Apparatus, method and system for determining credit derivative indices and estimating credit derivative credit curves, and a credit calculator for valuing credit derivatives based on the credit curves

Abstract

An apparatus, method and system for determining an estimate of at least one numerical attribute of at least one entity of a population when the population is changing and there are a limited number of observations on the attribute for the entities, in which a conditional index is determined to track how a value of the attribute changes from one time to another for an entity that is a member of the population at both times, and an unconditional index is determined representing an average level of the attribute for the entities of the population.

1 - 19 . (canceled) 
     
     
         20 . A method for providing a user interface with at least one estimated financial attribute of at least one entity of a population, the method comprising:
 providing financial attribute data for entities of the population, wherein the financial attribute data is for a period of time, and the period of time includes a particular day and prior days;   determining, using a processor arrangement, a conditional index for the particular day and for a particular entity based on a relationship of prior conditional indices, actual financial attribute data for the particular day and actual financial attribute data for the prior days by calculating a maximum likelihood estimator for the conditional index for the particular day;   determining, using a processor arrangement, an unconditional index representing an average level of the financial attribute data for the entities of the population; and   determining, using a processor arrangement, the at least one estimated financial attribute for the at least one entity based on the unconditional index;   populating, by the processor arrangement, the user interface with a data curve that includes the at least one estimate financial attribute;   wherein an entity is considered if it satisfies the following conditions: (1) the entity is currently a member of the population of interest; and (2) the entity was a member of the population at the time of the most recent observation on the entity, and   wherein the unconditional index is determined by averaging the attribute across both actual observations and estimated observations of the attribute that satisfy both of the conditions.   
     
     
         21 . The method of  claim 20 , wherein the conditional index for a particular time and for a particular entity is determined based on prior conditional indices, actual attribute data for the particular time and actual attribute data for the prior times. 
     
     
         22 . The method of  claim 20 , wherein the relationship between the numerical attribute and the conditional index is defined by a model of xij=Ii+aj+eij, wherein xij is an attribute value of a jth entity of the population on day i, Ii is the level of the conditional index on day i, aj is a constant associated with the jth entity of the population on day i, and each eij has independent identically distributed distributions. 
     
     
         23 . The method of  claim 22 , wherein an attribute is estimated for at least one of each of the entities for which there is no actual attribute data, wherein the attribute for xij is defined as xi−k,j+Ii−Ii−k, and an actual attribute value was last observed on day i−k, which is k days before the day i. 
     
     
         24 . The method of  claim 20 , wherein the relationship between the numerical attribute and the conditional index is defined by a model of In (xij)=In (Ii)+In (aj)+In (eij), wherein xij is an attribute value of the jth entity of the population on day i, Ii is the level of the conditional index on day i, aj is a constant associated with the jth entity of the population on day i, and each eij has independent identically distributed distributions. 
     
     
         25 . The method of  claim 24 , wherein an attribute is estimated for at least one of each of the entities for which there is no actual attribute data, wherein the attribute for xij is defined as xi−k,j (Ii/Ii−k), and an actual attribute value was last observed on day i−k, which is k days before the day i. 
     
     
         26 . The method of  claim 20 , wherein the unconditional index is determined for the particular time for each of the entities that is currently a member of the population, and that was a member of the population when a most recent attribute value of the member was observed. 
     
     
         27 . The method of  claim 20 , wherein the population includes a group of companies having the same credit rating. 
     
     
         28 . The method of  claim 20 , wherein the attribute data includes credit derivative pricing data. 
     
     
         29 . The method of  claim 20 , wherein the attribute data includes credit default swap spread data for five-year credit default swaps. 
     
     
         30 . The method of  claim 20 , further comprising: displaying on a display a graphical-user-interface to display a data curve for the at least one entity based on the at least one numerical attribute, wherein the data curve includes numerical attributes determined using the conditional index and the unconditional index. 
     
     
         31 . An apparatus for providing a user interface with at least one estimated financial attribute of at least one entity of a population, the apparatus comprising:
 a first arrangement to provide financial attribute data for entities of the population, wherein the financial attribute data is for a period of time, and the period of time includes a particular day and prior days;   a second arrangement to determine a conditional index for the particular day and for a particular entity based on a relationship of prior conditional indices, actual financial attribute data for the particular day and actual financial attribute data for the prior days by calculating a maximum likelihood estimator for the conditional index for the particular day;   a third arrangement to determine an unconditional index representing an average level of the financial attribute data for the entities of the population; and   a fourth arrangement to determine the at least one estimated financial attribute for the at least one entity based on the unconditional index;   a fifth arrangement to populate the user interface with a data curve that includes the at least one estimate financial attribute;   wherein an entity is considered if it satisfies the following conditions: (1) the entity is currently a member of the population of interest; and (2) the entity was a member of the population at the time of the most recent observation on the entity, and   wherein the unconditional index is determined by averaging the attribute across both actual observations and estimated observations of the attribute that satisfy both of the conditions.   
     
