This document provides a tutorial and examples for implementing the CreditRisk+ model in a spreadsheet. It describes 9 examples of applying the model to different portfolio structures and assumptions. For each example, it provides the input assumptions, how to set up the model parameters, and describes the output results. The examples illustrate how to model single or multiple sectors, correlated and uncorrelated sectors, and incorporate severity variations.

1. Tutorial
CreditRisk+ Model
Melchiori, Mario R.

2. CreditRisk+
Model
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Tutorial CreditRisk+ Model
Example Spreadsheet-Based Implementation
The purpose of this tutorial is to illustrate the application of the CREDITRISK+ Model to an example portfolio.
For illustrative purposes, we have used as example portfolio such as that used in CREDITRISK+ Technical Document.
However, there is no limit, in principle, to the number of obligors that can be handled by the CREDITRISK+ Model. Increasing
the number of obligors has only a limited impact on the processing time.
Example Portfolio and Static Data
Like in CREDITRISK+ Technical Document, the examples are based on a portfolio consisting of 25 obligors of varying credit
quality and size of exposure.
The examples are given, each based on the same portfolio, as follows:
• All obligors are allocated to a single specific sector. (Example 1.xlsm)
• All obligors are allocated to a single systemic sector. (Example 2.xlsm)
• Each obligor is allocated to only one sector. This example assumes that each obligor is subject to only one
systematic factor, which is responsible for all of the uncertainty of the obligor’s default rate. (Example 3.xlsm)
• Each obligor is apportioned to a number of sectors. This example reflects the situation in which the fortunes of an
obligor are affected by a number of systematic factors. The sectors are non-correlated. (Example 4.xlsm)
• Hold To Maturity Analysis. (Example 7.xlsm)
The examples correspond to original version of CREDITRISK+ (Wilde, 1997). The following enhance are covered:
• Each obligor is apportioned to a number of sectors. This example reflects the situation in which the fortunes of an
obligor are affected by a number of systematic factors. The sectors are correlated (Giese, 2003). (Example 5.xlsm)
• Severity Variation from Specific Factors and Systematic one are modeled (Bürgisser, Kurth, & Wagner, 2001).
(Example 6.xlsm)
• Equalization Severity Variation. (Example 8.xlsm)
• Combining Profit and Loss. (Example 9.xlsm)
• Summary risk measures by sub portfolio.
Excel file names in parentheses.
The examples are installed on the spreadsheet, together with the results generated by the model. For each example, the
inputs to the model have been set to generate the following:
• Percentiles of loss.
• Full loss distribution.
• Expected Loss.
• Unexpected Loss.
and, where appropriate:
• Risk contributions by CREDITRISK+ Model. (Giese, 2003)
• Risk contributions by Haaf and Tasche. (Haaf & Tasche, 2002)
• Risk contributions by Götz Giese. (Giese, 2003)
• Expected Shortfall by Haaf and Tasche. (Haaf & Tasche, 2002)
• Expected Shortfall by Götz Giese. (Giese, 2003)

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These measures are generated for each obligor
and sub portfolio using Recurrence – Panjer - or
fast Fourier Transform – FFT – model (Melchiori,
2004), when required. The steps to reproduce
the results are described in all cases. Each
worksheet is equipped with a sheet named
Control Panel that looks like the table below.
Clear All button erases both input and output
data. Set names button sets the worksheet
ranges of data to be read into the model. To
activate of model implementation, press the
button Activate Model.
The examples use a credit rating scale, which can
be entered in the Excel sheet labeled IN_Default
Rate, to assign default rates and default rate
volatilities to each obligor. This is showed below.
However, they can be assigned without to
employ the credit rating scale. The credit rating
scale and other data in the table are designed for
the purposes of the example only.
NOTE: To activate the model implementation, prior to press the
button Activate Model, you must provide data input in the sheets
labeled IN_Obligors and IN_Default Rate.

