804 Part VI: Measuring and Trading Volatility 
If one is interested in computing the probability of the stock being above the 
given price, the formula is 
P (above) = 1 - P (below) 
In the above formula, Vt = v✓t where t is time to expiration in years and v is 
annual volatility, as usual. 
This formula is quite elementary for predictive purposes, and it is used by 
many traders. This calculator can be found for free at the Web site www.option­
strategist.com. Its main problem is that it gives the probability of the stock being 
above or below the target price at the end of the time period, t. That's not a totally 
realistic way of approaching probability analysis. Most option traders are very con­
cerned with what happens to their positions during the life of the option, not just at 
expiration. 
Example: suppose a trader is a seller of naked put options. He sells $OEX October 
550 puts naked, with $OEX currently trading at 600. He would not normally just walk 
away from this position until October expiration, because of the large risk involved 
with the sale of a naked option. There are essentially three scenarios that can occur: 
1. $OEX might never fall to 550 by expiration. In this case, he would have a 
very comfortable trade that was never in jeopardy, and the options would 
expire worthless. 
2. $OEX might fall below 550 and remain there until expiration. In this case, 
he would surely have a loss unless $OEX were just a tiny bit below 550. 
3. $OEX might fall below 550 at some time between when the trade was estab­
lished and when expiration occurred, but then subsequently rally back above 
550 by the time expiration arrived. 
An experienced option trader would almost certainly adjust if scenario 3 arose, 
in order to prevent large losses from occurring. He might roll his naked puts down 
and out to another strike, or he might just close them out altogether. However, it is 
unlikely that he would do nothing. 
The simple probability calculator formula shown above does not take into 
account the trader's third scenario. Since it is only concerned with where the stock is 
at expiration of the options, only scenarios 1 and 2 apply to it. Hence the usage of this 
simple calculator is not really descriptive of what might happen to a trade during its 
lifetime. 
Let's assign some numbers to the above trade, so that you might see the differ­
ence. Suppose that the volatility estimate is 25%, there are 30 days until expiration, 
and the prices are as stated in the previous example: $OEX is at 600, and the strik-