Patent ID: 7925560

Claim:
A computer system for calculating a value of a derivative, the system comprising: at least one electronic processor and operatively associated memory, wherein the memory comprises instructions that when executed by the processor cause the processor to: receive data indicating historical values of a first index, wherein the first index indicates an interest rate for tax-exempt municipal bonds; receive data indicating historical values of a second index, wherein the second index indicates an interest rate for non-tax-exempt instruments; receive data indicating a value of the second index; estimate a ratio of the first index over the second index over at least a range of potential values of the second index as an index function, wherein: the ⁢ ⁢ index ⁢ ⁢ function = ( a T ⁢ F T 2 + b T ⁢ F T + c T ) ⁢ Θ ⁡ ( F T ) + ( c T - b T 2 4 ⁢ a T ) ⁢ ( 1 - Θ ⁡ ( F T ) ) the ⁢ ⁢ index ⁢ ⁢ function = 1 , ⁢ if ⁢ ⁢ F T ≤ - b T 2 ⁢ a T ; the ⁢ ⁢ index ⁢ ⁢ function = 0 ⁢ , ⁢ if ⁢ ⁢ F T > - - b T 2 ⁢ a T ; wherein F T is the second index, a T , b T and c T are parameters of the index function, and wherein estimating the ratio comprises calculating a T , b T and c T by comparing the index function to the data indicating historical values of the first index and the data indicating historical values of the second index; calculate a value for the index function based on the calculated values for a T , b T and c T and the value of the second index; and calculate the value of the derivative considering the calculated value of the index function and the value of the second index, wherein the value of the derivative is a function of the first index.