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## CHAPTER 2:  BINOMIAL MODEL

2.1  Overview

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n the one-period binomial model, there is a current stock price, say S.  The stock price can either have an "uptick" (i.e., move to price Su > S), or have a "downtick" (i.e., move to a price Sd < S).  Here, u is a number greater than 1, and d is a positive number less than 1.  The option expires (or matures) at the end of the period.  This is depicted in Figure 2.1.

To get an idea of how European options are priced, we will explore two important approaches to the valuation problem using two examples:  the Riskless Hedge Example (topic 2.2) and the Synthetic Option Example (topic 2.3).  In the first example, we point out the fundamental problem in valuing options, and explain how these approaches help us solve the valuation problem.  The general one-period analysis for both examples is presented in topic 2.4, Call Option Valuation: A Riskless Hedge Approach, topic 2.5, Put Option Valuation:  A Riskless Hedge Approach, and topic 2.6, Option Valuation:  A Synthetic Option Approach.

We then use this general one-period analysis to identify in topic 2.7, a very general  principle known as the Risk-Neutral Valuation Principle.  In topic 2.8, we consider how this principle can be reconciled with CAPM.  We conclude the one-period analysis with a study of an important arbitrage relationship that must hold among the stock price, put and call option prices and the strike price.  This relationship is known as the Put-Call Parity Relation, and is developed in topic 2.9.