Patent Document ID: 20110167022
Application ID: 12946892
Patent Flag: 0

Claim One:
1. A numerical modelling apparatus, the apparatus comprising: an input unit arranged to receive signals containing data having information relating to a set of assets; a processor unit arranged to: a) provide a set of Risk Relation Matrices V τ for set of investment horizons indicated by τ, wherein each of the Risk Relation Matrices V τ comprises a plurality of elements, wherein each of the elements represents a relationship of risk related to a respective pair of the assets and each element is given by a scalar product of two risk vectors, such that each of the assets has an associated risk vector according to the elements of the risk relation matrix; b) decompose each Risk Relation Matrix V τ into eigenvectors and eigenvalues according to: 
 V τ =E τ ·Λ τ ·E′ τ wherein, at each tenor τ, E τ is a set of eigenvectors of the risk matrix V τ in columns, Λ τ is the corresponding diagonal eigenvalue matrix, and E′ τ is the transpose of E τ ; and c) derive components of each of the risk vectors at each tenor τ in the basis of unit independent risks by the corresponding row of the matrix product E τ ·Λ τ 1/2 relating to each of the assets; and an output unit arranged to output the components of each of the risk vectors as a risk vector data set onto a tangible computer-readable recording medium or a display device.