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Example 1: All obligors are allocated to a single specific sector
Assumption Input Set up
All obligors are allocated to
a single sector
Sector 1 equals 100% for all
obligors in sheet IN_Obligors.
Zero in other sectors.
The Sector is a Specific one.
Switch on this facility via the
Execute Process Screen.
The exposure amounts are
net of recovery. There is not
Specific Severity Variation.
Each obligor belongs to the
same sub portfolio.
To each obligor corresponds to
one and only one Exposure.
Input 1 to each obligor in
column labeled Portfolio.
There is not Severity
Variation.
Switch off this facility via the
Execute Process Screen.
Compute Risk Contributions
to Unexpected Loss
No input is required.
Compute Risk Contributions
to Quantile Loss
Switch on this facility via the
Execute Process Screen.
Add up by Sub portfolio
Switch on this facility via the
Execute Process Screen.

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Panjer Mode
The data are entered on Excel sheets
labeled IN_Obligors .
The example computes Risk Contributions
and Expected Shortfall using the model
proposed by Haaf & Tasche. (Haaf & Tasche,
2002)
On activation, the model will show the
Execute Process Screen. This screen is used
to specify the calculation mode, the output
data required. Worksheet ranges of data to
be read into the model are automatically
set.
Execute Process Screen
Press Percentiles button to
change the percentiles values.
The following are the percentiles
set up by default:
Press OK, then Execute button on the Execute Process
Screen to proceed to the next step.

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Summary of Input Data Check
The model implementation has been preset to identify errors in the data read in before the calculation begins. The model
implementation ensures that the data satisfies the following three criteria:
The sector allocation table contains only numeric data.
The decomposition of each obligor to the various sectors adds up to 100%.
A sector must contain at least one allocation entry.
Other errors are identified during the process.
Press the OK button on the Summary
of Input Data Check Screen to proceed
with the calculation.
Output of the process
Loss Distribution
The model displays Loss Distribution and
its graph on the sheet named OUT_Loss
Distribution, using the results generated
from the steps above.
Mean, Unexpected and Percentiles Loss
Like the original CreditRisk+ model, if an
exact percentile does not exit, it is
compute by lineal interpolation. The
model shows on the sheet labeled
OUT_Percentiles, summary statistics of
the portfolio loss distribution.

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Risk Contributions
The model has been preset to output risk contributions for each obligor. The risk contributions calculated by the model are
defined as risk contributions to standard deviation on a chosen percentile of the loss distribution. This is the approach
employed by the original version of CreditRisk+. This risk measure will be present whatever model is chosen, unlike the
following risk measure, which shall be selected when required. The sum of the Risk Contributions computed via this
methodology equals to percentile chosen.
The model has been preset to calculate risk contributions by reference to the 99th percentile loss. This setting can be
altered to a different percentile via the Execute Process Screen.
The model permits to compute the Risk Contributions and Expected Shortfall per obligor using the methodology due to
Haaf and Tasche (Haaf & Tasche, 2002). It can always be chosen, except when the variable Sector covariance is greater than
zero, in this case we will use the Giese´s approach (Giese, 2003). The sum of the Risk Contributions computed via this
methodology equals to cumulated loss distribution greater than the percentile chosen, if it does not exist exactly. The
model computes the Risk Contributions and Expected Shortfall by sector.
Results are showed on OUT_Risk Contributions sheet.
Summary Information by sub portfolio
The information by sub portfolio is
displayed on OUT_RC Portfolio sheet.
FFT Mode
Execute Process screen changes when we choose FFT Mode. FFT 2N
parameter is highlights. 2N
governs the number of points
of the Loss distributions. A longer vector is generally required for a discrete representation of the loss distribution, since it
will take on large values with non-
zero probability. If there is not
enough room in the discrete vector,
then the tail probabilities will wrap
around and reappear at the
beginning. Therefore, it is crucial to
select a correct value for N. If N
equals to zero, the code calculates
the fit value. Sector Covariance
equals to zero in this example. Other

