WO2005029373A2 - System and method for performing risk analysis - Google Patents
System and method for performing risk analysis Download PDFInfo
- Publication number
- WO2005029373A2 WO2005029373A2 PCT/CH2003/000633 CH0300633W WO2005029373A2 WO 2005029373 A2 WO2005029373 A2 WO 2005029373A2 CH 0300633 W CH0300633 W CH 0300633W WO 2005029373 A2 WO2005029373 A2 WO 2005029373A2
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- WIPO (PCT)
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- risk
- copula
- random variables
- portfolio
- data
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
- G06Q40/00—Finance; Insurance; Tax strategies; Processing of corporate or income taxes
- G06Q40/08—Insurance
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
- G06Q40/00—Finance; Insurance; Tax strategies; Processing of corporate or income taxes
- G06Q40/06—Asset management; Financial planning or analysis
Definitions
- the present invention relates to a system and a computer implemented method for performing risk analysis of a portfolio.
- These tools and means are based on models, based on which simulations are performed to generate possible valuation scenarios . These simulations generally use the Monte Carlo method or other appropriate methods .
- the models use probability distributions and are calibrated with historical data. Such historical data may be obtained from various sources, such as DataStreamTM.
- simulations are usually implemented in computer software as part of a financial services system and are run on computer hardware.
- the input data for the simulations are risk factors, which are handled as random variables.
- risk factors can be equity indices, foreign exchange rates, interest rates, or insurance loss frequencies and severities.
- the result or output data of such simulations is at least one risk measure in the form of a numerical quantity or value. Usually, several risk measure values of different types can be obtained.
- risk measure values will be forwarded to an analyst or an actuary or an underwriter, i.e. a human representative of a financial services company. These risk measure values enable him to decide whether or not any actions should be taken to reduce the risk. Such actions can be changes in a credit or equities portfolio, or in a portfolio of insurance and reinsurance liabilities.
- the risk measures usually consist of a variety of values, such as the maximum value obtained, the standard deviation of the simulation, a shortfall, usually the 99% shortfall, or a value-at-risk (VARTM) .
- VARTM value-at-risk
- the VARTM is the greatest possible loss that the company may expect in the portfolio in question with a certain given degree of probability during a certain future period of time.
- the full distribution itself can be the risk measure as well .
- copulas are well known in the state of the art . They are joint distribution functions of random vectors with standard uniform marginal distributions. They provide a way of understanding how marginal distributions of single risks are coupled together to form joint distributions of groups of risks.
- copulas are known.
- closed form copulas are the Gumbel and the Clayton copula.
- implicit copulas i.e. copulas for which no closed form exists, are the Gaussian copula and the t- copula.
- the copula of Y can be written as where p . ⁇ ⁇ y / ⁇ ⁇ ⁇ for i, j e ⁇ l,...,d ⁇ and where t d v , P denotes the distribution function of vZl s , where S ⁇ X 2 V and Z ⁇ Nd (0,p) are independent (i.e. the usual multivariate t distribution function) and / founded denotes the marginal distribution function of tt ,P (i.e. the usual univariate t distribution function) .
- the copula expression can be written as
- H ⁇ ,-,H d be arbitrary continuous, strictly increasing distribution functions and let Y be given by (1) with ⁇ a linear correlation matrix. Then has a / admir-copula and marginal distributions H ⁇ ,-,H d .
- the distribution of X is referred to as a meta-t distribution. Note that X has a t-distribution if and only if H ⁇ ,-,H d . are univariate t v -distribution functions .
- the coefficient of tail dependence expresses the limiting conditional probability of joint quantile exceedences.
- the t-copula has upper and lower tail dependence with
- the calibration of the copula parameters (p,v) are typically done as follows :
- step (ii) the empirical marginals or fitted distribution functions from a parametric family can be used.
- the simulation from t-copula comprises the following steps:
- the inventive method and the method shall be more flexible and accurate than the known system based on the meta-t-model, but without the need to use more efficient data processing machines and without the need to have an increased number of input data based on historical data.
- the invention still uses t-copulas.
- the financial risk factors i.e. the random variables
- each group obtains its own degree-of- freedom parameter. Therefore, a random vector can be obtained which is partitioned into subvectors.
- Each subvector is properly described by a multi-dimensional t- distribution, wherein each multi-dimensional t-distribution has a different degree-of-freedom parameter and the groups in between each other still show dependency through correlation matrix and have tail dependency.
