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.
CreditRisk+ is a method for quantifying the probability of loss distributions and risk measures like Value at Risk for loan portfolios. It generates loss distributions based on probability generating functions and models defaults as independent Poisson processes. The document outlines the theoretical framework and assumptions of CreditRisk+, including how to model exposure bands, default correlations, and aggregate loans from multiple borrowers.
CreditRisk+ is a credit risk modeling framework that uses an actuarial approach to model default risk in a bond or loan portfolio. It models the frequency of defaults using a Poisson distribution and the severity of losses using a loss distribution. The portfolio is divided into exposure bands to simplify calculations. Probability generating functions are used to derive a closed-form expression for the probability distribution of portfolio losses. The model can incorporate sector analysis and correlations between obligors. Extensions of the model have been proposed to include migration risk and closed-form modeling of correlated credit events.
This document discusses different techniques for software testing, including static and dynamic techniques. It covers specification-based or black-box techniques like equivalence partitioning, boundary value analysis, decision tables, and state transition testing. Equivalence partitioning involves dividing inputs into equivalent partitions, while boundary value analysis focuses on testing values at the boundaries of partitions. Decision tables systematically test combinations of inputs. State transition testing models the different states a system can be in and the transitions between states.
This document describes an HLA Income Builder investment product that provides guaranteed yearly income, dividends, and death/total permanent disability benefits. It offers a 5.5% compounding interest rate and increases guaranteed yearly income every year. After 20 years of deposits, the investment is projected to pay out over RM1 million in guaranteed yearly income and dividends, as well as a death benefit of over RM1.3 million. The HLA Income Builder aims to provide the best returns in the medium to long term with no risk to deposits.
Mastering Information Technology Risk ManagementGoutama Bachtiar
This is the presentation slide as part of the courseware utilized when delivering Information Technology Risk Management training - workshop on May 2013.
The document discusses defects in software testing. It defines a defect as an error or bug in an application that causes it to not meet user expectations or software requirements. Tests can show the presence, not absence, of defects. There are various types of defects, including bugs, failures, mistakes, and errors from different perspectives. Defects are categorized as functional or non-functional. Examples are provided for different types of defects like wrong, missing, and extra. The document notes that finding and fixing defects later in the software development process costs significantly more than fixing them earlier.
Tips for IT Risk Management Prof. Hernan Huwyler Information Security InstituteHernan Huwyler, MBA CPA
This document provides tips for IT risk management, including what to do and what to avoid. It recommends facilitating risk assessments well before IT decisions are made. Key objectives for IT risks are confidentiality, integrity and availability of assets like data, hardware, software and skills. Examples are provided for measuring these objectives. Risk statements should identify measurable events, threats, consequences and probabilities. Quantitative methods like annualized loss expectancy and tools for calculating single loss can help measure impacts in monetary terms or other metrics. Internal and external data sources can provide statistics to tailor measurements to each organization. Subjective scales should be avoided in favor of statistical methods.
The document summarizes the key activities in the software testing process according to ISTQB, including test planning, monitoring and control, analysis, design, implementation, execution, evaluating exit criteria and reporting, and test closure activities. It provides details on each activity, such as the objectives of test planning, factors to consider for test analysis, and outputs that should be captured during test closure.
CreditRisk+ is a method for quantifying the probability of loss distributions and risk measures like Value at Risk for loan portfolios. It generates loss distributions based on probability generating functions and models defaults as independent Poisson processes. The document outlines the theoretical framework and assumptions of CreditRisk+, including how to model exposure bands, default correlations, and aggregate loans from multiple borrowers.
CreditRisk+ is a credit risk modeling framework that uses an actuarial approach to model default risk in a bond or loan portfolio. It models the frequency of defaults using a Poisson distribution and the severity of losses using a loss distribution. The portfolio is divided into exposure bands to simplify calculations. Probability generating functions are used to derive a closed-form expression for the probability distribution of portfolio losses. The model can incorporate sector analysis and correlations between obligors. Extensions of the model have been proposed to include migration risk and closed-form modeling of correlated credit events.
