Lesson 3: If we simulate lots of potential price paths and tabulate each final stock price with a little square, we can build a histogram. A histogram is a probability distribution.

To understand stock options and their value, you need to understand probability distributions. But not everyone has a clear understanding of what a probability distribution is and what it represents.

The easiest way to understand probability distributions is to build one.

Given a forecast of typical return and a forecast of how much we expect the stock price to jump around, we can simulate lots of different potential paths the stock price might follow over a given time horizon.

For each potential price path, we can tabulate the end-of-horizon price with a little square. As we accumulate little squares, we build a histogram. The histogram is a probability distribution.

To build a histogram from potential price paths, let's run a simulation.

(If you haven't already, to open the simulator, click the link at top right of this page. To jump quickly back and forth between the lesson and the simulator, hold down the Alt key on your keyboard and tap the Tab key.)

Type 3 in the Run Lesson Number box. Click Run Lesson Number.

For the first one hundred price- path simulations, the simulator draws the price paths. Then it speeds up. It doesn't draw the path. It just tabulates the final price with a little square.

Does the shape of the histogram we've built look like anything you've seen before? How about if you tilt your head to the left?

To continue to the next lesson, click arrow at top right of this page or...

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Option Pricing: Black- Scholes Made Easy
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