System and methods for modeling a multiplicative index
First Claim
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1. A computer-implemented method for valuing a derivative based on a first rate indicating interest paid on tax-exempt instruments, the method comprising:
- generating, by a computer, a model of a ratio of the first rate over a second rate as a function of;
the second rate, wherein the second rate indicates interest paid on taxed instruments,a stochastic noise function, anda seasonality process, wherein the computer comprises at least one processor and operatively associated memory, wherein the model is expressed as;
BMA/LIBOR=ƒ
(LIBOR(t))+N+s(t)wherein BMA/LIBOR is the ratio;
wherein LIBOR is the second rate;
wherein s(t) is the seasonality process; and
wherein N is the stochastic noise function;
generating a solution of the model, by the computer, for at least one value of the second rate; and
estimating, by the computer, a value of the derivative given the solution of the model.
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Abstract
Computer-implemented methods for valuing a derivative based on the BMA rate: the methods may comprise generating a model of the BMA/LIBOR ratio as a function of the LIBOR index, a stochastic noise function, and a seasonality process. The methods may also comprise solving the model for at least one value of the LIBOR index, and estimating a value of the derivative given the solution of the model. The value of the derivative may then be stored.
25 Citations
30 Claims
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1. A computer-implemented method for valuing a derivative based on a first rate indicating interest paid on tax-exempt instruments, the method comprising:
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generating, by a computer, a model of a ratio of the first rate over a second rate as a function of; the second rate, wherein the second rate indicates interest paid on taxed instruments, a stochastic noise function, and a seasonality process, wherein the computer comprises at least one processor and operatively associated memory, wherein the model is expressed as;
BMA/LIBOR=ƒ
(LIBOR(t))+N+s(t)wherein BMA/LIBOR is the ratio; wherein LIBOR is the second rate; wherein s(t) is the seasonality process; and wherein N is the stochastic noise function; generating a solution of the model, by the computer, for at least one value of the second rate; and estimating, by the computer, a value of the derivative given the solution of the model. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 29)
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17. A system for valuing a derivative based on a first rate indicating interest paid on tax-exempt municipal bonds, the system comprising at least one computer comprising at least one processor and operatively associated memory, wherein the memory comprises instructions that, when executed by the processor, causes the computer to:
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generate a model of a ratio of the first rate over a second rate as a function of; the second rate, wherein the second rate indicates interest paid on taxed instruments, a stochastic noise function, and a seasonality process, wherein the model is expressed as;
BMA/LIBOR=ƒ
(LIBOR(t))+N+s(t)wherein BMA/LIBOR is the ratio; wherein LIBOR is the second rate; wherein s(t) is the seasonality process; and wherein N is the stochastic noise function; generate a solution of the model for at least one value of the second rate; and estimate a value of the derivative given the solution of the model.
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18. A computer readable storage medium having instructions thereon that when executed by at least one processor cause the at least one processor to:
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generate a model of a ratio of a first rate over a second rate as a function of; the second rate, wherein the second rate indicates interest paid on taxed instruments and the first rate indicates interest paid on tax-exempt instruments, a stochastic noise function, and a seasonality process, wherein the model is expressed as;
BMA/LIBOR=ƒ
(LIBOR(t))+N+s(t)wherein BMA/LIBOR is the ratio; wherein LIBOR is the second rate; wherein s(t) is the seasonality process; and wherein N is the stochastic noise function; generate a solution of the model for at least one value of the second rate; and estimate a value of the derivative given the solution of the model, wherein the medium is a computer storage medium.
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19. A computer-implemented method for valuing a derivative based on a first rate indicating interest paid on tax-exempt instruments, the method comprising:
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generating, by a computer, a model of a ratio of the first rate over a second rate as a function of; the second rate, wherein the second rate indicates interest paid on taxed instruments, a stochastic tax-regime process, and a seasonality process, wherein the computer comprises at least one processor and operatively associated memory, wherein the model is expressed as;
BMA/LIBOR=ƒ
r(LIBOR(t))+sr(t)wherein BMA/LIBOR is the ratio; wherein LIBOR is the second rate; wherein s(t) is the seasonality process; and wherein r is the stochastic tax-regime process; generating a solution of the model, by the computer, for at least one value of the second rate; estimating, by the computer, a value of the derivative given the solution of the model. - View Dependent Claims (20, 21, 22, 23, 24, 25, 26, 30)
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27. A system for valuing a derivative based on the BMA rate, the system comprising at least one computer comprising at least one processor and operatively associated memory, wherein the memory comprises instructions that, when executed by the processor, causes the computer to:
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generate a model of a ratio of the first rate over a second rate as a function of; the second rate, wherein the second rate indicates interest paid on taxed instruments, a stochastic tax-regime process, and a seasonality process, wherein the model is expressed as;
BMA/LIBOR=ƒ
r(LIBOR(t))+sr(t)wherein BMA/LIBOR is the ratio; wherein LIBOR is the second rate; wherein s(t) is the seasonality process; and wherein r is the stochastic tax-regime process; generate a solution to the model for at least one value of the second rate; and estimate a value of the derivative given the solution of the model.
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28. A computer readable storage medium having instructions thereon that when executed by at least one processor cause the at least one processor to:
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generate a model of a ratio of the first rate over a second rate as a function of; the second rate, wherein the second rate indicates interest paid on taxed instruments, a stochastic tax-regime process, and a seasonality process, wherein the model is expressed as;
BMA/LIBOR=ƒ
r(LIBOR(t))+sr(t)wherein BMA/LIBOR is the ratio; wherein LIBOR is the second rate; wherein s(t) is the seasonality process; and wherein r is the stochastic tax-regime process; generate a solution to the model for at least one value of the second rate; and estimate a value of the derivative given the solution of the model, wherein the medium is a computer storage medium.
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Specification