Algorithms for Generating a Valid Correlation Matrix for Financial Applications

Practitioners often have to compute a correlation matrix for financial applications as in value-at-risk, asset allocation, and option pricing, etc. The computed correlation matrix, however, could be a non-positive semidefinite matrix due to various reasons. This article provides two simple algorithms that can remedy this problem while allowing parts of a given invalid correlation matrix to be fixed. Algorithm 1 keeps the top left submatrix unchanged, whereas Algorithm 2, under a condition, alters the bottom right submatrix only. In the extreme case, it is enough for Algorithm 2 to modify only one correlation coefficient to fix an invalid correlation matrix. These algorithms are quick because they do not employ any numerical optimization routines