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inputs remain unchanged with respect to Panjer mode.
Summary of Input Data screen and other outputs are identical to the previous mode.
Example 2: All obligors are allocated to a single systematic sector
Assumption Input Set up
All obligors are allocated to
a single
Sector 1 equals 100% for all
obligors in sheet IN_Obligors.
Zero in other sectors.
The Sector is a Systemic one.
Switch off Sector 1 for specific
risk facility via the Execute
Process Screen.
The exposure amounts are
net of recovery. There is not
Specific Severity Variation.
Each obligor belongs to the
same sub portfolio.
To each obligor corresponds to
one and only one Exposure.
Input 1 to each obligor in
column labeled Portfolio.
There is not Severity
Variation.
Switch off this facility via the
Execute Process Screen.
Compute Risk Contributions
to Unexpected Loss
No input is required.
Compute Risk Contributions
to Quantile Loss
Switch on this facility via the
Execute Process Screen.
Add up by Sub portfolio
Switch on this facility via the
Execute Process Screen

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Panjer Mode
Execute Process screen would look like below:
FFT Mode
The explanation of the Example 1, FFT Mode, applies. Execute Process screen would look like below:
Summary of Input Data screen and other outputs are similar to the previous example.

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Example 3: Each obligor is allocated to only one sector of several sectors. The sectors are non-
correlated
Assumption Input Set up
Each obligor is allocated to
only one sector of several
sectors
In sheet IN_Obligors, sector
where each obligor is allocated
equals to 100%. Zero in other
sectors.
There is not Specific Sector.
Switch on this facility via the
Execute Process Screen.
The exposure amounts are
net of recovery. Each obligor
belongs to the same sub
portfolio.
To each obligor corresponds to
one and only one Exposure.
Input 1 to each obligor in
column labeled Portfolio.
There is not Severity
Variation.
Switch off this facility via the
Execute Process Screen.
Compute Risk Contributions
to Unexpected Loss.
No input is required.
Compute Risk Contributions
to Quantile Loss.
Switch on this facility via the
Execute Process Screen.
Add up by Sub portfolio.
Switch on this facility via the
Execute Process Screen.

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Panjer Mode
Execute Process screen would look like below:
Summary of Input Data screen looks like below:

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FFT Mode
The explanation of the Example 1, FFT Mode, applies. Execute Process screen would look like below:
Summary of Input Data screen should look like in previous mode.
Example 4: Each obligor is apportioned to a number of sectors. The sectors are non-correlated
Assumption Input Set up
Each obligor is allocated to
only one sector of several
sectors
In sheet IN_Obligors, each
obligor is apportioned to a
number of sectors. The
decomposition of each obligor to
the various sectors must add up
to 100%.
The Sector 1 is a Specific
one.
Switch on this facility via the
Execute Process Screen.
The exposure amounts are
net of recovery. All obligors
belong to the same sub
portfolio.
To each obligor corresponds to
one and only one Exposure.
Input 1 to each obligor in
column labeled Portfolio.

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There is not Severity
Variation.
Switch off this facility via the
Execute Process Screen
Compute Risk Contributions
to Unexpected Loss
No input is required.
Compute Risk Contributions
to Quantile Loss
Switch on this facility via the
Execute Process Screen.
Add up by Sub portfolio
Switch on this facility via the
Execute Process Screen.
Panjer Mode
Execute Process screen would look like below:
Summary of Input Data screen looks like below:

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FFT Mode
The explanation of the Example 1, FFT Mode, applies. Execute Process screen would look like below:
Summary of Input Data screen should look like in previous mode.

