Abstract: A numerical modelling apparatus and method of performing numerical modelling are described. An input unit receives signals giving information relating to a set of assets. A processor unit is arranged to provide a set of Risk Relation Matrices V? for set of investment horizons indicated by ?. Each of the Risk Relation Matrices V? 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. The processor unit is arranged to decompose each of the Risk Relation Matrices V? into eigenvectors and eigenvalues according to V?=E?·??·E??, where, at each tenor ?, E? is a set of eigenvectors of the risk matrix V? in columns, ?? is the corresponding diagonal eigenvalue matrix, and E?? is the transpose of E?.

Abstract: A numerical modelling apparatus and method of performing numerical modelling are described. An input unit receives signals giving information relating to a set of assets. A processor unit is arranged to provide a Risk Relation Matrix v having elements that represent a relationship of risk related to a respective pair of the assets. Each element is 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. The Risk Relation Matrix v is decomposed into eigenvectors and eigenvalues according to V=E·?·E?, where E is a set of eigenvectors of the risk matrix v in columns, ? is the corresponding diagonal eigenvalue matrix, and E? is the transpose of E. Components of each of the risk vectors are derived in the basis of unit independent risks by the corresponding row of the matrix product E·?1/2 relating to each of the assets.

Abstract: A numerical modelling apparatus and method of performing numerical modelling are described. An input unit receives signals giving information relating to a set of assets. A processor unit is arranged to provide a set of Risk Relation Matrices V? for set of investment horizons indicated by ?. Each of the Risk Relation Matrices V? 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. The processor unit is arranged to decompose each of the Risk Relation Matrices V? into eigenvectors and eigenvalues according to V?=E?·??·E??, where, at each tenor ?, E? is a set of eigenvectors of the risk matrix V? in columns, ?? is the corresponding diagonal eigenvalue matrix, and E?? is the transpose of E?.