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Quantitative Finance by Matt Davison

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Chapter 18

Pricing Options Using Binomial Trees

18.1 CHAPTER SUMMARY

In this chapter, we discuss a European option written on a very simple stock price model: one in which, at each sequence of time steps, the stock price can either rise or fall. Such models are termed binomial trees. We begin by considering a European call option written on a stock, which either goes up or down over a single period. We show how to hedge such an option to remove all risks from the resulting portfolio, and hence to have a price that is the same for everyone, whatever their risk preference. In the next section, we show that this argument could work, not just for a call but for any option written on the stock with this simple model. This allows us to introduce a ...

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