毕博上海银行咨询Credit Risk Mgmt Sys Analytics UsersGuide012100.doc

DANIEL H. WAGNER ASSOCIATESINCORPORATEDCONSULTANTSOPERATIONS RESEARCH · MATHEMATICS · SOFTWARE DEVELOPMENTHQTRS AND PENNSYLVANIA OFFICEHAMPTON OFFICESUITE 200SUITE 50040 LLOYD AVENUE2 EATON STREETMALVERN, PA 19355HAMPTON, VA 23669610 644-3400757 727-7700FAX: 610 644-6293FAX: 757 722-0249WASHINGTON OFFICESANTA CLARA OFFICESUITE 206SUITE 400450 MAPLE AVENUE, EAST4677 OLD IRONSIDES DRIVEVIENNA, VA 22180SANTA CLARA, CA 95054703 938-2032408 987-0600FAX: 610 255-4781FAX: 408 987-0606January 21, 2000To:Korean Information ServiceFrom:Dr. S. SuchowerSubject:VaR Model Users Guide, Release 1.002This guide describes the use and structure of the Hanvit Bank VaR model. We address the following topics:1. Overview2. Command-line interface3. Input files4. Output files5. Error codes6. Source code roadmap1. OverviewThis software uses Monte Carlo simulation to build the portfolio credit VaR distribution. Credit risk is driven by risk rating migrations of the borrowers in the portfolio. The model captures the specific as well as systematic effects in these rating migrations. In particular, borrower-to-borrower correlation in rating migration depends on a set of industry indices . Each is the time series of normalized average equity returns for a specific industry.Each is modeled as a stationary Gaussian time series with steady-state mean zero and steady-state variance one. The matrix of correlations between the for different industries is assumed to have been estimated from historical data on Korean industry equity returns.We assume that one-year rating migrations reflect an underlying, continuous credit-change index that is distributed as a standard normal variate. Let represent the number of non-default rating grades and let be the probability of migrating from grade to . For an initial rating , we represent each rating grade transition as an interval on the real line. Specifically, the partition of the real line into intervals is determined by defining and using the relation,(1)where is the standard normal cumulative distribution function. This is equivalent to specifying for all grades (both default and non-default).In the subsections which follow we will describe the model for , the credit change index for borrower . This discussion divides into two cases. The first case addresses the model for in the absence of any chaebol effect. The second case describes how to modify the model to account for the chaebol effect. In either case, we will demonstrate that the model for has the following basic form:(2)where the industry factors may be augmented by a collection of chaebol-specific factors, is the borrower specific weight, and the are chosen so that has unit variance. For the purpose of these discussions, we will assume that the user provides the following information for each borrower in the portfolio:(i) the relative contribution of industry , , to the business of the given borrower; and(ii) the borrower specific weight .Additional information required for consideration of the chaebol effect will be addressed in subsequent subsections.The interval breakpoints , as defined above, remain fixed as the credit-change index varies stochastically from time period to time period. Changes in are linked to changes in the systematic factors and the idiosyncratic component through Eq. (2). Given an initial grade and an instance of the systematic factors , the probability that lies in the interval is given by.(3)The quantity in Eq. (3) represents the probability of migrating from to conditioned on the vector of systematic factors. This provides the mechanism for translating correlation between the systematic factors into correlation in the migration behavior of different borrowers.It follows from Eq. (2) that the rating migrations of different borrowers are conditionally independent given a set of values for each of the systematic factors. Under the assumption that the portfolios exposure to any single borrower is small, we can apply the central limit theorem and approximate the portfolio NPV distribution given as a Gaussian distribution. This implies that we only need to calculate the first two moments of the NPV distribution for each exposure in the portfolio. Standard Monte Carlo simulation must be applied to account for the contribution to portfolio NPV conditioned on contribution of any large exposure.On each Monte Carlo sample (replication) we obtain a Gaussian approximation of the aggregate portfolio NPV distribution. The conditional portfolio mean is obtained by adding to the sum of the conditional expected values of the small exposures the NPV instances of the large exposures. The conditional portfolio variance is the sum of the conditional variances of