CHAPTER 2

Probability Distributions

Everyday life contains many examples of probabilities. The weather forecast may predict a 40% probability of rain showers for tomorrow. Those of you who have played poker or blackjack are familiar with the probabilities of drawing a particular card to make a hand successful. In this chapter we will briefly explore the mathematics of probabilities that allow us to quantify our expectations of a particular event’s occurrence. For options traders, this is critical and foundational information because the pricing of options is rooted in the probabilities of stock price movement.

THE GAUSSIAN DISTRIBUTION

You have probably come across the so-called “bell-shaped curve” either in school or in your business career. Mathematicians refer to this as a Gaussian distribution or a normal distribution. An example is shown in Figure 2.1. At any point on the curve, the height of the curve gives us the probability of that value’s occurring in the population under consideration. It is common for large sets of measurements of many objects to roughly fit the bell-shaped curve of the normal distribution. For example, let’s assume I measure the shoe size of every male in the city of Chicago and plot the number of size 9 shoes and the number of size 9½ shoes, and so on until I have a curve similar to Figure 2.1. In this hypothetical example, I measured the largest number of size 11 shoes. Thus, if I were to randomly pick out a man in Chicago, the probability of his ...