System and method for determining a liquidity-adjusted value at risk (LA-VaR)
First Claim
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1. A computer-implemented method for calculating an xn-day liquidity-adjusted value-at-risk (LA-VaR) measure for a financial portfolio, the method comprising:
- determining, by a computer system, from an initial set of market risk factors for the portfolio, a core set of liquid risk factors for the portfolio, wherein the core set of liquid risk factors represents a space of liquid risks for the portfolio;
determining, by the computer system, a subset of illiquid risk factors from the initial set of risk factors via a linear regression of each illiquid risk factor on the space of liquid risks as represented by the core set of liquid risk factors;
storing, by the computer system, a liquidity time horizon for each illiquid risk factor;
calculating by the computer system a profit and loss (P&
L) distribution for the portfolio for a time interval [0,1 day];
calculating by the computer system one or more P&
L distributions for the portfolio for the time intervals day], wherein xi>
1 day by simulating only the illiquid risk factors having a liquidity time horizon greater than or equal to xn-days, where xi-1=1 day, where i=1, . . . n, and where n≧
1;
combining by the computer system the P&
L distributions for the [0,1] time interval and the one or more (xi-1,xi day] time intervals; and
calculating by the computer system the xn-day VaR for the portfolio based on the combined P&
L distributions,wherein the computer system comprises at least one computer device, wherein the computer device comprises at least one processor circuit and at least one memory circuit.
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Abstract
Computer-based systems and methods for calculating a liquidity-adjusted VaR for a portfolio. The liquidity-adjusted VaR accounts for the different liquidities of the risks. The process for calculating the liquidity-adjusted VaR may include adding to the standard 1-day VaR only the losses produced by illiquid risks that are orthogonal to the space of liquid risks.
27 Citations
27 Claims
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1. A computer-implemented method for calculating an xn-day liquidity-adjusted value-at-risk (LA-VaR) measure for a financial portfolio, the method comprising:
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determining, by a computer system, from an initial set of market risk factors for the portfolio, a core set of liquid risk factors for the portfolio, wherein the core set of liquid risk factors represents a space of liquid risks for the portfolio; determining, by the computer system, a subset of illiquid risk factors from the initial set of risk factors via a linear regression of each illiquid risk factor on the space of liquid risks as represented by the core set of liquid risk factors; storing, by the computer system, a liquidity time horizon for each illiquid risk factor; calculating by the computer system a profit and loss (P&
L) distribution for the portfolio for a time interval [0,1 day];calculating by the computer system one or more P&
L distributions for the portfolio for the time intervals day], wherein xi>
1 day by simulating only the illiquid risk factors having a liquidity time horizon greater than or equal to xn-days, where xi-1=1 day, where i=1, . . . n, and where n≧
1;combining by the computer system the P&
L distributions for the [0,1] time interval and the one or more (xi-1,xi day] time intervals; andcalculating by the computer system the xn-day VaR for the portfolio based on the combined P&
L distributions,wherein the computer system comprises at least one computer device, wherein the computer device comprises at least one processor circuit and at least one memory circuit. - View Dependent Claims (2, 3, 4, 5, 6, 7)
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8. A system for calculating an xn-day liquidity-adjusted value-at-risk (LA-VaR) measure for a financial portfolio, the system comprising:
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a computer data store; and a computer device in communication with the computer data store, wherein the computer device comprises at least one processor circuit and at least one memory circuit, and wherein the computer device is programmed to; determine, from an initial set of market risk factors for the portfolio, a core set of liquid risk factors for the portfolio, wherein the core set of liquid risk factors represents a space of liquid risks for the portfolio; determine a subset of illiquid risk factors from the initial set of risk factors via a linear regression of each illiquid risk factor on the space of liquid risks as represented by the core set of liquid risk factors, wherein a liquidity time horizon for each illiquid risk factor is stored in the computer data store; calculate a profit and loss (P&
L) distribution for the portfolio for a time interval [0,1 day];calculate one or more P&
L distributions for the portfolio for the time intervals (xi-1,xi day], wherein xi>
1 day by simulating only the illiquid risk factors having a liquidity time horizon greater than or equal to x, days, where xi-1=1 day, where i=1, . . . n, and where n≧
1;combine the P&
L distributions for the [0,1 day] time interval and the one or more (xi-1,xiday] time intervals; andcalculate the xn-day VaR for the portfolio based on the combined P&
L distributions. - View Dependent Claims (9, 10, 11, 12, 13, 14)
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15. A non-transitory storage medium having stored thereon instructions that when executed by a processor circuit cause the processor circuit to calculate an xn-day liquidity-adjusted value-at-risk (LA-VaR) measure for a financial portfolio by:
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determining, from an initial set of market risk factors for the portfolio, a core set of liquid risk factors for the portfolio, wherein the core set of liquid risk factors represents a space of liquid risks for the portfolio; determining a subset of illiquid risk factors from the initial set of risk factors via a linear regression of each illiquid risk factor on the space of liquid risks as represented by the core set of liquid risk factors; calculating a profit and loss (P&
L) distribution for the portfolio for a time interval [0,1 day];calculating one or more P&
L distributions for the portfolio for the time intervals (xi-1,xiday], wherein xi>
1 day by simulating only the illiquid risk factors having a liquidity time horizon greater than or equal to xidays, where xi-1=1 day, where i=1, . . . n, and where n≧