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Example 5: Each obligor is apportioned to a number of sectors. The sectors are correlated
Assumption Input Set up
Each obligor is allocated to
several sectors.
In sheet IN_Obligors, each
obligor is apportioned to a
number of sectors. The
decomposition of each obligor to
the various sectors must add up
to 100%.
The Sector 1 is a Specific
one.
Switch on this facility via the
Execute Process Screen
The Sector are correlated
Input Sector Covariance equals
to 0.15.
The exposure amounts are
net of recovery. Obligors
belong to different sub
portfolios.
To each obligor corresponds to
one and only one Exposure.
Input a value for each obligor
in column labeled Portfolio, to
identify the portfolio where
obligor belongs.
There is not Severity
Variation.
Switch off this facility via the
Execute Process Screen.
Compute Risk Contributions
to Unexpected Loss
No input is required.
Compute Risk Contributions
to Quantile Loss
Switch on this facility via the
Execute Process Screen.
Add up by Sub portfolio
Switch on this facility via the
Execute Process Screen.

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FFT Mode
In this example, only the FFT Mode is applied. Sector Covariance value must be lesser than a determined value, in this
example, that determined value equals to 0.25. Check out the Giese´s paper for more details. During the process, such
errors are identified.
The explanation of the Example 1, FFT Mode, applies. Execute Process screen would look like below:
Summary of Input Data screen should look like prior example.

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Example 6: Severity Variation from Specific Factors and Systematic one
Assumption Input Set up
All obligors must be
allocated to a single
Sector 1 equals 100% for all
obligors in sheet IN_Obligors.
Zero in other sectors.
The Sector must be a
Systemic one.
Switch off Sector 1 for specific
risk facility via the Execute
Process Screen.
The exposure amounts are
net of recovery. Specific
Severity Variation is
modeled. All obligors belong
to the same sub portfolio.
To each obligor corresponds to
one and only one Exposure.
Input a value for each obligor
in column labeled Portfolio, to
identify the portfolio where
obligor belongs.
Systematic Severity
Variation is modeled.
Switch on this facility via the
Execute Process Screen. Click
on Options to set the
parameters of Severity
Variation Process.
Options for Incorporating
Severity Variation.
Put Systemic volatility = 0.20.
Options for Incorporating
Severity Variation.
Set Manual Input option.
Options for Incorporating
Severity Variation.
Set Data Expand Mode to
“Normal” and Specific
Volatility = 0.15. This model
the severity density function
by discretizing a normal
distribution with mean equals
to, and standard deviation
equals to 15%.

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Compute Risk Contributions
to Unexpected Loss
No input is required.
Add up by Sub portfolio
Switch on this facility via the
Execute Process Screen.
Panjer Mode
Execute Process screen would look like below:
Click on Options to setup the parameters of Incorporating Severity Variation process:
For this implementation,
we have chosen to model
the obligor-specific
severity density function
by discretizing a normal
distribution with mean
equals to, and standard
deviation equals to 15% of,
non-stochastic exposure
used in previous example.
Systemic severity
variations are assumed
lognormal distributed
with mean parameter
equals to one and
standard deviation equals
to 0.20.
The implementation supports two modes of data expansion, “Normal” and “Lognormal”, other distributions to model the
severity variations can be implemented without any problem setting into expansion mode "None" and manually input data
into the worksheet “IN_Obligors”.

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Summary of Input Data screen looks like below:
FFT Mode
The explanation of the Example 6, Panjer Mode, applies. Execute Process screen would look like below:
Summary of Input Data screen should look like in previous mode.

