Method and apparatus for pricing securities
First Claim
1. A computer implemented method for relating a price or value of each of a plurality of securities associated with an underlying asset, a rate of return on each of the plurality of securities, and risk attributes of each of the plurality of securities, the method comprising the steps of:
- receiving, by one or more computers, data on a plurality of securities;
determining, by the one or more computers, a risk premium incorporated in the rate of return for each of the plurality of securities, wherein the risk premium for each of the plurality of securities comprises a difference between the rate of return for that security and a risk free rate of return;
determining, by the one or more computers, one or more priced risk factor premiums, wherein each of the priced risk factor premiums is a price per unit of risk for a priced risk factor multiplied by a measure of the security'"'"'s exposure to that priced risk factor, and wherein the risk premium for each of the securities is the priced risk factor premium, or, when the priced risk factor premium is part of a plurality of priced risk factor premiums, a sum of priced risk factor premiums;
wherein one of the priced risk factor premiums is in respect of volatility measured over a discrete time and wherein a price per unit of volatility is the same for two or more of each of the plurality of securities;
creating, by the one or more computers, a model for execution by the one or more computers, wherein the model calculates at least one value based on the determined priced risk factor premium; and
storing, by the one or more computers, the determined priced risk factor premiums for the plurality of securities, the calculated model and the at least one value.
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Abstract
The invention provides computer-implemented techniques and systems for parsimoniously modelling the price or value, expected rate of return or other relevant characteristics of securities issued by, or referenced to, firms (or other assets) by incorporating risk premia such that a range of different securities can be evaluated within a single, unified and coherent framework, thereby leading to significant reduction in the computing resources otherwise required.
41 Citations
126 Claims
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1. A computer implemented method for relating a price or value of each of a plurality of securities associated with an underlying asset, a rate of return on each of the plurality of securities, and risk attributes of each of the plurality of securities, the method comprising the steps of:
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receiving, by one or more computers, data on a plurality of securities; determining, by the one or more computers, a risk premium incorporated in the rate of return for each of the plurality of securities, wherein the risk premium for each of the plurality of securities comprises a difference between the rate of return for that security and a risk free rate of return; determining, by the one or more computers, one or more priced risk factor premiums, wherein each of the priced risk factor premiums is a price per unit of risk for a priced risk factor multiplied by a measure of the security'"'"'s exposure to that priced risk factor, and wherein the risk premium for each of the securities is the priced risk factor premium, or, when the priced risk factor premium is part of a plurality of priced risk factor premiums, a sum of priced risk factor premiums; wherein one of the priced risk factor premiums is in respect of volatility measured over a discrete time and wherein a price per unit of volatility is the same for two or more of each of the plurality of securities; creating, by the one or more computers, a model for execution by the one or more computers, wherein the model calculates at least one value based on the determined priced risk factor premium; and storing, by the one or more computers, the determined priced risk factor premiums for the plurality of securities, the calculated model and the at least one value. - 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, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34)
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35. A computer implemented method for applying an option-theoretic model of a firm comprising the steps of:
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receiving, by one or more computers, one or more risk parameters, wherein the one or more risk parameters are related to the firm; specifying, by the one or more computers, one or more input parameters, wherein the one or more input parameters are to be used in the option-theoretic model of the firm; defining, by the one or more computers, mathematical relationships between the input parameters, wherein the mathematical relationships are a set of one or more equations for execution by the one or more computers; creating, by the one or more computers, the option-theoretic model of the firm, based on the defined mathematical relationships; receiving, by the one or more computers, at least one value for each of the one or more input parameters; calculating, by the one or more computers, using the option-theoretic model, an estimated value for one or more of the risk parameters, measured over a discrete time period; re-calculating, by the one or more computers, using the option-theoretic model, a solution, the solution comprising at least one estimated value for each of the one or more input parameters that a user allows to vary from the at least one received value, such that the at least one estimated risk parameter value from the model equals the at least one risk parameter value received by the one or more computers; and storing, by the one or more computers, the calculated option-theoretic model and the at least one estimated value of each of the one or more input parameters that the user allows to vary. - View Dependent Claims (36, 37, 38, 39, 40, 41, 42)
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43. A system for relating a price or value of a plurality of securities associated with an underlying asset, a rate of return on each of the plurality of securities, and risk attributes of each of the plurality of securities, the system comprising:
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at least one processor; and at least one computer-readable memory communicatively coupled to the at least one processor, the memory storing processor-executable instructions that, when executed by the at least one processor, causes the system to perform operations comprising; receiving data on a plurality of securities; determining a risk premium incorporated in the rate of return for each of the plurality of securities, wherein the risk premium for each of the plurality of securities comprises a difference between the rate of return for that security and a risk free rate of return; determining one or more priced risk factor premiums, wherein each of the priced risk factor premiums is a price per unit of risk for a priced risk factor multiplied by a measure of the security'"'"'s exposure to that priced risk factor and wherein the risk premium for each of the securities is the priced risk factor premium, or, when the priced risk factor premium is part of a plurality of priced risk factor premiums, a sum of priced risk factor premiums; and
wherein one of the priced risk factor premiums is in respect of volatility measured over a discrete time and wherein a price per unit of volatility is the same for two or more of each of the plurality of securities;creating a model, wherein the model calculates at least one value based on the determined priced risk factor premium; and storing the determined priced risk factor premiums for the plurality of securities, the calculated model and the at least one value. - View Dependent Claims (44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 73, 74, 75, 76)
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68. The computer system of 53, wherein the at least one memory further bears processor-executable instructions that, when executed on the at least one processor, cause the at least one processor to perform operations comprising:
generating one or more parameters from the model and solving the model so that the parameters equal values specified by a user, where one of the parameters is the correlation between the returns of a pair of securities issued by, or referenced to, the firm.
