The binomial options pricing model is a method for valuing put and call options. We split the time until the option’s expiration date into a discrete number of steps (e.g. if the option matures in six months, a three-step binomial model divides this into three two-month periods) and assume the price of the underlying stock either moves up or down in each step. We represent this in a diagram called a “binomial price tree”, where each cell branches up and down into two subsequent cells, depending on whether the stock price rises or falls. Starting from the current stock price in the leftmost cell, we work rightwards to fill in the possible future stock prices. For each of the final stock prices in the cells at the end of the tree, we work out what the put or call is worth when it matures. Then we work back to the left, calculating the value of the option at earlier times, until we find its price today. In certain cases (e.g. an American put) we must consider whether it is best to exercise the option early as we do this.
I regularly tutor binomial options pricing to students taking MBA, MSc and undergraduate finance courses, and find it helpful to have blank templates available for the binomial tree diagrams. Here is a downloadable spreadsheet with empty binomial trees from one-step to four-step (XLS), which is ideal if you want to create work through the options price calculation in Excel. I have actually put two cells at each node, one for the underlying share price and one for the option itself — some lecturers prefer to fill these out on two separate trees. For copying and pasting into worksheets, or to fill in on an online whiteboard session, I use the following image files: click on each image to be taken to a full-sized version to save or copy.
One-step blank binomial options tree
Two-step blank binomial options tree
Three-step blank binomial options tree
Four-step blank binomial options tree
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