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  PFE Chapter 26, Binomial option pricing page 1 CHAPTER 26: THE BINOMIAL OPTION PRICING MODEL *   Current version: July 18, 2005 Chapter contents  Overview..............................................................................................................................2 26.1. The binomial pricing model.......................................................................................6 26.2. What can you learn from the binomial model?........................................................11 26.3. Multi-period binomial model...................................................................................14 26.4. Advanced topic: Using the binomial model to price an American put...................19 Conclusion.........................................................................................................................24 Exercises............................................................................................................................25 *  This is a preliminary draft of a chapter of Principles of Finance with Excel . © 2001 – 2005 Simon Benninga ( benninga@wharton.upenn.edu ).  PFE Chapter 26, Binomial option pricing page 2 Overview In Chapter 25 we discussed the Black-Scholes formula, the most common method for  pricing options. In this chapter we discuss the other major technique for determining option  prices, the binomial option pricing model . This model gives some insights into how to price an option, and it’s also used widely (though not as widely as the Black-Scholes equation). The basis of the binomial model is a very simple description of stock price uncertainty. Here’s an example: Suppose the current stock price of MicroDigits (MD) is $100. What can you say about the MD stock price one year from now? The binomial model  assumes that the  price of the stock in one year will either go up  by a certain percentage or down  by a certain  percentage. Here’s an example: 12345678910111213141516 ABCDUp30%Down-10% MD stock price one year from now 130<-- =100*(1+B2)10090<-- =A7*(1+B3) Date 0todayDate 1one year from now MD stock price returns 0.3<-- =C6/A7-1-0.1<-- =C8/A7-1 Date 0todayDate 1one year from now BINOMIAL MODEL FOR MICRODIGITS (MD) STOCK PRICE    PFE Chapter 26, Binomial option pricing page 3 In the example above the MD stock price will either go up by 30% or down by 10% one year from today. This means that the return  on the stock will be either 30% or -10% (cells C13 and C15). It is difficult to believe that such a simple description of stock price uncertainty could be useful. However, if we extend the model to more periods, it turns out that the binomial model can describe a wide range of stock price behaviors. In the example below we assume that the  price of MD stock goes up in each of the next two years by 30% or goes down by 10%. This means that there are three possible outcomes for the stock price at Date 2: It can be either $169, $117, or $81. 12345678910 ABCDEFUp30%Down-10%169<-- =C6*(1+B2)130100117<-- =C6*(1+B3)9081<-- =C8*(1+B3) Date 0todayDate 1one year from nowDate 2two years from now TWO-PERIOD BINOMIAL MODEL FOR MICRODIGITS (MD) STOCK PRICE  If we extend the model to more periods, we’ll get a wide range of possible prices and returns. In the spreadsheet below we look at stock prices after 10 periods:  PFE Chapter 26, Binomial option pricing page 4 123456789101112131415161718192021222324252627 ABCDEFGHIJKUp30%Down-10% Date012345678910 1378.581060.45815.73954.40627.49734.16482.68564.74660.74371.29434.41508.26285.61334.16390.97457.44219.70257.05300.75351.87169.00197.73231.34270.67316.69130.00152.10177.96208.21243.61100.00117.00136.89160.16187.39219.24117.00105.30123.20144.15168.6581.0094.77110.88129.73151.7872.9085.2999.79116.7665.6176.7689.81105.0859.0569.0980.8353.1462.1872.7547.8355.9643.0550.3638.7434.87 MULTIPERIOD BINOMIAL MODEL FOR MICRODIGITS (MD) STOCK PRICE  If you plot the stock return and the probabilities of the returns after 10 years, you get a graph such as the one below. 1   1  The mathematics required to produce such a graph are too much for this book. For further details see my book Financial Modeling , MIT Press (2 nd   edition, 2000).
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