Input File

This page describes the XML input file for ccruncher-2.6.0. You can find the DTD, the XSD and some XML samples under the $CCRUNCHER/samples directory. The XML used in the example is not intended to reflect a real case, but to see the CCruncher configuration options.

The XML input file structure is as follows: 

<?xml version="1.0" encoding="UTF-8"?>
<ccruncher>
  <title>your simulation title here</title>
  <description>your simulation description here</description>
  <defines>        ...        </defines>
  <paramaters>     ...     </parameters>
  <interest>       ...       </interest>
  <ratings>        ...        </ratings>
  <transitions>    ...    </transitions>
  <factors>        ...        </factors>
  <correlations>   ...   </correlations>
  <segmentations>  ...  </segmentations>
  <portfolio>      ...      </portfolio>
</ccruncher>

The encoding attribute can be one of these values: UTF-8, UTF-16, ISO-8859-1, US-ASCII. Take into account that XML is case-sensitive. Title and description tags are optional.

The values of type double can be set as a numeric value (eg. 0.053) or percentage (eg. 5.3%). This type also supports the evaluation of numerical expressions (eg. (+2.5+2*(7+7)/10)/100). The supported operators are the usual (+,-,*,/,^), and the supported functions are: sqrt, sin, cos, tan, abs, exp, log, min, max, pow, if. Expression evaluation combined with macros (eg. 2000*$EUR2USD) gives a flexible way to parameterize your input file.

Section Defines

This section allows you to define macros, that is, identifiers with associated values. In the rest of the file, you can refer to these values using the identifier preceded by '$'. This feature is useful when simulating the same file repeatedly varying slightly the parameters as in the case of sensitivity analysis. In these cases, the usage of macros combined with the command line argument '-D' allows using the same file without having to modify it each time. This section is optional.

Example

<defines>
  <define name="numsims" value="30000"/>
  <define name="ndf" value="5"/>
</defines>

Define Attributes

Name Description Required Type Format Default
name The define identifier. Any occurrence of this identifier preceded by '$' (eg. $numsims) in the configuration file will be replaced by its value (eg. 30000). The define name can only consist of letters, numbers and the character '_'. yes string see desc. -
value The value used to replace the define identifier.
You can put any value that does not contain XML special characters (< & > " '). 		yes string see desc -

Section Parameters

This section contains the parameters of the problem that needs to be solved. The parameters list can be delivered in any order.

Example

<parameters>
  <parameter name="time.0" value="18/10/2009"/>
  <parameter name="time.T" value="15/07/2015"/>
  <parameter name="maxiterations" value="$numsims"/>
  <parameter name="maxseconds" value="3600"/>
  <parameter name="copula" value="t($ndf)"/>
  <parameter name="rng.seed" value="0"/>
  <parameter name="antithetic" value="true"/>
  <parameter name="blocksize" value="128"/>
</parameters>

Supported Parameters

Name Description Required Type Format Default
time.0 Starting date of the simulation. Interest curve, debtors' rating, transition matrix and default probabilities functions are relative to this date. yes date DD/MM/YYYY -
time.T Ending date of the simulation. Portfolio credit risk is computed at this date. yes date DD/MM/YYYY -
maxiterations The maximum number of iterations performed by the Monte Carlo algorithm. If it has value 0, this stop criterion is not considered. CCruncher stops when the maxiterations or maxseconds criterion is achieved. no int ≥ 0 1000000
maxseconds The maximum number of seconds that the current execution can last. If it has value 0, this stop criterion is not considered. CCruncher stops when the maxiterations or maxseconds criterion is achieved. no int ≥ 0 0
copula Type of copula used to generate correlated default times. Two families of copulas are implemented:
  • gaussian: the Gaussian copula
  • t(n): the t-Student copula, where n ≥ 2 is the number of degrees of freedom
no string gaussian
t(ndf)		 gaussian
rng.seed Seed used to initialize a random number generator. If it has value 0 then a random number based on the current time will be used. Note that you need to set distinct and non-consecutive seeds if you are planning to do multiple simulations of the same input file and merge the outputs. It requires being non-consecutive because each thread has its how RNG seeded with the seed value plus the thread index (zero-based indexing). no int ≥ 0 0
antithetic Specifies whether to use the 'antithetic' variance reduction technique. If you have doubts about setting this parameter then set it to 'false', otherwise, set it to 'true'. no boolean true
false		 false
blocksize The number of simultaneous simulations realized for each thread. If you enable antithetic mode then blocksize needs to be a multiple of 2. It is desirable that the number of simulations be a multiple of blocksize×numthreads. no int > 0 128

Section Interest

This section shows how to define the interest rates curve used to compute the Current Net Value of simulated losses. If you skip this section then the amounts will not be updated to their Current Net Value. In the euro area, you can obtain these values from ECB .