- this model can be calibrated using historical data in the same way as a t-copula model is calibrated with the exception that a maximum likelihood estimation of the multiple degrees of freedom parameters is performed separately on each of the multiple risk factor groups . Simulation is afterwards also performed in the same way as when using the t-copula model, and the same types of risk measure values are obtained.
- figure 1 illustrates the inventive system S and its input data
- figure 2 illustrates the inventive system S being used for a multiple of portfolios.
- Z ⁇ N d ( ⁇ ,p), where p is an arbitrary linear correlation matrix, is independent of U , a random variable uniformly distributed on [0,1].
- G Y . denotes the distribution function of ⁇ jv/x .
- a partition ⁇ ,...,d ⁇ into m subsets of sizes s ⁇ ,-,s screw, is made, wherein m is different from 1.
- p k denotes the distribution function of ⁇ k and H ⁇ ,-,H d are some arbitrary continuous distribution functions .
- the 4 risk factors are described by 4 random variables that are dependent among each other.
- the 4 random variables are divided in groups. Here, we choose to divide them by country: i.e. we receive two groups of two risk factors, wherein each group represents a country.
- a 4d random vector Y (Y Y 2 ,Y 3 ,Y 4 ) with grouped t- copula dependency among the 4 components is needed.
- the grouped t-copula can be written down in a form similar to (3) .
- the expression is quite complex and it is therefore not given explicitly.
- a person skilled in the art will know how to write this expression.
- We believe, that the properties of the grouped t-copula is best understood from (7) and the above stochastic representation.
- there is no need for an explicit copula expression as can be seen below:
- the simulation from the inventive grouped t-copula is no more difficult than simulation from a t-copula.
- the simulation comprises the following steps :
- the eigenvalue method may have to be applied to assure positive definiteness.
- ⁇ k is the state variable for counterparty k at time horizon T .
- ⁇ k takes values in ⁇ ,l ⁇ : the value 0 represents the default state, the value 1 is the non-default state.
- ⁇ k is a random variable with continuous distribution function
- the parameter d k is called the default threshold and ( ⁇ k ,d k ) is the latent variable model for ⁇ k .
- the following interpretation is put on ⁇ k .
- A* be the asset value of
- the model (10) says that asset value monthly log return can be linked to the risk factors by a' k X, which gives the systematic component of the risk and same additional independent idiosyncratic component e ⁇ .
- the parameter ⁇ k is the coefficient of determination for the systematic risk (how much of the variance can be explained by the risk factors) and
- the conditional probability of default for counterparty k given the risk factors X can be written as
- ⁇ denotes the standard normal cumulative distribution function.
- ⁇ k is normally distributed and thus the ⁇ A -quantile F k '( ⁇ k ) can be easily computed.
- the distribution function of ⁇ k is unknown: FJ. l [ ⁇ ) is replaced by the empirical quantile estimate P ⁇ k ⁇ k ) • Consequently, the estimated conditional probability of default Q k (x) is obtained by replacing F ⁇ k ⁇ k )
- Bernoulli-mixture model is that it can be easily extended to a Binomial-mixture model for a sub-portfolio of homogeneous counterparties .
- Table 1 shows the estimated degrees of freedom parameters for various subsets of risk factors and the overall estimated degrees of freedom parameter. Because of the difference between the various subset degrees of freedom parameters a grouped t-copula is more appropriate for describing the dependence structure .
- Table 1 Estimated degrees of freedom v for various sets of risk factors.
- the country equities indices are for major industrial sectors.
- Each counterparty is assigned to a country so that there are 25 from each country.
- Each counterparty is then described by two different risk factors (labelled ii and i 2 ) from the country to which it has been assigned, and the value of a (and hence also that of ⁇ ) are drawn from a uniform distribution on (0,1) such that 1.
- each counterparty has a total exposure of 1000 CHF and the loss given default is assumed to be uniformly distributed on [0,1] .
- Table 2 Risk measures of the sample portfolio using a t 29 - copula or a grouped t-copula to model the dependence among the 92 risk factors. The values shown are the percentage deviations from those obtained with the normal copula.
- - input means (a, b, c) - for entering or choosing calibration data for obtaining by using the modelling and calibration means values for the v k degrees of freedom parameters for each of the m subvectors Y k separately and for obtaining values for the correlation matrix p for all the random variables i to X d , - for entering or choosing at least one risk mapping function L (X) , in particular a profit and loss function, and - for entering portfolio data of the portfolio to be analysed;
- the system comprises at least three input levels: - a first level comprising a first input means (a) for entering or choosing the calibration data, wherein these data are used by the modelling and calibration means Mod/Cal; - a second level comprising a second input means (b) for entering or choosing at least one risk mapping function L (X) , wherein this function is preferably handled by a risk mapping means RM; this risk mapping means RM can be a stand alone means or being part of the simulation means SIM; and - a third level with third input means (c) for entering the specific portfolio data being used by the simulation means SIM.
