Patent ID: 7778897

Claim:
A computer-implemented method for estimating risk characteristics of portfolios of financial instruments, the computer-implemented method comprising the steps of: maintaining a database of electronically stored information comprising a plurality of scenarios, sets of instruments, sets of risk factors, and portfolio weights for the instruments; selecting a required number of scenarios, a set of instruments with corresponding amounts, a set of risk factors, and one or more sets of portfolio weights for each of the set of instruments from the database by a user through an input device for input into a memory; maintaining a network operatively coupled and providing communication between the database, the input device, and a computer processor coupled to the memory; processing the selected information by the computer processor coupled to the memory, comprising: transforming historical observations for the set of risk factors to a stationary homogenous time-series comprising transformed historical observations; obtaining stable Paretian parameters describing a heavy tailed and asymmetric distribution for the transformed historical observations in the set of risk factors by estimating stable Paretian parameters based on the transformed historical observations; generating a set of stable Paretian scenarios from the heavy tailed and asymmetric distribution for the set of risk factors by simulating dependent stable Paretian random variables based on the estimated Paretian parameters, wherein the distribution is performed in accordance with the equation: Φ ⁢ ⁢ R ⁡ ( θ ) = E ⁡ ( exp ⁡ ( iR ⁢ ⁢ θ ) ) = exp ⁢ { - σ α ⁢  θ  α ⁢ ( 1 - i ⁢ ⁢ β ⁡ ( sgn ⁢ ⁢ θ ) ⁢ tan ⁢ ⁢ πα 2 ) + i ⁢ ⁢ μθ } , if ⁢ ⁢ α ≠ 1 and Φ ⁢ ⁢ R ⁡ ( θ ) = E ⁡ ( exp ⁡ ( iR ⁢ ⁢ θ ) ) = exp ⁢ { - σ ⁢  θ  ⁢ ( 1 + i ⁢ ⁢ β ⁡ ( sgn ⁢ ⁢ θ ) ⁢ ln ⁢ ⁢ θ ) + i ⁢ ⁢ μθ } , if ⁢ ⁢ α = 1 where α, β, σ, and μ are the estimated Paretian parameters, α is an index of stability, 0<α≦2, β is a skewness parameter, −1≦β≦1, σ is a scale parameter, σ≧0, and μ is a location parameter, Φ is notation for the characteristic function of the random variable R which is stable distributed, θ is a parameter of the characteristic function and is any real number, R is a stable random variable, i is an imaginary unit, where i 2 =−1, E is notation for mathematical expectation; transforming the stable Paretian scenarios into risk factor value scenarios by applying a transformation inverse to the one performed on the historical observations; estimating instrument characteristics of at least one instrument in the set of instruments under each risk factor value scenario; estimating risk characteristics of the portfolio of instruments based on the estimated instrument characteristics; and generating a report for the risk characteristics of the portfolio of instruments for output.