CHAPTER 2: BINOMIAL MODEL
2.1
Overview

n
the oneperiod 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 oneperiod
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 oneperiod analysis to identify in topic 2.7, a very
general principle known as the RiskNeutral
Valuation Principle. In topic
2.8, we consider how this principle can be reconciled with CAPM.
We conclude the oneperiod 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 PutCall Parity
Relation, and is developed in topic 2.9.