This document discusses different techniques for software testing, including static and dynamic techniques. It covers specification-based or black-box techniques like equivalence partitioning, boundary value analysis, decision tables, and state transition testing. Equivalence partitioning involves dividing inputs into equivalent partitions, while boundary value analysis focuses on testing values at the boundaries of partitions. Decision tables systematically test combinations of inputs. State transition testing models the different states a system can be in and the transitions between states.
This document describes an HLA Income Builder investment product that provides guaranteed yearly income, dividends, and death/total permanent disability benefits. It offers a 5.5% compounding interest rate and increases guaranteed yearly income every year. After 20 years of deposits, the investment is projected to pay out over RM1 million in guaranteed yearly income and dividends, as well as a death benefit of over RM1.3 million. The HLA Income Builder aims to provide the best returns in the medium to long term with no risk to deposits.
Mastering Information Technology Risk ManagementGoutama Bachtiar
This is the presentation slide as part of the courseware utilized when delivering Information Technology Risk Management training - workshop on May 2013.
The document discusses defects in software testing. It defines a defect as an error or bug in an application that causes it to not meet user expectations or software requirements. Tests can show the presence, not absence, of defects. There are various types of defects, including bugs, failures, mistakes, and errors from different perspectives. Defects are categorized as functional or non-functional. Examples are provided for different types of defects like wrong, missing, and extra. The document notes that finding and fixing defects later in the software development process costs significantly more than fixing them earlier.
Tips for IT Risk Management Prof. Hernan Huwyler Information Security InstituteHernan Huwyler, MBA CPA
This document provides tips for IT risk management, including what to do and what to avoid. It recommends facilitating risk assessments well before IT decisions are made. Key objectives for IT risks are confidentiality, integrity and availability of assets like data, hardware, software and skills. Examples are provided for measuring these objectives. Risk statements should identify measurable events, threats, consequences and probabilities. Quantitative methods like annualized loss expectancy and tools for calculating single loss can help measure impacts in monetary terms or other metrics. Internal and external data sources can provide statistics to tailor measurements to each organization. Subjective scales should be avoided in favor of statistical methods.
The document summarizes the key activities in the software testing process according to ISTQB, including test planning, monitoring and control, analysis, design, implementation, execution, evaluating exit criteria and reporting, and test closure activities. It provides details on each activity, such as the objectives of test planning, factors to consider for test analysis, and outputs that should be captured during test closure.
Conférence Mercredi de la Finance - Nov 2012 mwaresearch
le Cabinet MWA Conseil vous présente la conférence des mercredis de la finance de novembre 2012 "Approche opérationnelle et économique du risque de contrepartie"
The document discusses using probabilistic risk analysis and Monte Carlo simulation to increase the probability of project success. It explains that modeling tasks as probability distributions rather than single point estimates allows for a more accurate assessment of overall schedule and budget risk. Capturing the uncertainty and dependencies between different tasks and cost/schedule drivers is important for generating reliable forecasts. The goal is to quantify confidence levels and establish appropriate margins to account for risks and uncertainties.
Comment disposer d’un modèle dynamique de gestion des risques clients ?Pénélope Cardera
Lors de cette web conférence des responsables du credit management, des analystes crédit et des consultants évoquent les outils, indicateurs et processus de gestion des risques clients.
- Comment déployer un scoring sur ses clients ?
- Quels processus pour un recouvrement optimisé ?
- Comment gérer le plus finement possible ses encours clients ?
- Comment dimensionner et organiser ses équipes ? Comment mettre en place une gestion pro-active de ses risques clients?
À travers leurs expériences et des exemples concrets, nos interlocuteurs apportent des réponses précises sur les meilleures pratiques tant en France qu’à l’international.
www.au-group.fr
Modelling the expected loss of bodily injury claims using gradient boostingGregg Barrett
This document summarizes an effort to model the expected loss of bodily injury claims using gradient boosting. Frequency and severity models are built separately and then combined to estimate expected loss. Gradient boosting is chosen as the modeling approach due to its flexibility. Tuning parameters like shrinkage, number of trees, and depth must be selected. The goal is predictive accuracy over interpretability. Performance is evaluated on a test set not used for model selection.
