The Most General Methodology to Create a Valid Correlation Matrix for Risk Management and Option Pricing Purposes

Abstract

We have presented two simple methods to produce a feasible (i.e. real, symmetric, and positivesemidefinite) correlation matrix when the econometric one is either noisy, unavailable, or inappropriate. The first method is to the knowledge of the authors more general than any of the approaches which have been proposed in the literature, and computationally faster. It can actually produce the optimal feasible solution in a sense specified by the user. The second method is, in principle, not as general, but we show that i) it is extremely fast and ii) it produces results very close to those obtained using the general procedure. It can therefore be used in its own right, or as a starting point for the general optimisation procedure, thereby making the latter even faster.

Keywords: Covariance, correlation, robustness

JEL Classification: C10, C13