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Oct 3, 2009, 11:04:55 AM10/3/09

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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

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

In article <31106f6c-fe3e-4323...@p15g2000vbl.googlegroups.com>,

John Goche <johng...@googlemail.com> wrote:

:

:Hello,

--

Prof. Lester Ingber les...@ingber.com ing...@alumni.caltech.edu

http://www.ingber.com http://alumni.caltech.edu/~ingber

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