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A Course in Financial Calculus by Alison Etheridge

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2 Binomial trees and discrete parameter martingales

Summary

In this chapter we build some more sophisticated market models that track the evolution of stock prices over a succession of time periods. Over each individual time period, the market follows our simple binary model of Chapter 1. The possible trajectories of the stock prices are then encoded in a tree. A simple corollary of our work of Chapter 1 will allow us to price claims by taking expectation with respect to certain probabilities on the tree under which the stock price process is a discrete parameter martingale.

Definitions and basic properties of discrete parameter martingales are presented and illustrated in §2.3, and we see for the first time how martingale methods can be employed ...

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