimates that the Jumpco April 75 Call will rise 320 percent to 2.10. While such a scenario is enticing, Joe does not immediately buy a call because he also realizes that market action might differ from his forecast.

Even if his stock-price and time forecasts are accurate, Joe wants to consider the consequences of implied volatility declining. A little research, as explained in Chapter 7, shows that 25 percent is a more typical level of volatility for Jumpco options than the current level of 38 percent. Joe therefore creates Scenario 2 to estimate the impact of volatility returning to 25 percent.