US2013066808A1PendingUtilityA1
Method and apparatus for pricing securities
Est. expiryDec 24, 2023(expired)· nominal 20-yr term from priority
Inventors:John Michael Redmayne
G06Q 40/03G06Q 40/00G06Q 40/06G06Q 30/0283
39
PatentIndex Score
0
Cited by
0
References
0
Claims
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.
Claims
exact text as granted — not AI-modified1 . A computer implemented method of measuring a credit risk of an asset, the method comprising the steps of:
receiving, by one or more computers, data representative of the said asset and data representative of a second asset; calculating, by the one or more computers, an estimate of a covariance of rates of return of the two assets using the data; determining, by the one or more computers, a measure of the credit risk of the said asset based on the estimate of covariance; and storing, by the one or more computers, the determined measure of credit risk of the said asset.
2 . The computer implemented method of claim 1 , wherein a financial instrument is traded based on the measure of the credit risk of the said asset, the method further comprising the steps of:
trading, or providing a service for at least one customer to trade, the at least one financial instrument; calculating, by the one or more computers, the covariance of the two assets based on a formula applied to the rates of return of the two assets over a period; and determining, by the one or more computers, a price of at least one financial instrument at its maturity based at least in part on the aforesaid calculated covariance.
3 . The computer implemented method of claim 2 , wherein the service is provided for the at least one customer to trade the at least one financial instrument, the method further comprising the steps of:
transmitting, by the one or more computers, pricing information on the at least one financial instrument to the at least one customer; and effecting, by the one or more computers, one or more trades in the at least one financial instrument for the at least one customer.
4 . The computer implemented method of claim 2 , wherein the formula is selected from the group consisting of:
σ
jk
=
∑
i
=
1
N
-
1
R
i
j
R
i
k
N
-
1
σ
jk
=
(
1
-
λ
)
(
1
-
λ
N
-
1
)
∑
i
=
1
N
-
1
λ
N
-
i
-
1
R
i
j
R
i
k
σ
jk
=
(
1
-
λ
)
∑
i
=
1
N
-
1
λ
N
-
i
-
1
R
i
j
R
i
k
+
λ
N
-
1
σ
jk
*
wherein:
σ jk is a covariance of assets j and k;
N is an actual number of pairs of asset values for j and k used to calculate rates of return over the period;
R i j is a rate of return for asset j at a time i+1 wherein
R
i
j
=
ln
(
P
i
+
1
j
P
i
j
)
R i k is a rate of return for asset k at the time i+1 wherein
R
i
k
=
ln
(
P
i
+
1
k
P
i
k
)
P i j is a value for asset j at a time i;
P i+1 j is a value for asset j at a time i+1;
P i k is a value for asset k at the time i;
P i+1 k is a value for asset k at the time i+1;
λ is an exponential weighted moving average parameter; and
σ* jk is an estimate of σ jk at the beginning of the period.
5 . The computer implemented method of claim 4 , wherein the formula is adjusted by applying, by the one of more computers, one or more adjustments selected from the following group:
an annualization adjustment; a contract multiplier; a minimum value for a calculation of R i j R i k ; a maximum value for the calculation of R i j R i k ; a minimum value for a calculation of σ jk ; a maximum value for the calculation of σ jk ; a signal processing algorithm for the calculation of R i j R i k ; a signal processing algorithm for the calculation of σ jk .
6 . The computer implemented method of claim 1 , wherein the two assets are securities issued by, or referenced to, a firm and using the calculated covariance as a measure of credit risk of a security of the two securities that ranks highest in priority upon a liquidation or default event.
7 . The computer implemented method of claim 1 , wherein an annualized expected default loss (EDL j ) on the said asset, asset j, is calculated by the one or more computers using one or both of the following equations:
EDL j =ln(ρ jk √{square root over (( e σ j 2 T −1)( e σ k 2 T −1))}{square root over (( e σ j 2 T −1)( e σ k 2 T −1))}+1)/ T
EDL j =ρ jk σ j σ k
wherein:
k is the second asset, being an asset that ranks behind asset j in terms of priority upon a liquidation or default event
T is a time horizon of interest to a user, in years
σ j is a standard deviation of a rate of return, per annum, of j
σ k is a standard deviation of a rate of return, per annum, of k
ρ jk is a correlation coefficient of the rates of return for j and k;
the equation is fitted; and
parameters of interest from the fitted equation are output to a user.