Example

<interest type="compound">
  <rate t="1D" r="3.99%"/>
  <rate t="1M" r="4.0%"/>
  <rate t="2M" r="4.1%"/>
  <rate t="3M" r="4.5%"/>
  <rate t="6M" r="4.55%"/>
  <rate t="1Y" r="4.8%"/>
  <rate t="2Y" r="4.9%"/>
  <rate t="5Y" r="5.0%"/>
  <rate t="10Y" r="5.2%"/>
</interest>

Interest Attributes

Name Description Required Type Format Default
type Determine how to apply interest curve. no string simple
compound
continuous		 compound
spline Indicates how the curve is interpolated. no string linear
cubic		 linear

Rate attributes

Name Description Required Type Format Default
t Time. Can be a date or an increment from the initial date time.0. Use suffix 'D' to indicate days (eg. 3D), suffix 'M' to indicate months (eg. 6M) and suffix 'Y' to indicate years (eg. 15Y). If a value between two given dates is needed, the value will be interpolated. yes date DD/MM/YYYY
int[DMY]		 -
r The interest rate at time t. yes double [-0.5, 1.0] -

Section Ratings

This section shows how to define the credit ratings. A minimum of two ratings is required (a non-default rating and a default rating).

Example

<ratings>
  <rating name="AAA" description="prime"/>
  <rating name="AA" description="high grade"/>
  <rating name="A" description="upper medium grade"/>
  <rating name="BBB" description="lower medium grade"/>
  <rating name="BB" description="non-investment grade speculative"/>
  <rating name="B" description="highly speculative"/>
  <rating name="CCC" description="extremely speculative"/>
  <rating name="D" description="in default"/>
</ratings>

Rating Attributes

Name Description Required Type Format Default
name Credit rating identifier. All references to a credit rating (eg. obligor rating) are made using this value. Include default rating in this list. yes string - -
description Credit rating description. no string -

Section Transition Matrix

This section shows how to define the transition matrix. The number of elements to be established is NxN, where N is the number of credit ratings. All no-fixed values are considered 0. CCruncher checks that the sum of elements of each row is 1.0, that exist only one defaulted rating, and that the transition matrix is an absorbing Markov chain (any rating may end up as defaulted). CCruncher will take care to convert the given transition matrix in the corresponding default probability functions. Alternatively, you can define directly the default probability functions using the dprobs tag instead of a transitions tag.

