Lattice Methods

Binomial Lattice

One of the most powerful features of the binomial approach to option pricing is the ability to value complex options
One complex option is known as a digital option.

The digital option pays a certain dollar amount only if the stock price is above or below a specified strike price.
The dollar cash flow from owning this type of option is known as the digital payout.

One Step Binomial

Binomial Trees

This is an extension of the one-step binomial process
A binomial model can be described by providing 3 parameters
p - the probability of the an up move
u - the price multiplier for an up move
d - the price multiplier for a down move

There is only a single path to each of the extreme nodes and a large number of different paths to the two central nodes.
Nodes in the middle are more probable than the extremes
This clustering of paths produces a normal distribution.