# binomial tree models

7 views

### John Goche

Oct 3, 2009, 11:04:55 AM10/3/09
to

Hello,

I would like to ask the following question.
Throughout mathematical finance there are
models of stock prices based on binomial trees
including the derivation of Brownian motion which
the Black-Scholes equation for European Option
Pricing is derived. What is not clear to me is,
how does one go about using a binomial tree
model of stock prices in practice?

I thought that if the probability of up and down
prices is 1/2 then we can interpret the high and
low stock values as the first and third quartile
from a corresponding continuous rather than
discrete distribution.

I would like to hear from anyone else whether
there is some way of using the binomial tree
model of stock prices in practice.

Thanks,

John Goche

### Lester Ingber

Oct 7, 2009, 10:48:30 AM10/7/09
to
John:

Binomial trees can be used to propagate probability distributions in
time, not only to calculate options. So, yes, given your model of a
probability distribution for stocks, if you wish to look at stocks,
that can be done. This is quite straightforward if your distribution
is of the form multiplicative noise -- means and variances that may
depend on time and the random variable itself.

You should define the means and variances of your distributions, as
well as any functional forms of these means and variances. Contrary to
textbook methods of just putting these first and second moments on the
tree, if instead you place the short-time conditional probability on
the tree, you can use the tree beyond Gaussian or Black-Shcoles
distributions.

See:

%A L. Ingber
%A C. Chen
%A R.P. Mondescu
%A D. Muzzall
%A M. Renedo
%T Probability tree algorithm for general diffusion processes
%J Physical Review E
%V 64
%N 5
%P 056702-056707
%D 2001
%O URL http://www.ingber.com/path01_pathtree.pdf

Lester