Example

<transitions period="12">
  <transition from="AAA" to="AAA" value="92.83%" />
  <transition from="AAA" to="AA" value="6.5%" />
  <transition from="AAA" to="A" value="0.56%" />
  <transition from="AAA" to="BBB" value="0.06%" />
  <transition from="AAA" to="BB" value="0.05%" />
  <transition from="AAA" to="B" value="0.0%" />
  <transition from="AAA" to="CCC" value="0.0%" />
  <transition from="AAA" to="D" value="0.0%" />
  <transition from="AA" to="AAA" value="0.63%" />
  <transition from="AA" to="AA" value="91.87%" />
  <transition from="AA" to="A" value="6.64%" />
  <transition from="AA" to="BBB" value="0.65%" />
  <transition from="AA" to="BB" value="0.06%" />
  <transition from="AA" to="B" value="0.11%" />
  <transition from="AA" to="CCC" value="0.04%" />
  <transition from="AA" to="D" value="0.0%" />
  <transition from="A" to="AAA" value="0.08%" />
  <transition from="A" to="AA" value="2.26%" />
  <transition from="A" to="A" value="91.65%" />
  <transition from="A" to="BBB" value="5.11%" />
  <transition from="A" to="BB" value="0.61%" />
  <transition from="A" to="B" value="0.23%" />
  <transition from="A" to="CCC" value="0.02%" />
  <transition from="A" to="D" value="0.04%" />
  <transition from="BBB" to="AAA" value="0.05%" />
  <transition from="BBB" to="AA" value="0.27%" />
  <transition from="BBB" to="A" value="5.84%" />
  <transition from="BBB" to="BBB" value="87.76%" />
  <transition from="BBB" to="BB" value="4.74%" />
  <transition from="BBB" to="B" value="0.98%" />
  <transition from="BBB" to="CCC" value="0.15%" />
  <transition from="BBB" to="D" value="0.21%" />
  <transition from="BB" to="AAA" value="0.04%" />
  <transition from="BB" to="AA" value="0.11%" />
  <transition from="BB" to="A" value="0.64%" />
  <transition from="BB" to="BBB" value="7.85%" />
  <transition from="BB" to="BB" value="81.13%" />
  <transition from="BB" to="B" value="8.27%" />
  <transition from="BB" to="CCC" value="0.89%" />
  <transition from="BB" to="D" value="1.07%" />
  <transition from="B" to="AAA" value="0.0%" />
  <transition from="B" to="AA" value="0.11%" />
  <transition from="B" to="A" value="0.3%" />
  <transition from="B" to="BBB" value="0.42%" />
  <transition from="B" to="BB" value="6.75%" />
  <transition from="B" to="B" value="83.08%" />
  <transition from="B" to="CCC" value="3.86%" />
  <transition from="B" to="D" value="5.48%" />
  <transition from="CCC" to="AAA" value="0.19%" />
  <transition from="CCC" to="AA" value="0.0%" />
  <transition from="CCC" to="A" value="0.38%" />
  <transition from="CCC" to="BBB" value="0.75%" />
  <transition from="CCC" to="BB" value="2.44%" />
  <transition from="CCC" to="B" value="12.03%" />
  <transition from="CCC" to="CCC" value="60.71%" />
  <transition from="CCC" to="D" value="23.5%" />
  <transition from="D" to="AAA" value="0.0%" />
  <transition from="D" to="AA" value="0.0%" />
  <transition from="D" to="A" value="0.0%" />
  <transition from="D" to="BBB" value="0.0%" />
  <transition from="D" to="BB" value="0.0%" />
  <transition from="D" to="B" value="0.0%" />
  <transition from="D" to="CCC" value="0.0%" />
  <transition from="D" to="D" value="100%" />
</transitions>

The above matrix is the S&P 1-year transition matrix, which is adjusted for unrated bonds and covers the period between 01-Jan-1981 and 31-Dec-1998. It has been extracted from Estimating Credit Rating Transition Probabilities for Corporate Bonds .

Transitions Attributes

Name Description Required Type Format Default
period The number of months covered by the transition matrix. Usually, the transition matrix covers 1 year, and in such case, set the value to 12. yes int > 0 -

Transition Attributes

Name Description Required Type Format Default
from Initial credit rating. This value must be a credit rating identifier, see 'name' attribute in the credit rating tag. yes string identifier -
to Final credit rating. This value must be a credit rating identifier, see 'name' attribute in the credit rating tag. yes string identifier -
value The probability for credit rating migration and must have a value between 0 and 1. yes double [0, 1] -

Section Factors

This section shows how to define the factors. A minimum of one factor is required.

Example

<factors>
  <factor name="S1" loading="15.1%" description="Consumer/service sector"/>
  <factor name="S2" loading="17.9%" description="Forest/building products"/>
  <factor name="S3" loading="17.5%" description="High technology"/>
  <factor name="S4" loading="12.8%" description="Utilities"/>
  <factor name="S5" loading="15.0%" description="Other sectors"/>
</factors>

Factor Attributes

Name Description Required Type Format Default
name Factor identifier. All references to a factor (eg. obligor factor) are made using this value. yes string - -
loading Factor loading value (wi in the multi-factor model). yes double [0, 1] -
description Factor description. no string -

Section Correlations

This section shows how to define the correlation matrix between factors, R in the multi-factor model. The diagonal values are always 1 and don't need to be specified. The non-diagonal elements are the correlation matrix coefficients. You only need to set up the non-zero upper triangle elements. The number of elements to set up is (numfactors-1) x numfactors / 2. If you have only had 1 factor or you desire the identity matrix then you can skip this section or just set <correlations/> and jump to the following section.