- the calibration data are all the data needed for calibrating the model. Usually, they comprise historical data, marginals and information concerning the groups to be formed, i.e. a maximum number of groups and the information in view of which aspects or criteria the groups are formed.
- the risk mapping function is preferably a profit and loss function and it depends of the general type of portfolio to be analysed.
- the portfolio data depend on the specific portfolio to be analysed and can change daily.
- the calibration is performed periodically, for example once a year, with updated data.
- the risk mapping function must only be changed when a new general type of portfolio is entered.
- the portfolio data are entered more often, i.e. each time, when an updated risk measure or a new prize shall be obtained. Depending on the kind of business and the kind of portfolio, this is usually done daily or at least once a week.
- the system can be used by different users, which allows the users to have different levels of mathematical understanding.
- the modelling and calibration steps are usually performed by a first person, this person usually having a fundamental mathematical background.
- the risk mapping step is performed by a second person, who is usually a well trained senior risk analyst and has preferably some sort of mathematical background.
- the simulation is done by a risk analyst being responsible for the portfolio.
- the system also allows to perform simulation with different types of portfolios and with different portfolios within the same type, thereby using the same modelling and calibration means Mod/Cal .
- the calibration data then comprise information about all the portfolios to be handled. For example, when a first portfolio comprises 50 equities of 10 countries and a second portfolio comprises 70 equities of 20 countries, 30 of the equities and 5 of the countries being the same as in the first portfolio, the calibration data consider 90 different kinds of equities and can define 25 groups of different countries.
- a separate risk mapping means RM for entering the specific risk mapping function L(X).
- a separate simulation SIM can be performed.
- the system comprises a data storage for storing the historical data.
- the historical data may be stored on other means and to transfer it into the system when performing the calibration.
- a different computer or subsystem for the calibration and the simulation, transferring the data from the calibration computer or subsystem to the simulation computer or subsystem.
- the inventive system may then comprise storing means for storing the calibrated correlation matrix p and the calibrated parameters Vk describing the degrees of freedom. Like this, simulations can be run on different computers at the same time .
- the inventive system further comprises input means for grouping the d interdependent risk factors manually or for choosing manually a grouping from a range of several kind of groupings. This enables a user to group the risk factors according to the countries or according to the industrial sectors or other criteria.
- grouping the t-copulas enables to model large sets of risk factors of different classes.
- This grouped t-copula has the property that the random variables within each group have a t-copula with possibly different degrees of freedom parameters in the different groups. This gives a more flexible overall dependence structure more suitable for large sets of risk factors .
- the system allows to more accurately model the tail dependence present in the data than the popular Gaussian and t-copulas.
Description
Claims
Priority Applications (5)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
US10/547,296 US7647263B2 (en) | 2003-09-19 | 2003-09-19 | System and method for performing risk analysis |
DE10394036T DE10394036T5 (en) | 2003-09-19 | 2003-09-19 | System and method for performing a risk analysis |
CH01099/05A CH696749A5 (en) | 2003-09-19 | 2003-09-19 | Data processing system for performing risk analysis of portfolio, simulates realization of risk factors by using calibrated correlation matrix, calibration values of parameters, risk mapping function and portfolio data |
AU2003264217A AU2003264217B2 (en) | 2003-09-19 | 2003-09-19 | System and method for performing risk analysis |
PCT/CH2003/000633 WO2005029373A2 (en) | 2003-09-19 | 2003-09-19 | System and method for performing risk analysis |
Applications Claiming Priority (1)
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PCT/CH2003/000633 WO2005029373A2 (en) | 2003-09-19 | 2003-09-19 | System and method for performing risk analysis |
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WO2005029373A2 true WO2005029373A2 (en) | 2005-03-31 |
