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+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-