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Example 7: Hold to Maturity Analysis
Assumption Input Set up
All obligors are allocated to
a single.
Sector 1 equals 100% for all
obligors in sheet IN_Obligors.
Zero in other sectors.
The Sector must be a
Systemic one.
Switch off Sector 1 for specific
risk facility via the Execute
Process Screen.
The exposure amounts are
net of recovery. Obligors
belong to different sub
portfolios.
To each obligor has several
probably exposure with its
correspond Default
Probability. Input a value for
each obligor in column labeled
Portfolio, to identify the
portfolio where obligor
belongs.
There is not Systematic
Severity Variation.
Switch off this facility via the
Execute Process Screen.
Compute Risk Contributions
to Unexpected Loss.
No input is required.
Compute Risk Contributions
to Quantile Loss.
Switch on this facility via the
Execute Process Screen.
Modes of Execution
Execute Process screen and Summary of Input Data screen are the same as in Example 2, for the modes of Panjer, FFT, and
Giese.
This Example illustrates the use of the model for analyzing the portfolio over its hold to maturity time horizon. To illustrate
a multi - year time horizon, the data used in this example has been extended as follows:
The obligor details used in the other examples have been extended to show the exposures rolling off over a
period of up to three years. Before use, the data is rearranged in the IN_Obligors.
The static data (default rates and default rate standard deviations) used in the other examples have been
extended over three years. The one-year default rates are the same as in the other examples, but this example

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also introduces a term structure of default rates by specifying marginal probabilities of default in years 2 and 3 of
the portfolio.
The model outputs are the same as the other example, but in this example, the model calculates a risk contribution for each
obligor for each year in which the obligor has an exposure outstanding.
Example 8: Equalization Severity Variation
Assumption Input Set up
Each obligor is allocated to
several sectors.
In sheet IN_Obligors, each
obligor is apportioned to a
number of sectors. The
decomposition of each obligor
to the various sectors must
add up to 100%.
Each obligor is allocated to
several sectors of collateral.
In sheet IN_Obligors, each
obligor is apportioned to a
number of collaterals. The
decomposition of each obligor
to the various collaterals must
add up to 100%.
The Sector 1 is a Specific
one.
Switch on this facility via the
Execute Process Screen
The exposure amounts are
net of recovery. Specific
Severity Variation is
modeled. All obligors belong
to the same sub portfolio.
To each obligor has several
probably exposure with its
correspond Default
Probability. Input a value for
each obligor in column labeled
Portfolio, to identify the
portfolio where obligor
belongs.
Severity Variation is
modeled.
Switch on this facility via the
Execute Process Screen. Click
on Options to set the
parameters of Severity
Variation Process.

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Options for Incorporating
Severity Variation.
Put Systemic volatility = 0.20.
Options for Incorporating
Severity Variation.
Set Equalization Input option.
Options for Incorporating
Severity Variation.
Set Calculate Mode to “Sys.
Default” and Specific Volatility
= 0.15.
Options for Incorporating
Severity Variation.
The Collateral 1 is a Specific
one. Check this option.
Compute Risk Contributions
to Quantile Loss
Switch on this facility via the
Execute Process Screen.
Add up by Sub portfolio
Switch on this facility via the
Execute Process Screen.
Panjer Mode
Execute Process screen would look like below:

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Click on Options to setup the parameters of Incorporating Severity Variation process:
Equalization input:
First, we calculate the unexpected loss of the portfolio, taking into account the segment structure. Then we estimate single
systematic default and severity volatilities and such that the unexpected loss of the portfolio, computed with the single
segment formula matches the unexpected loss computed before. Finally, the loss distribution is calculated as in the single
segment situation, where the systematic default behavior is gamma and systematic severity variation is lognormally
distributed. There are three possibilities to estimate the implied overall systematic volatilities in the number of defaults
and in the severities :
Alternatives modes of calculating the Equalization of Incorporating Severity Variation:
Systematic default: We estimate (systematic default volatility) by equating the unexpected loss formulas of
the single and multisegment situation by setting (systematic severity volatility) and (specific severity
volatility) equals to zero. This mode permits to compute both Risk Contributions and Expected Shortfall.
Systematic severity: We focus on severity systematic risk and determine by equating the unexpected Loss
formulas of the single and multisegment situation by setting = 0 and = 0. This mode does not permit to
compute Risk Contributions and Expected Shortfall.
Specific severity: We focus on severity specific risk and determine by equating the unexpected loss formulas
of the single and multisegment situation by setting = 0 and = 0. This mode permits to compute Risk
Contributions and Expected Shortfall.
Note: The example permits to model both Correlation Sectors and Correlation Collaterals via the average correlation
approach. In this environment, the specific sector and specific collateral are independent.
Summary of Input Data screen looks like the
following:

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FFT Mode
The explanation of the Example 8, Panjer Mode, applies. Execute Process screen would look like below:
Summary of Input Data screen should look like in previous mode.