     
         32 . The apparatus of  claim 31 , wherein the relationship between the numerical attribute and the conditional index is defined by a model of In (xij)=In (Ii)+In (aj)+In (eij), wherein xij is an attribute value of the jth entity of the population on day i, Ii is the level of the conditional index on day i, aj is a constant associated with the jth entity of the population on day i, and each eij has independent identically distributed distributions. 
     
     
         33 . The apparatus of  claim 31 , further comprising: an estimating arrangement to estimate an attribute for at least one of each of the entities for which there is no actual attribute data, wherein the attribute for xij is defined as xi−k,j (Ii/Ii−k), and an actual attribute value was last observed on day i−k, which is k days before the day i. 
     
     
         34 . A non-transitory computer-readable storage medium having a computer program, which is executable by a processor, comprising:
 a program code arrangement having program code for determining at least one estimated financial attribute of at least one entity of a population, by performing the following:   providing financial attribute data for entities of the population, wherein the financial attribute data is for a period of time, and the period of time includes a particular day and prior days;   determining a conditional index for the particular day and for a particular entity based on a relationship of prior conditional indices, actual financial attribute data for the particular day and actual financial attribute data for the prior days by calculating a maximum likelihood estimator for the conditional index for the particular day;   determining an unconditional index representing an average level of the financial attribute data for the entities of the population; and   determining the at least one estimated financial attribute for the at least one entity based on the unconditional index;   populating a user interface with a data curve that includes the at least one estimate financial attribute   wherein an entity is considered if it satisfies the following conditions: (1) the entity is currently a member of the population of interest; and (2) the entity was a member of the population at the time of the most recent observation on the entity, and   
       wherein the unconditional index is determined by averaging the attribute across both actual observations and estimated observations of the attribute that satisfy both of the conditions. 
     
     
         35 . The computer-readable storage medium of  claim 34 , wherein the conditional index for a particular time and for a particular entity is determined based on prior conditional indices, actual attribute data for the particular time and actual attribute data for the prior times. 
     
     
         36 . The computer-readable storage medium of  claim 34 , wherein the relationship between the numerical attribute and the conditional index is defined by a model of xij=Ii+aj+eij, wherein xij is an attribute value of a jth entity of the population on day i, Ii is the level of the conditional index on day i, aj is a constant associated with the jth entity of the population on day i, and each eij has independent identically distributed distributions. 
     
     
         37 . The computer-readable storage medium of  claim 36 , wherein an attribute is estimated for at least one of each of the entities for which there is no actual attribute data, wherein the attribute for xij is defined as xi−k,j+Ii−Ii−k, and an actual attribute value was last observed on day i−k, which is k days before the day i. 
     
     
         38 . The computer-readable storage medium of  claim 34 , wherein the relationship between the numerical attribute and the conditional index is defined by a model of In (xij)=In (Ii)+In (aj)+In (eij), wherein xij is an attribute value of the jth entity of the population on day i, Ii is the level of the conditional index on day i, aj is a constant associated with the jth entity of the population on day i, and each eij has independent identically distributed distributions. 
     
     
         39 . The computer-readable storage medium of  claim 38 , wherein an attribute is estimated for at least one of each of the entities for which there is no actual attribute data, wherein the attribute for xij is defined as xi−k,j (Ii/Ii−k), and an actual attribute value was last observed on day i−k, which is k days before the day i. 
     
     
         40 . The computer-readable storage medium of  claim 34 , wherein the unconditional index is determined for the particular time for each of the entities that is currently a member of the population, and that was a member of the population when a most recent attribute value of the member was observed. 
     
     
         41 . The computer-readable storage medium of  claim 34 , wherein the population includes a group of companies having the same credit rating. 
     
     
         42 . The computer-readable storage medium of  claim 34 , wherein the attribute data includes credit derivative pricing data. 
     
     
         43 . The computer-readable storage medium of  claim 34 , wherein the attribute data includes credit default swap spread data for five-year credit default swaps.