Example

<correlations>
  <correlation factor1="S1" factor2="S2" value="6.2%"/>
  <correlation factor1="S1" factor2="S3" value="8.6%"/>
  <correlation factor1="S1" factor2="S4" value="3.9%"/>
  <correlation factor1="S1" factor2="S5" value="9.1%"/>
  <correlation factor1="S2" factor2="S3" value="6.3%"/>
  <correlation factor1="S2" factor2="S4" value="10.2%"/>
  <correlation factor1="S2" factor2="S5" value="8.8%"/>
  <correlation factor1="S3" factor2="S4" value="7.3%"/>
  <correlation factor1="S3" factor2="S5" value="7.1%"/>
  <correlation factor1="S4" factor2="S5" value="6.4%"/>
</correlations>

Correlation Attributes

Name Description Required Type Format Default
factor1 First factor. This value must be a factor identifier, see 'name' attribute in factor tag. yes string identifier -
factor2 Second factor. This value must be a factor identifier, see 'name' attribute in factor tag. yes string identifier -
value Correlation between factor1 and factor2. yes double [0, 1] -

Section Segmentations

This section shows how to define portfolio segmentations. Segmentations allow you to disaggregate your portfolio's risk according to a hierarchical organization or another type of classification. Segmentation is composed of segments.

All segmentations must be complete so that an asset belongs to only one segment and the union of all segments constitutes the whole portfolio. Each segmentation has a segment named 'unassigned' that is implicitly declared. If an asset does not belong to any segment, then it is considered part of the 'unassigned' segment. We recommend creating a segmentation with no segments in order to evaluate the whole portfolio losses (all losses will accumulate in the 'unassigned' segment).

Example

<segmentations>
  <segmentation name="portfolio"/>
  <segmentation name="sectors">
    <segment name="S1"/>
    <segment name="S2"/>
    <segment name="S3"/>
    <segment name="S4"/>
    <segment name="S5"/>
  </segmentation>
  <segmentation name="size">
    <segment name="large"/>
    <segment name="medium"/>
    <segment name="small"/>
  </segmentation>
  <segmentation name="products">
    <segment name="bond"/>
    <segment name="loan"/>
    <segment name="lease"/>
    <segment name="mortgage"/>
    <segment name="line of credit"/>
    <segment name="bank guarantee"/>
  </segmentation>
  <segmentation name="offices">
    <segment name="0001"/>
    <segment name="0002"/>
    <segment name="0003"/>
    <segment name="0004"/>
  </segmentation>
</segmentations>

Segmentation Attributes

Name Description Required Type Format Default
name Segmentation identifier. All references to a segmentation (eg. belongs-to tag) are made using this value. yes string - -
enabled Indicates if this segmentation is enabled (ie. losses will be computed for this segmentation). no boolean - true

Segment Attributes

Name Description Required Type Format Default
name Segment name. Different segmentations can have segments with the same name. All references to a segment, eg. belongs-to tag, are made using this value and always in conjunction with the segmentation. If a segmentation doesn't have any segments, all the elements belong to the 'unassigned' segment. yes string - -

Section Portfolio

This section shows how to define the portfolio. A portfolio is a set of assets, where assets are grouped by obligors. The description of each asset is done by listing the expected Exposures At Default (EAD) and Loss Given Default rates (LGD).

For every segmentation, each asset is tied to a segment. The dependence relationships can be defined at the asset level or the obligor level (in this case all assets are included in the same segmentation-segment). If segmentation-segment asset relationship is not given, then the asset is assigned to the segment 'unassigned'.

LGD can be defined at three different levels: obligor, asset, and data value. When a default occurs at time t, we get the data value LGD at time t (or the closest date above). If this value is not reported, we get the asset LGD. Finally, if even the asset LGD is not reported, we get the obligor LGD. The obligor' LGD is shared by all assets that have not defined an LGD.

