In this section, we consider a symmetric random walk, which is the discrete-time version of Brownian motion, introduced in Chapter 3 of Volume II. We derive several properties of a random walk, and shall ultimately see that Brownian motion has similar properties. In particular, in this chapter we consider first passage times and the reflection principle for a symmetric random walk. For Brownian motion, these concepts are used in the computation of the price of a variety of exotic options.
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