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Example 9: Combining Profit and Loss
This example combines the rating migration concept of CreditMetrics with the approach of CreditRisk+, incorporating the
effect of ratings changes in CreditRisk+.
It allows integrating the rating migration concept into CreditRisk+, modeling the possible profits and losses due to rating
changes in the same way as the default events are modeled.
Migration rates must be assigned separately to a subportfolio of profits due to upgrades and a subportfolio of losses due to
downgrades.
In the example, twenty, equal and independent obligors of bonds BBB are chosen, for each it is necessary to calculate the
total value of each bond for different rating categories at the end of the period.
Determine the possible value changes caused by individual up/downgrades, and assign the migration rates (four rating of
profits, and four rating of losses). The chart below shows the first three steps of the approach:
The step four consists in evaluates the distributions of profits and losses separately. The absolute amounts of profits and
losses are used as net exposures and the default rate corresponds to the migration rate. It is not adequate to use the
CreditRisk+ concepts of default rate volatility and sector analysis because of the assumption of independent obligors.
Finally, the convolution process obtains the total loss distribution and the Risk contribution of each obligor.

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Assumption Input Set up
All obligors are allocated to
a single sector
Sector 1 equals 100% for all
obligors in sheet IN_Obligors.
Zero in other sectors.
Migration rates must be
assigned separately to a
subportfolio of profits and a
subportfolio of losses.
Each obligor has several
exposures with associated
default probability. Input a
value for each obligor in
column labeled Portfolio, to
identify the profits (upgrades)
and losses (downgrades).
Combining Profit and Loss
Migrations is modeled.
Switch on this facility via the
Execute Process Screen.
Panjer Mode
Execute Process screen would look like below:
Summary of Input Data screen looks like below:

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FFT Mode
The explanation of the Example 9, Panjer Mode, applies. Execute Process screen would look like below:
Summary of Input Data screen should look like in previous mode.
Note:
The Giese Model always applies.
Risk Contributions and Expected Shortfall always apply even though the severity specific variation is used. It permits to
model stochastically the Loss Given Default without to limit the output, i.e. it is possible to calculate Risk Contributions and
Expected Shortfall in all its dimensions and to allocate each obligor to one or more sectors and to take into account the
correlation between several sectors. To model stochastic Loss Given Default goes the following steps:
References

28. CreditRisk+
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Incorporating Severity Variations into Credit Risk: Bürgisser, P., Kurth, A., & Wagner, A. (2001). Downloded 17/05/2009, from
http://math-www.uni-paderborn.de/agpb/work/CRQ.pdf
Enhancing CreditRisk+: Giese, G. (April 2003). Downloded 17/05/2009, from: http://www.defaultrisk.com/pp_model162.htm
Calculating Value-at-Risk Contributions in CreditRisk+.: Haaf, H., & Tasche, D. (28/02/2002). Downloded 17/05/2009, from:
http://www.defaultrisk.com/pp_model_26.htm
CreditRisk+ by FFT: Melchiori, M. (July 2004).. Downloded 17/05/2009, from Social Science Research Network
http://ssrn.com/abstract=1122844
Good Migrations: Rolfes,Bernd, Broeker, Frank (November 1998). Downloded 17/05/2009, from
http://www.gloriamundi.org/ShowTracking.asp?ResourceID=453055008
CreditRisk+ Technical Document: Wilde, T. (October 1997). Downloded 17/05/2009, from
http://www.defaultrisk.com/pp_model_21.htm