## CHAPTER 3: BINOMIAL MODEL Two-Period Analysis

**3.1
Overview
**

I |

n
the one-period binomial model, there are only two possible terminal stock
values. In this chapter, we extend the binomial model to
two periods, where the stock value can move up or down in each period.
This means that there are two possible stock values at the end of the
first period and four possible values at the end of the second period.

We
derive the values of European options in topic
3.2, __Two-Period Binomial Model: European Option__.
These options can be exercised only at maturity. We then introduce you to
American options, where you can exercise the options either in period 1
or in period 2. American options
bring a lot of richness to the option pricing problem, and we start having to
consider puts and calls separately. Topic 3.3, __American
Call Option: Zero-Dividend Case__ examines the implications of the right to
exercise in both periods on the call valuation problem.
Put options are studied in topic 3.4 __American
Put Option: Zero-Dividend Case__.

Dividends
also complicate the American option pricing problem. We introduce dividends in
topic 3.5 __Dividends and American Options__
and apply the principles of the
two-period model to valuing European and American options in the topic 3.6, __Two-Period
European versus American Option Example__.
Finally, in topic 3.7, we apply the principles of the binomial option
pricing model to a popular "exotic" option called the __Asian
Option__.