System and method for pricing default insurance
First Claim
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1. A method for calculating default times for securities contained in a basket of securities, wherein said method is implemented with a computer system comprising one or more computer processors, said method comprising the steps of:
- determining, with at least one of said one or more computer processors, for each of said securities, a hazard rate that is a stochastic process that represents the instantaneous probability of default for a corresponding one of said securities, wherein said hazard rates are correlated;
determining, with at least one of said one or more computer processors, for each of said securities, a compensator based on integrating the hazard rate associated with the corresponding one of said securities over time;
determining, with at least one of said one or more computer processors, for each of said securities, a barrier value selected according to a multivariate distribution of barriers with exponential marginals, thereby establishing random correlated barriers;
the method also comprising the steps of;
(a) determining, with at least one of said one or more computer processors, a proposed default time increment value;
(b) determining, with at least one of said one or more computer processors, a current proposed default time by adjusting a prior proposed default time based on the proposed default time increment value;
(c) calculating, with at least one of said one or more computer processors, for each of a plurality of said securities, a compensator value of said compensator associated with said corresponding security at said current proposed default time;
(d) determining, with one of said one or more computer processors, for each of said plurality of securities, whether said corresponding compensator value is in a relative relationship with said corresponding barrier value, and if so assigning a default time to said corresponding security based on said current proposed default time; and
(e) repeating steps (a)-(d) at least with respect to one or more unassigned securities.
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Abstract
A system for modeling a basket of securities containing a plurality of securities is provided and includes a default/recovery model database for storing default/recovery data regarding the plurality of securities. Also included is a default simulation engine for calculating a default time for at least one of the plurality of securities based on the default/recovery data. Finally, a cash flow engine is included for generating cash flows for the basket of securities based on the default times.
18 Citations
29 Claims
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1. A method for calculating default times for securities contained in a basket of securities, wherein said method is implemented with a computer system comprising one or more computer processors, said method comprising the steps of:
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determining, with at least one of said one or more computer processors, for each of said securities, a hazard rate that is a stochastic process that represents the instantaneous probability of default for a corresponding one of said securities, wherein said hazard rates are correlated; determining, with at least one of said one or more computer processors, for each of said securities, a compensator based on integrating the hazard rate associated with the corresponding one of said securities over time; determining, with at least one of said one or more computer processors, for each of said securities, a barrier value selected according to a multivariate distribution of barriers with exponential marginals, thereby establishing random correlated barriers; the method also comprising the steps of; (a) determining, with at least one of said one or more computer processors, a proposed default time increment value; (b) determining, with at least one of said one or more computer processors, a current proposed default time by adjusting a prior proposed default time based on the proposed default time increment value; (c) calculating, with at least one of said one or more computer processors, for each of a plurality of said securities, a compensator value of said compensator associated with said corresponding security at said current proposed default time; (d) determining, with one of said one or more computer processors, for each of said plurality of securities, whether said corresponding compensator value is in a relative relationship with said corresponding barrier value, and if so assigning a default time to said corresponding security based on said current proposed default time; and (e) repeating steps (a)-(d) at least with respect to one or more unassigned securities. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23)
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24. A method for calculating default times for securities contained in a basket of securities, wherein said method is implemented with a computer system comprising one or more computer processors, said method comprising the steps of:
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determining, with at least one of said one or more computer processors, for each of said securities, a hazard rate that is a stochastic process that represents the instantaneous probability of default for a corresponding one of said securities, wherein said hazard rates are correlated; determining, with at least one of said one or more computer processors, for each of said securities, a compensator based on integrating the hazard rate associated with the corresponding one of said securities over time; determining, with at least one of said one or more computer processors, for each of said securities, a barrier value selected according to a multivariate distribution of barriers with exponential marginals, thereby establishing random correlated barriers; the method also comprising the steps of; (a) determining, with at least one of said one or more computer processors, a proposed default time increment value; (b) determining, with at least one of said one or more computer processors, a current proposed default time by adjusting a prior proposed default time based on the proposed default time increment value; (c) calculating, with at least one of said one or more computer processors, for each of a plurality of said securities, a compensator value of said compensator associated with said corresponding security at said current proposed default time; (d) determining, with at least one of said one or more computer processors, for each of said plurality of said securities, an adjusted default time based on said corresponding compensator and said corresponding barrier value, and determining, based on said adjusted default time, whether to assign a default time to said corresponding security, where said default time is based on said current proposed default time; and (e) repeating steps (a)-(d) at least with respect to one or more unassigned securities. - View Dependent Claims (25, 26, 27, 28, 29)
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Specification