Example

<portfolio>
  <obligor rating="A" factor="S1" id="000001">
    <belongs-to segmentation="sectors" segment="S1"/>
    <belongs-to segmentation="size" segment="medium"/>
    <asset id="op1" date="01/01/2005" lgd="20%">
      <belongs-to segmentation="products" segment="bond"/>
      <belongs-to segmentation="offices" segment="0001"/>
      <data>
        <values t="01/06/2005" ead="2000.0" />
        <values t="01/06/2006" ead="1900.0" />
        <values t="01/06/2007" ead="1800.0" />
        <values t="01/06/2008" ead="1700.0" />
        <values t="01/06/2009" ead="1600.0" />
        <values t="01/06/2010" ead="1500.0" />
        <values t="01/06/2011" ead="1400.0" />
        <values t="01/06/2012" ead="1300.0" />
        <values t="01/06/2013" ead="1200.0" />
        <values t="01/06/2014" ead="1100.0" />
      </data>
    </asset>
    <asset id="op2" date="01/06/2008">
      <belongs-to segmentation="offices" segment="0004"/>
      <belongs-to segmentation="products" segment="bond"/>
      <data>
        <values t="01/07/2009" ead="4400.0" lgd="25%" />
        <values t="01/07/2011" ead="3920.0" lgd="30%" />
        <values t="01/07/2013" ead="3340.0" lgd="35%" />
        <values t="01/07/2015" ead="2960.0" lgd="40%" />
        <values t="01/07/2017" ead="2480.0" lgd="45%" />
      </data>
    </asset>
  </obligor>
  <obligor rating="B" factor="S2" id="000002" lgd="20%">
    <belongs-to segmentation="sectors" segment="S2"/>
    <belongs-to segmentation="size" segment="large"/>
    <asset id="op3" date="01/06/2003">
      <belongs-to segmentation="offices" segment="0003"/>
      <belongs-to segmentation="products" segment="bond"/>
      <data>
        <values t="01/01/2005" ead="1750.0" />
        <values t="01/06/2007" ead="1600.0" />
        <values t="01/01/2009" ead="1450.0" />
        <values t="01/06/2011" ead="1300.0" />
        <values t="01/01/2013" ead="1150.0" />
      </data>
    </asset>
  </obligor>
  <obligor rating="CCC" factor="S2" id="000003">
    <belongs-to segmentation="sectors" segment="S2"/>
    <belongs-to segmentation="size" segment="medium"/>
    <asset id="op4" date="01/01/1999" lgd="beta(2.5,2.7)">
      <belongs-to segmentation="offices" segment="0003"/>
      <belongs-to segmentation="products" segment="bond"/>
      <data>
        <values t="01/01/2000" ead="2400.0" />
        <values t="01/01/2001" ead="2300.0" />
        <values t="01/01/2002" ead="2200.0" />
        <values t="01/01/2003" ead="2100.0" />
        <values t="01/01/2004" ead="lognormal(6.5,1.0)" />
        <values t="01/01/2005" ead="1900.0" />
        <values t="01/01/2006" ead="exponential(1800.0)" />
        <values t="01/01/2007" ead="1700.0" />
        <values t="01/01/2008" ead="uniform(1500.0,1700.0)" />
        <values t="01/01/2009" ead="1500.0" />
        <values t="01/01/2010" ead="gamma(2800.0,0.5)" />
        <values t="01/01/2011" ead="1300.0" />
        <values t="01/01/2012" ead="normal(1200.0,100.0)" />
        <values t="01/01/2013" ead="1100.0" />
      </data>
    </asset>
  </obligor>
</portfolio>

Portfolio Attributes

Name Description Required Type Format Default
include Indicates the filepath to portfolio file relative to the main input file location. The format of the portfolio file is exactly the same of the section portfolio where the root tag of this file is portfolio. If your portfolio is large and you plan to simulate it multiple times using distinct parameters use this feature, otherwise this attribute can be omitted. no string -

Obligor Attributes

Name Description Required Type Format Default
id Unique obligor identifier. yes string - -
rating Initial obligor credit rating at time t0, see attribute time.0 at the parameters section. This value must be a credit rating identifier, see 'name' attribute in rating tag. yes string identifier -
factor Factor where this obligor is included. This value must be a factor identifier, see 'name' attribute in factor tag. yes string identifier -
lgd Default LGD used in absence of LGD in the description of assets. LGD can be a fixed value or a probability distribution. In the second case, you can model LGD using the following distributions:
  • beta(α,β), where α > 0 and β > 0
  • uniform(a,b), where 0 ≤ a < b ≤ 1
 no double
string

 [0,1]
beta(α,β)
uniform(a,b)		 100%

Belongs-To Attributes

Name Description Required Type Format Default
segmentation Segmentation identifier. This value must be a segmentation identifier, see 'name' attribute in segmentation tag. yes string identifier -
segment Segment identifier. This value must be a segment identifier, see 'name' attribute in segment tag. yes string identifier -