8 . A financial instrument engine system for measuring a credit risk of an asset, the system comprising at least one processor and at least one computer-readable memory communicatively coupled to the at least one processor, the at least one memory storing processor-executable instructions that, when executed by the at least one processor, cause the system to perform operations comprising:
receiving, by one or more computers, data representative of the said asset and data representative of a second asset; calculating, by the one or more computers, an estimate of a covariance of rates of return of the two assets using the data; determining, by the one or more computers, a measure of the credit risk of the said asset based on the estimate of covariance; and storing, by the one or more computers, the determined measure of credit risk of the said asset.
9 . The computer system of claim 8 , wherein a financial instrument is traded based on the measure of the credit risk of the said asset and wherein the at least one memory further stores processor-executable instructions that, when executed by the at least one processor, cause the system to perform operations comprising:
trading, or providing a service for at least one customer to trade, the at least one financial instrument; calculating, by the one or more computers, the covariance of the two assets based on a formula applied to the rates of return of the two assets over a period; and determining, by the one or more computers, a price of at least one financial instrument at its maturity based at least in part on the aforesaid calculated covariance.
10 . The computer system of claim 9 , wherein the service is provided for the at least one customer to trade the at least one financial instrument and wherein the at least one memory further stores processor-executable instructions that, when executed by the at least one processor, cause the system to perform operations comprising:
transmitting, by the one or more computers, pricing information on the at least one financial instrument to the at least one customer; and effecting, by the one or more computers, one or more trades in the at least one financial instrument for the at least one customer.
11 . The computer system of claim 9 , wherein the at least one memory further stores processor-executable instructions that, when executed by the at least one processor, cause the system to perform operations wherein the formula is selected from the group consisting of:
σ
jk
=
∑
i
=
1
N
-
1
R
i
j
R
i
k
N
-
1
σ
jk
=
(
1
-
λ
)
(
1
-
λ
N
-
1
)
∑
i
=
1
N
-
1
λ
N
-
i
-
1
R
i
j
R
i
k
σ
jk
=
(
1
-
λ
)
∑
i
=
1
N
-
1
λ
N
-
i
-
1
R
i
j
R
i
k
+
λ
N
-
1
σ
jk
*
wherein:
σ jk is a covariance of assets j and k;
N is an actual number of pairs of asset values for j and k used to calculate rates of return over the period;
R i j is a rate of return for asset j at a time i+1 wherein
R
i
j
=
ln
(
P
i
+
1
j
P
i
j
)
R i k is a rate of return for asset k at the time i+1 wherein
R
i
k
=
ln
(
P
i
+
1
k
P
i
k
)
P i j is a value for asset j at a time i;
P i+1 j is a value for asset j at a time i+1;
P i k is a value for asset k at the time i;
P i+1 k is a value for asset k at the time i+1;
λ is an exponential weighted moving average parameter; and
σ* jk is an estimate of σ jk at the beginning of the period.
12 . The computer system of claim 11 , wherein the at least one memory further stores processor-executable instructions that, when executed by the at least one processor, cause the system to perform operations wherein the formula is adjusted by applying, by the one of more computers, one or more adjustments selected from the following group:
an annualization adjustment; a contract multiplier; a minimum value for a calculation of R i j R i k ; a maximum value for the calculation of R i j R i k ; a minimum value for a calculation of σ jk ; a maximum value for the calculation of σ jk ; a signal processing algorithm for the calculation of R i j R i k ; a signal processing algorithm for the calculation of σ jk .
13 . The computer system of claim 8 , wherein the at least one memory further stores processor-executable instructions that, when executed by the at least one processor, cause the system to perform operations comprising:
allowing selection by a user of two securities issued by, or referenced to, a firm as the two assets; and using the calculated covariance as a measure of credit risk of a security of the two securities that ranks highest in priority upon a liquidation or default event.
14 . The computer system of claim 8 , wherein the at least one memory further stores processor-executable instructions that, when executed by the at least one processor, cause the system to perform operations wherein an annualized expected default loss (EDL j ) on the said asset, asset j, is calculated by the one or more computers using one or both of the following equations:
EDL j =ln(ρ jk √{square root over (( e σ j 2 T −1)( e σ k 2 T −1))}{square root over (( e σ j 2 T −1)( e σ k 2 T −1))}+1)/ T
EDL j =ρ jk σ j σ k
wherein:
k is the second asset, being an asset that ranks behind asset j in terms of priority upon a liquidation or default event
T is a time horizon of interest to a user, in years
σ j is a standard deviation of a rate of return, per annum, of j
σ k is a standard deviation of a rate of return, per annum, of k
ρ jk is a correlation coefficient of the rates of return for j and k;
the equation is fitted; and
parameters of interest from the fitted equation are output to a user.
