**13.7 Binomial Method
**

One way to
solve for the value of an American option is to use the binomial approximation,
a method attributed to Cox, Ross, and Rubinstein (1979).

From the
technical topic, __Limit of the Binomial__, you
already know that if you make the appropriate translations of the up and down
parameters and the risk-free interest rate, the binomial model converges to the
Black-Scholes model.

Here, we
are simply going the other way. We
are given the risk-free rate, *r*, and
the volatility, *s*. First,
decide on the number of steps in the binomial approximation (i.e., how finely we
want to divide time between now and the maturity date of the option).
Let *n* be the number of steps.
Then, we choose the *u* and *d* parameters as follows:

Given
these parameters, we simply solve the binomial tree for the option value,
checking for early exercise at every node.
Online, you can check for yourself the convergence properties of the
binomial approximation to the Black-Scholes price for European options by
selecting the **Limit of the Binomial**
subject.