The Latent Inadequacies of Assuming a Normal Distribution

The implementation of a standard normal distribution is inherently flawed as it rejects the inexorable absence of randomity in securities. Trends, patterns, and probabilistic models predict the delineation between various price points of which is subject to exploitation by traders and statisticians whom institute a custom curve designed of adherence to the said parameters. John Bender states in Stock Market Wizards by John Schwager, The standard approach, which is based on the Black-Scholes formula, assumes that the probability distribution will conform to a normal curve “[the familiar bell-shaped curve frequently used to depict probabilities, such as the probability distribution of IQ scores among the population]. The critical statement is that it ‘assumes a normal probability distribution.’ Who ran out and told these guys that was the correct probability distribution? Where did they get this idea? [The Black-Scholes formula (or one of its variations) is the widely used equation for deriving an option's theoretical value. An implicit assumption in the formula is that the probabilities of prices being at different levels at the time of the option expiration can be described by a normal curve*—the highest probabilities being for prices that are close to the current level and the probabilities for any price decreasing the further above or below the market it is.] A probability distribution is simply a curve that shows the probabilities of sonic event occurring—in this case, the probabilities of a given stock being at any price on the option expiration date. The x-axis (horizontal line) shows the price of the stock. The y-axis (vertical line) shows the relative probability of the stock being at different prices. The higher the curve at any price interval, the greater the probability that the stock price will be in that range when the option expires. The area under the curve in any price interval corresponds to the probability of the stock being in that range on the option expiration date.  A trader who is able to come up with a more accurate estimate of the probability distribution would have a strong edge over other traders.”