Methods and systems for generating transition probability matrices through an optimization framework
First Claim
1. A method for generating an optimized transition probability matrix (OTPM), said method performed using a computer coupled to a database, said method comprising:
- storing in the database financial data including obligor credit ratings;
generating multi-period empirical transition probability matrices (ETPMs) for a selected time horizon using the financial data stored within the database, wherein each generated ETPM includes transition probability values indicating a likelihood that a credit rating of an obligor will migrate from one credit state to another credit state during a time period included within the selected time horizon, the transition probability values included within the generated ETPMs are defined as target ETPM values;
generating a mathematical expression to minimize a difference between target ETPM values and candidate OTPM values, wherein the mathematical expression is generated using an objective function including at least one of a probit transform function and an exponential function, and by applying predetermined constraints to the objective function;
calculating the OTPM from the generated mathematical expression and the financial data stored within the database, wherein the calculated OTPM includes a first set of optimized transition probability values for predicting a likelihood that a credit rating of an obligor will migrate from one credit state to another credit state during a first time interval in the future, wherein the calculating is performed by the computer; and
predicting the likelihood that the credit rating of the obligor will migrate from one credit state to another credit state during the first time interval based at least in part on the calculated OTPM.
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Abstract
A method for generating an optimized transition probability matrix (OTPM) is provided. The method is performed using a computer system coupled to a database. The method includes storing in the database financial data including obligor credit ratings, generating multi-period empirical transition probability matrices (ETPMs) for a selected time horizon using the financial data stored within the database, generating a mathematical expression to minimize a difference between target ETPM values and candidate OTPM values, and calculating the OTPM from the generated mathematical expression and the financial data stored within the database, wherein the calculated OTPM includes a first set of optimized transition probability values for predicting a likelihood that a credit rating of an obligor will migrate from one credit state to another credit state during a first time interval in the future.
29 Citations
51 Claims
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1. A method for generating an optimized transition probability matrix (OTPM), said method performed using a computer coupled to a database, said method comprising:
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storing in the database financial data including obligor credit ratings; generating multi-period empirical transition probability matrices (ETPMs) for a selected time horizon using the financial data stored within the database, wherein each generated ETPM includes transition probability values indicating a likelihood that a credit rating of an obligor will migrate from one credit state to another credit state during a time period included within the selected time horizon, the transition probability values included within the generated ETPMs are defined as target ETPM values; generating a mathematical expression to minimize a difference between target ETPM values and candidate OTPM values, wherein the mathematical expression is generated using an objective function including at least one of a probit transform function and an exponential function, and by applying predetermined constraints to the objective function; calculating the OTPM from the generated mathematical expression and the financial data stored within the database, wherein the calculated OTPM includes a first set of optimized transition probability values for predicting a likelihood that a credit rating of an obligor will migrate from one credit state to another credit state during a first time interval in the future, wherein the calculating is performed by the computer; and predicting the likelihood that the credit rating of the obligor will migrate from one credit state to another credit state during the first time interval based at least in part on the calculated OTPM. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17)
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18. A system for generating an optimized transition probability matrix (OTPM), said system comprising:
a computer comprising a processor for executing computer-readable instructions, said computer configured to; store financial data including obligor credit ratings within a database; generate multi-period empirical transition probability matrices (ETPMs) for a selected time horizon using the financial data stored within the database, wherein each generated ETPM includes transition probability values indicating a likelihood that a credit rating of an obligor will migrate from one credit state to another credit state during a time period included within the selected time horizon, the transition probability values included within the generated ETPMs are defined as target ETPM values; generate a mathematical expression to minimize a difference between target ETPM values and candidate OTPM values, wherein the mathematical expression is generated using an objective function including at least one of a probit transform function and an exponential function, and by applying predetermined constraints to the objective function; and calculate the OTPM from the generated mathematical expression and the financial data stored within the database, wherein the calculated OTPM includes a first set of optimized transition probability values for predicting a likelihood that a credit rating of an obligor will migrate from one credit state to another credit state during a first time interval in the future. - View Dependent Claims (19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34)
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35. A non-transitory computer readable medium comprising instructions thereon, said instructions configured to instruct a computer to generate an optimized transition probability matrix (OTPM), said instructions comprising at least one code segment that:
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stores in a database financial data including obligor credit ratings; generates multi-period empirical transition probability matrices (ETPMs) for a selected time horizon using the financial data stored within the database, wherein each generated ETPM includes transition probability values indicating a likelihood that a credit rating of an obligor will migrate from one credit state to another credit state during a time period included within the selected time horizon, the transition probability values included within the generated ETPMs are defined as target ETPM values; generates a mathematical expression to minimize a difference between target ETPM values and candidate OTPM values, wherein the mathematical expression is generated using an objective function including at least one of a probit transform function and an exponential function, and by applying predetermined constraints to the objective function; and calculates the OTPM from the generated mathematical expression and the financial data stored within the database, wherein the calculated OTPM includes a first set of optimized transition probability values for predicting a likelihood that a credit rating of an obligor will migrate from one credit state to another credit state during a first time interval in the future. - View Dependent Claims (36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51)
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Specification