the small exposures. The final (unconditional) NPV distribution is a weighted sum of the conditional Gaussian distributions obtained on each replication (equal weighting).We observe that although the conditional portfolio NPV distribution is closely approximated as Gaussian for each sampled , the unconditional portfolio NPV distribution is in general non-Gaussian and will exhibit the heavy lower tail characteristic of portfolio VaR distributions.There are several advantages of this approach. We obtain significant variance reduction by combining analytic methods with standard Monte Carlo techniques. This allows us to generate very accurate approximations of the tail of the distribution using far fewer replications than would be required if the central limit theorem were not used. We also get the added benefit of improved computational performance and reduced execution times.We now address various details of the modeling approach.1.1. Non-Chaebol ProcessingIn this subsection we describe the model for , the credit change index for borrower , in the absence of the chaebol effect.In this case, we decompose into a borrower-specific (idiosyncratic) component and industry (systematic) components as follows:.(4)where(i) for the weight is proportional to ;(ii) the borrower specific weight is determined by the fraction of the variance of attributable to borrower specific risk; and(iii) the are chosen so that has unit variance. Clearly, the expression in Eq. (4) is consistent with the form specified in Eq. (2).1.2. Chaebol ProcessingAn important modeling feature is the explicit treatment of chaebols, groups of Korean companies that operate as conglomerates and whose business fortunes are therefore linked. The resulting chaebol effect represents a second source of correlation in the migrations of borrowers not accounted for in Eq. (4).The approach we take to account for the chaebol effect is to treat each chaebol as an “industry” and add a corresponding risk factor to the vector of systematic risk factors. Whereas the for actual industries are calibrated to equity returns, the risk factors for chaebols are constructed synthetically. Each is represented as a weighted linear combination of the industry-specific risk factors and a chaebol-specific risk factor . Thus, (5)where(i) for the weights are proportional to the revenue contribution of each industry to the chaebol (these are derived from the revenue contributions of the borrowers and their associated industry weights );(ii) the weight of the chaebol-specific risk factor is based on the fraction of the variance of attributable to chaebol-specific risk; and(iii) the are such that has unit variance.Note that the chaebol-specific risk factors are taken to be both independent from chaebol to chaebol and independent of the for actual industries. The chaebol-specific weight must be provided by the user.Fix attention on a specific borrower . Then in the presence of the chaebol effect, the credit-change index for borrower is given by ,(6)where(i) the parameter (with ) controls the relative strength of the chaebol effect and the industry effects for chaebol c and borrower j (a calculated quantity requiring a user-input value for the borrower-to-chaebol correlation);(ii) the risk specific to borrower j is associated with the unit normal variate with weight specified by (a user-specified input);(iii) for the weights are proportional to ; and(iv) the are normalized so that has unit variance.The parameter is given by,(7)where the quantity must be provided by the user.Overall then, the decomposition of accounts for (i) direct exposure to each industry through the , (ii) exposure to the chaebol risk (both industry risk inherited through the chaebol and chaebol-specific risk), and (iii) the specific risk of the borrower. The expression in Eq. (6) can be rewritten in the form specified in Eq. (2), with the addition of chaebol-specific risk factors.1.3. NPV CalculationsThe model is designed to address six financial instrument types: loans, financial guarantees, bonds, derivatives, miscellaneous, and equities. The valuations of the first five instruments are performed using precomputed revaluation tables provided by the user. The revaluation tables are indexed by instrument term, loss in the event of default (LIED), and facility usage (if applicable). A separate entry appears in a given revaluation table for each combination of initial borrower rating grade and final borrower rating grade. An entry in a revaluation table provides the NPV of the instrument after six months as a percentage of the commitment or outstanding amount.Equities are treated using a simple model for the change in equity value. We assume that the final value depends on the credit-change index in the following way:,(8)where the volatility depends on the size class of the borrower. We take as the NPV of the equity.1.4. Moment CalculationsIn order to apply the central limit theorem, we need to calculate the first and second moments of the NPV distribution for each financial instrument in the portfolio conditioned on . For five of the instrument types (loans, guarantees, bonds, derivatives, and miscellaneous) the moment calculations are straightforward. For initial grade we have,(9)where is the commitment or outstanding amount, is the term index, is the LIED index, is the usage index, is the migration matrix conditioned on , and is the NPV value read from the appropriate revaluation table. We also have.