Method and System to Solve Dynamic Multi-Factor Models in Finance

Abstract

A method is for determining a factor exposure of an asset collection for each of time intervals in a period of time, the asset collection including at least one asset. An objective function which includes an estimation error term or at least one transition error term is determined. The estimation error term represents an estimation error at each time interval between a performance of the asset collection and a sum of products of each of the factor exposure and its respective factor. The transition error term represents a transition error at each time interval after a first time interval for each of the factor exposure between the time interval and a prior time interval. At least one hedging or leveraging constraint on the factor exposure for at least one of the time intervals is defined. The factor exposure by optimizing a value of the objective function is determined.

1 .- 117 . (canceled) 
     
     
         118 . A method for determining at least one factor exposure of an asset collection for each of a plurality of time intervals in a period of time, the asset collection including at least one asset, comprising:
 determining an objective function which includes an estimation error term or at least one transition error term, the estimation error term representing an estimation error at each time interval between a performance of the asset collection and a sum of products of each of the at least one factor exposure and its respective factor, the at least one transition error term representing a transition error at each time interval after a first time interval for each of the at least one factor exposure between the time interval and a prior time interval;   defining at least one hedging constraint or leveraging constraint on the at least one factor exposure for at least one of the plurality of time intervals; and   determining the at least one factor exposure by optimizing a value of the objective function, wherein each step of determining the objective function and the step of determining the least one factor exposure is performed using at least one processor.   
     
     
         119 . The method of  claim 118 , wherein the hedging constraint is specified for a subset of factors. 
     
     
         120 . The method of  claim 118 , wherein the hedging constraint includes a plurality of constraints dependent on a plurality of hedging instruments in the asset collection. 
     
     
         121 . The method of  claim 118 , wherein the leveraging constraint is specified for a subset of factors. 
     
     
         122 . A method for determining at least one factor exposure of an asset collection for each of a plurality of time intervals in a period of time, the asset collection including at least one asset, comprising:
 determining an objective function which includes an estimation error term or at least one transition error term, the estimation error term representing an estimation error at each time interval between a performance of the asset collection and a sum of products of each of the at least one factor exposure and its respective factor, the at least one transition error term representing a transition error at each time interval after a first time interval for each of the at least one factor exposure between the time interval and a prior time interval;   formulating the objective function as a parameter-weighted sum, the parameter-weighted sum includes a quadratic norm of the estimation error;   defining at least one constraint on the quadratic norm of each of the at least one transition error term for the at least one factor exposure for at least one of the plurality of time intervals; and   determining the at least one factor exposure by optimizing a value of the objective function, wherein each step of determining the objective function and the step of determining the least one factor exposure is performed using at least one processor.   
     
     
         123 . A method for determining at least one factor exposure of an asset collection for each of a plurality of time intervals in a period of time, the asset collection including at least one asset, comprising:
 determining an objective function which includes an estimation error term or at least one transition error term, the estimation error term representing an estimation error at each time interval between a performance of the asset collection and a sum of products of each of the at least one factor exposure and its respective factor, the at least one transition error term representing a transition error at each time interval after a first time interval for each of the at least one factor exposure between the time interval and a prior time interval;   defining a budget constraint for the at least one exposure factor for a subset of factors;   defining individual bound constraint for the budget constraint, wherein the individual bound constraint establishes the factors excluded from the subset as the factors representing hedging instruments in the asset collection;   defining a hedging constraint on the at least one factor exposure for at least one of the plurality of time intervals; and   determining the at least one factor exposure by optimizing a value of the objective function based on at least one of the budget constraint, the individual bound constraint and the hedging constraint, wherein each step of determining the objective function and the step of determining the least one factor exposure is performed using at least one processor.