1;combining the P&
L distributions for the [0,1 day] time interval and the one or more (xi-1,xiday] time intervals; andcalculating the xn-day VaR for the portfolio based on the combined P&
L distributions. - View Dependent Claims (16, 17, 18, 19, 20, 21)
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22. A computer-implemented method for calculating a liquidity-adjusted value-at-risk (LA-VaR) measure for a financial portfolio for a n-day VaR calculation period, the method comprising:
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where the n-day VaR calculation period has a number m of sub-time intervals indexed by k=1, . . . , m, each sub-time interval k having a start time tk-1 and an end time tk, and t0=0, (a) determining, by a computer system, a core set of liquid risk factors available in a first sub-time interval [t0, t1], wherein the liquid risk factors available in the first sub-time interval are risk factors that have liquidity horizons less than or equal to the end time t1 of the first sub-time interval and represent a space of liquid risks for the portfolio for the first sub-time interval, wherein risk factors with liquidity horizons greater than the end time t1 of the first sub-time interval are illiquid risk factors in the first sub-time interval; (b) extracting, by the computer system, liquid risk components of the illiquid risk factors in the first sub-time interval [t0, t1] via linear regression of each illiquid risk factor on the core set of liquid risk factor in the first sub-time interval, wherein residuals of the linear regression represent the illiquid risk factors in the first sub-time interval after extraction of the liquid risk components of the illiquid risk factors; (c) calculating, by the computer system, a profit and loss (P&
L) distribution for the portfolio for the first sub-time interval [t0, t1] based on the residuals and the liquid risk factors for the first sub-time interval;(d) repeating steps (a)-(c) for sub-time intervals indexed by k=2, . . . , m; (e) computing, by the computer system, a combined P&
L distribution for the portfolio by combining the P&
L distributions for each of the sub-time intervals indexed by k=1, . . . , m; and(f) calculating, by the computer system, the VaR for the portfolio for the n-day VaR calculation period based on the combined P&
L distribution. - View Dependent Claims (23)
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24. A system for calculating a liquidity-adjusted value-at-risk (LA-VaR) measure for a financial portfolio for a n-day VaR calculation period, the system comprising:
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at least one computer device that comprises at least one processor circuit and at least one memory circuit, and wherein the at least one computer device is programmed to; where the n-day VaR calculation period has a number m of sub-time intervals indexed by k=1, . . . , m, each sub-time interval k having a start time tk-1, and an end time tk, and t0=0, (a) determine a core set of liquid risk factors available in a first sub-time interval [t0, t1], wherein the liquid risk factors available in the first sub-time interval are risk factors that have liquidity horizons less than or equal to the end time t1 of the first sub-time interval and represent a space of liquid risks for the portfolio for the first sub-time interval, wherein risk factors with liquidity horizons greater than the end time t1 of the first sub-time interval are illiquid risk factors in the first sub-time interval; (b) extract liquid risk components of the illiquid risk factors in the first sub-time interval [t0, t1] via linear regression of each illiquid risk factor on the core set of liquid risk factor in the first sub-time interval, wherein residuals of the linear regression represent the illiquid risk factors in the first sub-time interval after extraction of the liquid risk components of the illiquid risk factors; (c) calculate a profit and loss (P&
L) distribution for the portfolio for the first sub-time interval [t0, t1] based on the residuals and the liquid risk factors for the first sub-time interval;(d) repeat steps (a)-(c) for sub-time intervals indexed by k=2, . . . , m; (e) compute a combined P&
L distribution for the portfolio by combining the P&
L distributions for each of the sub-time intervals indexed by k=1, . . . , m; and(f) calculate the VaR for the portfolio for the n-day VaR calculation period based on the combined P&
L distribution. - View Dependent Claims (25)
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26. A non-transitory storage medium having stored thereon instructions that when executed by a processor circuit cause the processor circuit to calculate a liquidity-adjusted value-at-risk (LA-VaR) measure for a financial portfolio for a n-day VaR calculation period by:
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where the n-day VaR calculation period has a number m of sub-time intervals indexed by k=1, . . . , m, each sub-time interval k having a start time tk-1 and an end time tk, and t0=0, (a) determining a core set of liquid risk factors available in a first sub-time interval [t0, t1], wherein the liquid risk factors available in the first sub-time interval are risk factors that have liquidity horizons less than or equal to the end time t1 of the first sub-time interval and represent a space of liquid risks for the portfolio for the first sub-time interval, wherein risk factors with liquidity horizons greater than the end time t1 of the first sub-time interval are illiquid risk factors in the first sub-time interval; (b) extracting liquid risk components of the illiquid risk factors in the first sub-time interval [t0, t1] via linear regression of each illiquid risk factor on the core set of liquid risk factor in the first sub-time interval, wherein residuals of the linear regression represent the illiquid risk factors in the first sub-time interval after extraction of the liquid risk components of the illiquid risk factors; (c) calculating a profit and loss (P&
L) distribution for the portfolio for the first sub-time interval [t0, t1] based on the residuals and the liquid risk factors for the first sub-time interval;(d) repeating steps (a)-(c) for sub-time intervals indexed by k=2, . . . , m; (e) computing a combined P&
L distribution for the portfolio by combining the P&
L distributions for each of the sub-time intervals indexed by k=1, . . . , m; and(f) calculating the VaR for the portfolio for the n-day VaR calculation period based on the combined P&
L distribution. - View Dependent Claims (27)
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Specification