(10)The conditional NPV mean and variance can be calculated directly from these two quantities.Now we consider the NPV of equities. For borrower let , , and . Then for borrower we have (11) and.(12)The mean and variance can be calculated directly from these two quantities.2. Command-line InterfaceThe VaR Model is a command-line program. Most of the input data is provided to the model via flat files. The various outputs of the model are also provided as flat files. The execution of the program is controlled by several parameters, which must be set when the program is invoked from the command-line. The syntax of the command-line interface is as follows:RUNVARexposure_in=<exposure data filename>revaluetable_in=<revaluaton table filename>rfcov_in=<risk factor covariance data filename>eqtvol_in=<equity volatility data filename> migmat_in=<risk rating migration matrix filename>nrep_in=<number of replications>seed_in=<initial random number seed (integer)>expbd_in=<large exposure bound in Won>idiobd_in=<idiosyncratic weight bound>chblflag_in=<chaebol processing flag>values_out=<replication data filename>stats_out=<statistics data filename>hist_out=<histogram data filename>dbg_out=<debug output filename>cmd=<command file filename>where items in square brackets () are optional and items in angle brackets (<>) are descriptive text. Although the description above puts one parameter on each line for illustration purposes, the program requires that all parameters appear on the same line.We now describe the purpose of each command-line parameter. A description of each input and output file is provided in Sections 3 and 4.exposure_inThis parameter is used to specify the input exposure filename. It is required.revaluetable_inThis parameter is used to specify the input revaluation table filename. It is required.rfcov_inThis parameter is used to specify the input factor correlation filename. It is required.eqtvol_inThis parameter is used to specify the input equity volatility filename. It is required.migmat_inThis parameter is used to specify the input migration matrix filename. It is required.nrep_inThis parameter is used to specify the number of replications for the simulation. It must be a positive integer and is required.seed_inThis parameter is used to specify the random number seed for the simulation. It must be a positive integer and is optional. The default value is 1223334444.expbd_inThis parameter is used to specify the large exposure bound. The total exposure to a particular borrower is the sum of the commitment/outstanding amounts of each facility associated with the borrower. When the total exposure exceeds this bound the borrower is labeled as a “large exposure” and treated with a standard Monte Carlo; small exposures are treated with the central limit theorem. A general rule-of-thumb is to set this bound equal to approximately 0.5% of the total portfolio. This parameter is in units of Won and is optional. The default value is 1020 Won (i.e., for most practical applications this forces all borrowers to be treated with the central limit theorem). A value of zero forces the program to treat all borrowers using a standard Monte Carlo.idiobd_inThis parameter is used to specify the idiosyncratic weight bound. If the idiosyncratic weight of a particular borrower is less than this threshold, then the software treats the borrower using a standard Monte Carlo. Use of the central limit theorem is based on the assumption that idiosyncratic risk is the dominant risk. A general rule of thumb is to set this bound equal to 50.0% (i.e., the value 50.0). This parameter is in percentage units and is optional. The default value is zero (i.e., all borrowers are treated with the central limit theorem). A value of 100.0 forces the program to treat all borrowers using a standard Monte Carlo.chblflag_inThis parameter is used to turn chaebol processing on and off. A value of 0 turns chaebol processing off; any non-zero value turns chaebol processing on. This parameter is optional. The default value is 1.values_outThis parameter is