828 Part VI: Measuring and Trading Volatility 
make the move to profitability (or not make the move into loss territory, if you're sell­
ing options). This is where historical volatility plays a big part, for it is the input into 
the probability calculator. In fact, no probability calculator will give reasonable pre­
dictions without a good estimate of volatility. Please refer to the previous chapter for 
a more in-depth discussion of probability calculators and stock price distributions. 
The use of probability analysis also mitigates some of the problems inherent in 
the method of selection that compares implied and historical volatilities. If the prob­
abilities are good for success, then we might not care so much whether the options 
are currently in a low percentile of implied volatility or not (although we still would 
not want to buy volatility when the options were in a high percentile of implied 
volatility and we would not want to sell options that are in a low percentile). 
In using the probability calculator, one first selects a strategy (straddle buying, 
for example, if options are cheap) and then calculates the break-even points as 
demonstrated in the previous section. Then the probability calculator is used to 
determine what the chances are of the underlying instrument ever trading at one or 
the other of those break-even prices at any time during the life of the option position. 
It was shown in the previous chapter that a Monte Carlo simulation using the fat tail 
distribution is best used for this process. 
An attractive volatility buying situation should have probabilities in excess of 
80% of the underlying ever exceeding the break-even point, while an attractive 
volatility selling situation should have probabilities of less than 25% of ever trading 
at prices that would cause losses. The volatility seller can, of course, heavily influence 
those probabilities by choosing options that are well out-of-the-money. As noted 
above, the volatility seller should, in fact, calculate the probabilities on several dif­
ferent striking prices, striving to find a balance between high probability of success 
and the ability to take in enough premium to make the risk worthwhile. 
Example: The OEX Index is trading at 650. Suppose that one has determined that 
volatilities are too high and wants to analyze the sale of some naked options. 
Furthermore, suppose that the choices have been narrowed down to selling the 
September options, which expire in about five weeks. The main choices under con­
sideration are those in Table 39-2. The option prices in this example, being index 
options, reflect a volatility skew (to be discussed later) to make the example realistic. 
The two right-hand columns should be rejected because the probabilities of 
the stock hitting one or the other of the striking prices prior to expiration are too 
high well in excess of the 25% guideline mentioned earlier. That leaves the 
September 500-800 strangle or the September 550-750 strangle to consider. The 
probabilities are best for the farthest out-of-the-money options (September 500-
800 strangle), but the options are selling at such small prices that they will not pro-