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+The Distribution of 
+Stock Prices 
+Much of the work that has been done in statistics and related areas regarding the 
+stock market has made the assumption that stock prices are distributed normally, or 
+more specifically, lognonnally. In actual practice, this is usually an incorrect assump­
+tion. For the option strategist, this means that some of the things one might believe 
+about certain option strategies having an advantage over certain other option strate­
+gies might be incorrect. In this chapter, a number of facts concerning stock price dis­
+tribution will be brought to light, including how it might affect the option strategist. 
+MISCONCEPTIONS ABOUT VOLATILITY 
+Statistics are used to estimate stock price movement (and futures and indices as well) 
+in many areas of financial analysis. Many authors have written extensively about the 
+use of probabilities to aid in choosing viable option strategies. Stock mutual fund 
+managers often use volatility estimates to help them determine how risky their port­
+folios are. The uses are myriad. Unfortunately, almost all of these applications are 
+wrong! Perhaps wrong is too strong a word, but almost all estimates of stock price 
+movement are overly conservative. This can be very dangerous if one is using such 
+estimates for the purposes of, say, writing naked options or engaging in some other 
+such strategy in which volatile stock price movement is undesirable. 
+As a review for those not familiar with mathematical distributions, the lognor­
+mal distribution is what's commonly used to describe stock prices because its shape 
+is intuitively similar to the way stocks behave - they can't go below zero, they can rise 
+to infinity, and most of the time they don't go much of anywhere. On top of that, the 
+distribution's shape is based on the historical volatility of the underlying instrument. 
+In a lognormal distribution (and normal distribution, too), stocks remain within 3 
+standard deviations of their current price 99. 7 4% of the time. A standard deviation 
+783