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PCT/CH2003/000633 WO2005029373A2 (en) | 2003-09-19 | 2003-09-19 | System and method for performing risk analysis |
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US (1) | US7647263B2 (en) |
AU (1) | AU2003264217B2 (en) |
CH (1) | CH696749A5 (en) |
DE (1) | DE10394036T5 (en) |
WO (1) | WO2005029373A2 (en) |
Families Citing this family (19)
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US7546270B1 (en) * | 2004-05-26 | 2009-06-09 | Fannie Mae | Method and system for estimating economic risk associated with a group of loans |
US7870047B2 (en) * | 2004-09-17 | 2011-01-11 | International Business Machines Corporation | System, method for deploying computing infrastructure, and method for identifying customers at risk of revenue change |
US20060195391A1 (en) * | 2005-02-28 | 2006-08-31 | Stanelle Evan J | Modeling loss in a term structured financial portfolio |
US20080167941A1 (en) * | 2007-01-05 | 2008-07-10 | Kagarlis Marios A | Real Estate Price Indexing |
US20080168001A1 (en) * | 2007-01-05 | 2008-07-10 | Kagarlis Marios A | Price Indexing |
US7809872B2 (en) | 2007-12-14 | 2010-10-05 | Infineon Technologies Ag | Master and slave device for communicating on a communication link with limited resource |
US20090187528A1 (en) * | 2008-01-17 | 2009-07-23 | Robert Craig Morrell | Method and system for assessing risk |
WO2009093441A1 (en) * | 2008-01-23 | 2009-07-30 | Itid Consulting, Ltd. | Information processing system, program, and information processing method |
US8131571B2 (en) * | 2009-09-23 | 2012-03-06 | Watson Wyatt & Company | Method and system for evaluating insurance liabilities using stochastic modeling and sampling techniques |
US20110264602A1 (en) * | 2010-04-22 | 2011-10-27 | Donald James Erdman | Computer-Implemented Systems And Methods For Implementing Dynamic Trading Strategies In Risk Computations |
US8688477B1 (en) | 2010-09-17 | 2014-04-01 | National Assoc. Of Boards Of Pharmacy | Method, system, and computer program product for determining a narcotics use indicator |
US8355976B2 (en) * | 2011-01-18 | 2013-01-15 | International Business Machines Corporation | Fast and accurate method for estimating portfolio CVaR risk |
JP5804492B2 (en) * | 2011-03-29 | 2015-11-04 | 日本電気株式会社 | Risk management device |
US9052358B2 (en) * | 2012-01-27 | 2015-06-09 | Portland State University | Copula-based system and method for management of manufacturing test and product specification throughout the product lifecycle for electronic systems or integrated circuits |
US9336771B2 (en) * | 2012-11-01 | 2016-05-10 | Google Inc. | Speech recognition using non-parametric models |
US20140180755A1 (en) * | 2012-12-21 | 2014-06-26 | Fluor Technologies Corporation | Identifying, Assessing, And Tracking Black Swan Risks For An Engineering And Construction Program |
US9974512B2 (en) | 2014-03-13 | 2018-05-22 | Convergence Medical, Llc | Method, system, and computer program product for determining a patient radiation and diagnostic study score |
US9858922B2 (en) | 2014-06-23 | 2018-01-02 | Google Inc. | Caching speech recognition scores |
US9299347B1 (en) | 2014-10-22 | 2016-03-29 | Google Inc. | Speech recognition using associative mapping |
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US20030061152A1 (en) * | 2001-09-26 | 2003-03-27 | De Rabi S. | System and method for determining Value-at-Risk using FORM/SORM |
EP1479024A4 (en) * | 2002-01-31 | 2007-01-03 | Seabury Analytic Llc | Business enterprise risk model and method |
US7337137B2 (en) * | 2003-02-20 | 2008-02-26 | Itg, Inc. | Investment portfolio optimization system, method and computer program product |
US20050209959A1 (en) * | 2004-03-22 | 2005-09-22 | Tenney Mark S | Financial regime-switching vector auto-regression |
GB0422411D0 (en) * | 2004-10-08 | 2004-11-10 | Crescent Technology Ltd | RiskBlade - a distributed risk budgeting architecture |
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2003
- 2003-09-19 AU AU2003264217A patent/AU2003264217B2/en not_active Expired
- 2003-09-19 CH CH01099/05A patent/CH696749A5/en not_active IP Right Cessation
- 2003-09-19 US US10/547,296 patent/US7647263B2/en active Active
- 2003-09-19 DE DE10394036T patent/DE10394036T5/en not_active Withdrawn
- 2003-09-19 WO PCT/CH2003/000633 patent/WO2005029373A2/en active Application Filing
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Publication number | Publication date |
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AU2003264217A1 (en) | 2005-04-11 |
US7647263B2 (en) | 2010-01-12 |
US20070027698A1 (en) | 2007-02-01 |
AU2003264217B2 (en) | 2007-07-19 |
CH696749A5 (en) | 2007-11-15 |
DE10394036T5 (en) | 2005-12-01 |
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