Financial markets are incredible systems. Thousands of instruments are traded by millions of participants every day, around the world, in a never ending battle to make money. Is it possible to capture the workings of the markets in a mathematical model, and possible to find neglected areas of the markets where a careful application of statistics.

This study is an attempt to apply a new nonlinear statistical modeling technique, Radial Basis Functions, to the rather bold task of stock market prediction and analysis. The success of our approach will ultimately depend on whether or not there are significant nonlinear relationships in the markets that can be discovered empirically.

Certainly numbers and quantitative analysis are invaluable for the accounting side of the financial markets, to “keep score” of how participants are doing. But in the last 30 years the financial world has embraced a decidedly quantitative orientation for many parts of the decision making processes as well, widely adopting quantitative theories such as modern portfolio theory, the Capital Asset Pricing Model, and option pricing theory.

Radial Basis Function
Radial basis faction were first used to solve interpolation problems, fitting curve exactly tough a set of points. Moore recently radial basis functions have been extended by several researchers to perform more general task approximations. (Campbell, Lo dan MacKinlay, 1997). The formula of radial basis function can be written as:

than we can define radial basis function with kernel Gaussian as

Building Radial Basis Function Networks (RBFN) Model
We can simply build RBFN model with combination J radial basis function (see chapter 2) with several center, if we have x input vector, than radial basis function networks model can be written as :

With kernel function suppose Gaussian; than we can continue define structure of the RBFN model.

RBFN Structure Model
RBFN model have two hidden layer with J number of neuron, and linier layer for the second layer . we can see the structure of RBFN model as follow:

At part of accept input vector and weight matrices, t=1,…,N (number of data) and j=1,…J (and number of neuron) then produce vector. The elements of vector are distance between input vector and. Generally, RBFN model can be written as (Powel, 1998) :

To illustrate application of RBFN for option modeling, we use option price S&P 500 CBOE (Chicago Board Exchange). Because we can not have the asset data, so we must simulate the asset price. We will use method from Hutchinson, Lo, Poggio (1994) to simulate the asset data and Black Scholes theory who said that option price following Brownian motion:

If we had generate the xt (compounded return) with several black scholes assumption, than we can compute asset price with formula:

After we define the structure of model, we can build the model with software Trajan 6.0, Matlab, and Spreadsheet. Than we can get the fitting of model

Written By Febriandi Rahmatulloh
Homepage : Analisadata.blogspot.com