Financial Modelling Agency

19 First Avenue East, Parktown North, 2193, South Africa

Phone & Fax: +27-11-447-2901

E-mail: lydia at finmod dot co dot za

Some code and spreadsheet resources to make life easy, and some analyses.

 

· Spreadsheet for calculating cointegration statistics for time series. The spreadsheet tests if the input series are I(1), and if the cointegration regression residuals are I(0), according to the Engle-Granger methodology. The spreadsheet outputs the statistics and comments on each statistic to guide the decision as to the cointegration relationship. This spreadsheet accompanies the article on the relationship between prime and JIBAR.

 

· Spreadsheet for performing sundry matrix calculations that occur in mathematical finance:

¨ Perform the LU decomposition of a given matrix.

¨ Given T a tridiagonal matrix and a vector b, solve for x in Tx = b

¨ Given a symmetric matrix (only the lower trianglur part need be provided) perform the Choleski decomposition of the matrix.

¨ Given A a matrix and a vector b, solve for x in Ax = b

¨ Given an invertible matrix, find the inverse and the determinant.

¨ Calculate the eigenvalues and eigenvectors of a given symmetric matrix.

¨ Perform PCA on a given correlation matrix.

  The mathematics code is performed by visible vb class modules. These modules can be exported to other spreadsheets, or included in a vb project for compilation to a vb dll.

 

· A mathematical explanation of principal component analysis. Most texts are very vague at the point where one must prove that what one has discarded is small, and in fact, in finance, although it is small, it cannot be ignored. We give precise derivations of the covariance matrix of the principal components selected and the covariance matrix of those ignored, verifying that they are 'small'. We review the simplest way in financial mathematics of adjusting for the missing volatility. We briefly survey three applications: at the money volatility term structures, risk free rates, and stock market index constituents. pdf

 

· An explanation of convertible bonds and their common features.  The 1.5 factor model of Ayache, Forsyth and Vetzal is discussed. pdf

Financial Modelling Agency