Options  |  DEC 1998

Using Normal Distribution For Writing Options by Mark Vakkur, MD

How can you go about selecting the best strike price for writing an option? Perhaps no branch of knowledge has been as abused or misunderstood as statistics. Yet, without some grounding in basic statistical concepts, our ability to trade profitably is limited. Trading does not require a doctorate in mathematics, but mastering some basic fundamentals should help stack the odds in our favor. This is particularly helpful in developing an options trading strategy. Many trading software packages automatically generate statistics on any tradable or indicator; often included are mean, median, and standard deviation. Although most people understand that a standard deviation is a measure of how volatile an asset is, beyond that, their understanding is fuzzy. Yet a wealth of information is buried in that number. NORMAL DISTRIBUTION To understand the standard deviation, you must first have some grasp of what the normal distribution is. Although entire academic careers have been devoted to arguing whether the market is random, if you were to graph the percentage change in the stock market over any period and then graph the frequency of each percentage change by interval as a histo-gram, you would get a bell curve. This bell curve conforms closely to what one would predict mathematically if the market were a random process with a slight upward bias. For example, if you were to measure the four-week percentage change in the Standard & Poor’s 100 index (OEX) for all rolling four-week periods (close of the last trading day of the week through the close of the last trading day of the next week) from October 1976 through December 1995, you would get a distribution with a mean of 0.7% and a standard deviation of 3.9%.

by Mark Vakkur, M.D.