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77. A system for applying an option-theoretic model of a firm, the system comprising:
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at least one processor; and at least one computer-readable memory communicatively coupled to the at least one processor, the memory storing processor-executable instructions that, when executed by the at least one processor, causes the system to perform operations comprising; receiving one or more risk parameters, wherein the one or more risk parameters are related to the firm; specifying one or more input parameters, wherein the one or more input parameters are to be used in the option-theoretic model of the firm; defining mathematical relationships between the input parameters, wherein the mathematical relationships are a set of one or more equations for; creating, the option-theoretic model of the firm, based on the defined mathematical relationships; receiving at least one value for each of the one or more input parameters; calculating using the option-theoretic model, an estimated value for one or more of the risk parameters, measured over a discrete time period; re-calculating using the option-theoretic model, a solution, the solution comprising at least one estimated value for each of the one or more input parameters that a user allows to vary from the at least one received value, such that the at least one estimated risk parameter value from the model equals the at least one risk parameter value received; and storing the calculated option-theoretic model and the at least one estimated value of each of the one or more input parameters that the user allows to vary. - View Dependent Claims (78, 79, 80, 81, 82, 83, 84)
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85. A non-transitory computer-readable medium for relating a price or value of a plurality of securities associated with an underlying asset, a rate of return on each of the plurality of securities, and risk attributes of each of the plurality of securities, storing computer-executable instructions that, upon execution by one or more computers, cause the one or more computers to perform operations comprising:
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receiving data on a plurality of securities; determining a risk premium incorporated in the rate of return for each of the plurality of securities, wherein the risk premium for each of the plurality of securities comprises a difference between the rate of return for that security and a risk free rate of return; determining one or more priced risk factor premiums, wherein each of the priced risk factor premiums is a price per unit of risk for a priced risk factor multiplied by a measure of the security'"'"'s exposure to that priced risk factor and wherein the risk premium for each of the securities is the priced risk factor premium, or, when the priced risk factor premium is part of a plurality of priced risk factor premiums, a sum of priced risk factor premiums; and
wherein one of the priced risk factor premiums is in respect of volatility measured over a discrete time and wherein a price per unit of volatility is the same for two or more of each of the plurality of securities;creating a model, wherein the model calculates at least one value based on the determined price risk factor premium; and storing the determined price risk factor premiums for the plurality of securities, the calculated model and the at least one value. - View Dependent Claims (86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118)
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119. A non-transitory computer-readable medium for applying an option-theoretic model of a firm, storing computer-executable instructions that, upon execution by one or more computers, cause the one or more computers to perform operations comprising:
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receiving one or more risk parameters, wherein the one or more risk parameters are related to the firm; receiving one or more input parameters, wherein the one or more input parameters are to be used in the option-theoretic model of the firm; receiving instructions on mathematical relationships between the input parameters, wherein the mathematical relationships are a set of one or more equations for execution by the one or more computers; creating the option-theoretic model of the firm, based on the received instructions on mathematical relationships; calculating, using the option-theoretic model, an estimated value for one or more of the risk parameters, measured over a discrete time period; re-calculating, using the option-theoretic model, a solution, the solution comprising at least one estimated value for each of the one or more input parameters that a user allows to vary from the at least one received value, such that the at least one estimated risk parameter value from the model equals the at least one risk parameter value received by the one or more computers; and storing the calculated option-theoretic model and the at least one estimated value of each of the one or more input parameters that the user allows to vary. - View Dependent Claims (120, 121, 122, 123, 124, 125, 126)
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Specification