Asset Attributes

Name Description Required Type Format Default
id Unique asset identifier. yes string identifier -
date Date from which there is the credit risk, eg. bond buy date or loan signature. yes date DD/MM/YYYY -
lgd Default LGD used in absence of LGD in the description of assets. LGD can be a fixed value or a probability distribution. In the second case, you can model LGD using the following distributions:
  • beta(α,β), where α > 0 and β > 0
  • uniform(a,b), where 0 ≤ a < b ≤ 1
 no double
string

 [0,1]
beta(α,β)
uniform(a,b)

Values Attributes

Name Description Required Type Format Default
t The date where the values take place. Can be a date (in format 'DD/MM/YYYY') bigger or equal than asset date or an interval from asset date. Use suffix 'D' to indicate days (eg. 3D), suffix 'M' to indicate months (eg. 6M) and suffix 'Y' to indicate years (eg. 15Y). yes date DD/MM/YYYY
int[DMY]		 -
ead The amount that lender can lose in case of obligor's default at date "t". EAD can be a fixed value or a probability distribution. In the first case, set the numeric value that represents the EAD (eg. 50000). In the second case, you can model EAD using the following distributions:
  • lognormal(μ,σ), where μ > 0 and σ > 0
  • exponential(β), where β > 0 is the survival parameter
  • uniform(a,b), where a > 0 and b > 0
  • gamma(k,θ), where k > 0 and θ > 0
  • normal(μ,σ), where μ > 0 and σ > 0. Values less than 0 are truncated to 0.
 yes double
string




 ≥ 0
lognormal(μ,σ)
exponential(β)
uniform(a,b)
gamma(k,θ)
normal(μ,σ)		 -
lgd The portion of the loss that will not be recovered in case of default at date "t". This value takes into account guarantees, the cost to take legal actions, recovery rate based on historical data, etc. LGD can be a fixed value or a probability distribution. In the second case, you can model LGD using the following distributions:
  • beta(α,β), where α > 0 and β > 0
  • uniform(a,b), where 0 ≤ a < b ≤ 1
 no double
string

 [0,1]
beta(α,β)
uniform(a,b)

Section Default Probability Functions

Working with a transition matrix implies that the credit rating transitions follow a Markov model. Sometimes this assumption is not acceptable because we desire that transition probabilities change over the simulation period or we plan to do stress tests over the default probabilities. In these cases, you can define the default probability functions explicitly. You must define either a transition matrix or the default probability functions, but not both.

The dprobs section contains the default probability function for each rating. For all credit ratings (distinct than the defaulted rating) the default probability function is monotonously increasing, with a value of 0 at time 0, and a value of 1 at time ∞. The default probability function of the defaulted rating is always 1.

You don't need to fill all time values. The default probability functions are approximated using cubic splines when possible (minimum number of available points, monotone increasing) and linear splines when not.

Example

<dprobs>
  <dprob rating="AAA" t="0M" value="0.0%"/>
  <dprob rating="AA" t="0M" value="0.0%"/>
  <dprob rating="A" t="0M" value="0.0%"/>
  <dprob rating="BBB" t="0M" value="0.0%"/>
  <dprob rating="BB" t="0M" value="0.0%"/>
  <dprob rating="B" t="0M" value="0.0%"/>
  <dprob rating="CCC" t="0M" value="0.0%"/>
  <dprob rating="D" t="0M" value="100.0%"/>

  <dprob rating="AAA" t="6M" value="0.04%"/>
  <dprob rating="AA" t="6M" value="1.46%"/>
  <dprob rating="A" t="6M" value="2.81%"/>
  <dprob rating="BBB" t="6M" value="4.02%"/>
  <dprob rating="BB" t="6M" value="7.37%"/>
  <dprob rating="B" t="6M" value="14.28%"/>
  <dprob rating="CCC" t="6M" value="21.12%"/>
  <dprob rating="D" t="6M" value="100.0%"/>
  ...
</dprobs>

Dprob Attributes

Name Description Required Type Format Default
rating This value must be a credit rating identifier, see 'name' attribute in the rating tag. yes string identifier -
t Time. A date bigger or equal than time.0 or an interval from starting date time.0. Use suffix 'D' to indicate days (eg. 3D), suffix 'M' to indicate months (eg. 6M) and suffix 'Y' to indicate years (eg. 15Y). yes date DD/MM/YYYY
int[DMY]		 -
value The probability that an obligor with initial rating rating defaults in the time range [time.0,t]. yes double [0,1] -