Abstract
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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© 2005 Springer Science+Business Media New York
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Shreve, S.E. (2005). Random Walk. In: Stochastic Calculus for Finance I. Springer Finance. Springer, New York, NY. https://doi.org/10.1007/978-0-387-22527-2_5
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DOI: https://doi.org/10.1007/978-0-387-22527-2_5
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-24968-1
Online ISBN: 978-0-387-22527-2
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