15 . A non-transitory computer readable medium storing computer-executable instructions for measuring a credit risk of an asset that, upon execution by one or more computers, cause the one or more computers to perform operations comprising:
receiving, by one or more computers, data representative of the said asset and data representative of a second asset; calculating, by the one or more computers, an estimate of a covariance of rates of return of the two assets using the data; determining, by the one or more computers, a measure of the credit risk of the said asset based on the estimate of covariance; and storing, by the one or more computers, the determined measure of credit risk of the said asset.
16 . The non-transitory computer-readable medium of claim 15 , wherein a financial instrument is traded based on the measure of the credit risk of the said asset and wherein the non-transitory computer-readable medium further stores computer-executable instructions that, upon execution by one or more computers, cause the one or more computers to perform operations comprising:
trading, or providing a service for at least one customer to trade, the at least one financial instrument; calculating, by the one or more computers, the covariance of the two assets based on a formula applied to the rates of return of the two assets over a period; and determining, by the one or more computers, a price of at least one financial instrument at its maturity based at least in part on the aforesaid calculated covariance.
17 . The non-transitory computer-readable medium of claim 16 , wherein the service is provided for the at least one customer to trade the at least one financial instrument and wherein the non-transitory computer-readable medium further stores processor-executable instructions that, when executed by the at least one processor, cause the one or more computers to perform operations comprising:
transmitting, by the one or more computers, pricing information on the at least one financial instrument to the at least one customer; and effecting, by the one or more computers, one or more trades in the at least one financial instrument for the at least one customer.
18 . The non-transitory computer-readable medium of claim 16 , further storing processor-executable instructions that, when executed by the at least one processor, cause the one or more computers to perform operations wherein the formula is selected from the group consisting of:
σ
jk
=
∑
i
=
1
N
-
1
R
i
j
R
i
k
N
-
1
σ
jk
=
(
1
-
λ
)
(
1
-
λ
N
-
1
)
∑
i
=
1
N
-
1
λ
N
-
i
-
1
R
i
j
R
i
k
σ
jk
=
(
1
-
λ
)
∑
i
=
1
N
-
1
λ
N
-
i
-
1
R
i
j
R
i
k
+
λ
N
-
1
σ
jk
*
wherein:
σ jk is a covariance of assets j and k;
N is an actual number of pairs of asset values for j and k used to calculate rates of return over the period;
R i j is a rate of return for asset j at a time i+1 wherein
R
i
j
=
ln
(
P
i
+
1
j
P
i
j
)
R i k is a rate of return for asset k at the time i+1 wherein
R
i
k
=
ln
(
P
i
+
1
k
P
i
k
)
P i j is a value for asset j at a time i;
P i+1 j is a value for asset j at a time i+1;
P i k is a value for asset k at the time i;
P i+1 k is a value for asset k at the time i+1;
λ is an exponential weighted moving average parameter; and
σ* jk is an estimate of σ jk at the beginning of the period.
19 . The non-transitory computer-readable medium of claim 18 , further storing processor-executable instructions that, when executed by the at least one processor, cause the one or more computers to perform operations wherein the formula is adjusted by applying, by the one of more computers, one or more adjustments selected from the following group:
an annualization adjustment; a contract multiplier; a minimum value for a calculation of R i j R i k ; a maximum value for the calculation of R i j R i k ; a minimum value for a calculation of σ jk ; a maximum value for the calculation of σ jk ; a signal processing algorithm for the calculation of R i j R i k ; a signal processing algorithm for the calculation of σ jk .
20 . The non-transitory computer-readable medium of claim 15 , further storing computer-executable instructions that, upon execution by one or more computers, cause the one or more computers to perform operations comprising:
allowing selection by a user of two securities issued by, or referenced to, a firm as the two assets; and using the calculated covariance as a measure of credit risk of a security of the two securities that ranks highest in priority upon a liquidation or default event.
21 . The non-transitory computer-readable medium of claim 15 , further storing computer-executable instructions that, upon execution by one or more computers, cause the one or more computers to calculate an annualized expected default loss (EDL j ) on the said asset, asset j, using one or both of the following equations:
EDL j =ln(ρ jk √{square root over (( e σ j 2 T −1)( e σ k 2 T −1))}{square root over (( e σ j 2 T −1)( e σ k 2 T −1))}+1)/ T
EDL j =ρ jk σ j σ k
wherein:
k is the second asset, being an asset that ranks behind asset j in terms of priority upon a liquidation or default event
T is a time horizon of interest to a user, in years
σ j is a standard deviation of a rate of return, per annum, of j
σ k is a standard deviation of a rate of return, per annum, of k
ρ jk is a correlation coefficient of the rates of return for j and k;
the equation is fitted; and
parameters of interest from the fitted equation are output to a user.Join the waitlist — get patent alerts
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