Patent Document ID: 9082152
Application ID: 12946892
Patent Flag: 1

Claim One:
1. A numerical modeling apparatus, the apparatus comprising: an input arranged to receive signals containing data having information relating to a set of assets; a processor unit arranged to: 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; 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 set components of each of the risk vectors at each tenor τ in the basis of unit independent risks to the corresponding row of the matrix product E τ ·Λ τ 1/2 relating to each of the assets; provide a dataset of the term structure of the price of risk m τ at each tenor τ for each of the assets i according to: d ⁢ ⁢ P i ⁢ ⁢ τ P i ⁢ ⁢ τ ⁢ χ i ⁢ ⁢ τ τ = d ⁢ ⁢ c i ⁢ ⁢ τ c i ⁢ ⁢ τ ⁢ χ i ⁢ ⁢ τ τ - d ⁢ ⁢ r f ⁢ ⁢ τ - d ⁢ ⁢ m τ ⁢ ∑ j ⁢ ψ ij ⁢ ⁢ τ - m τ ⁢ ∑ j ⁢ d ⁢ ⁢ ψ ij ⁢ ⁢ τ wherein, with respect to the tenor τ and asset i, dP iτ is the change in contribution to price P iτ the cash flow c iτ over a period, dc iτ is the change in the said cash flow c iτ over the said period, dr fτ is the change in the risk free interest rate r fτ over the said period, ψ ijτ the jth component of the risk vector for the asset i, dψ ijτ is the change in the jth component of the risk vector for the ith asset over the said period, dm τ is the change in the price of risk m τ over the said period, χ iτ is given as ( 1 + r f ⁢ ⁢ τ + m τ ⁢ ∑ j ⁢ ψ ij ⁢ ⁢ τ ) , and the value for m τ is estimated by one or more methods of cross-sectional analysis over a subset of assets from the set of assets; and an output 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.