More Information:
https://flevy.com/browse/business-document/business-case-template-excel-683
DOCUMENT DESCRIPTION
For individuals who are fairly new at developing business cases, the Business Case Template Excel file provides a step-by-step methodology for developing a high level business case.
This Template Excel is also a companion document of the "How to Develop a Business Case" presentation which guide business leaders make investment decisions by helping them understand the financial impact of those decisions throughout the planning stage of a project to help justify a strategic direction and operating strategy
This Excel template includes the following sections:
- Instruction Guide
- Step 1. Input Variables
- Step 2. Generate Baseline Data
- Step 3. Input Benefit Estimate
- Step 4. Review Benefit Calc
- Step 5. Enter Investment
- Step 6. Review Cap Ex
- Step 7. Review Cash Flow Result
- Step 8. What-If Analysis
- Financial Summary
- Example Charts
Got a question about the product? Email us at support@flevy.com or ask the author directly by using the form to the right. If you cannot view the preview above this document description, go here to view the large preview instead.
The document summarizes key changes in the Basel Committee's revised market risk framework, known as Fundamental Review of the Trading Book (FRTB). It introduces more complex capital calculations under the internal models approach, with requirements for multiple scenario analyses and risk factor combinations that significantly increase processing needs. It also requires clearer position classification and metadata for regulatory capital calculations. Banks will need enhanced data management and risk aggregation capabilities to integrate information across business units. The substantial technology impacts suggest a long-term, flexible implementation approach rather than short-term minimum compliance.
This document discusses using attribute reduction to increase the efficiency of credit card fraud detection using decision trees. It analyzes a credit card transaction dataset containing attributes like credit usage, employment status, and purpose. Attribute statistics show some attributes have a single dominant value. The paper performs tests removing these attributes and finds the correctly classified instances increases from 70.5% to 72.9%, showing attribute reduction improves efficiency. By removing unnecessary attributes that don't contribute useful information, decision trees can more accurately classify transactions as fraudulent or genuine.
"Multilayer perceptron (MLP) is a technique of feed
forward artificial neural network using back
propagation learning method to classify the target
variable used for supervised learning. It consists of multiple layers and non-linear activation allowing it to distinguish data that is not linearly separable."
Pillar III presentation 2 27-15 - redacted versionBenjamin Huston
This document provides an overview of a market-based indicators approach to stress testing financial institutions in the United States. It describes using a systemic risk dashboard to monitor risks, a contingent claims analysis model to estimate institutions' default probabilities, and generalized additive models to project default probabilities under stress scenarios. Historical results are also recapped. Key findings on macroeconomic contributions and inter-sector spillovers are presented. Annexes provide details on modeling methodologies.
In this paper I compare a conventional classification regression method with the state of the art machine learning technique XGBoost. This results in a major performance gain in terms of classification and expected loss.
Conférence Mercredi de la Finance - Nov 2012 mwaresearch
le Cabinet MWA Conseil vous présente la conférence des mercredis de la finance de novembre 2012 "Approche opérationnelle et économique du risque de contrepartie"
The document discusses using probabilistic risk analysis and Monte Carlo simulation to increase the probability of project success. It explains that modeling tasks as probability distributions rather than single point estimates allows for a more accurate assessment of overall schedule and budget risk. Capturing the uncertainty and dependencies between different tasks and cost/schedule drivers is important for generating reliable forecasts. The goal is to quantify confidence levels and establish appropriate margins to account for risks and uncertainties.
Comment disposer d’un modèle dynamique de gestion des risques clients ?Pénélope Cardera
Lors de cette web conférence des responsables du credit management, des analystes crédit et des consultants évoquent les outils, indicateurs et processus de gestion des risques clients.
- Comment déployer un scoring sur ses clients ?
- Quels processus pour un recouvrement optimisé ?
- Comment gérer le plus finement possible ses encours clients ?
- Comment dimensionner et organiser ses équipes ? Comment mettre en place une gestion pro-active de ses risques clients?
À travers leurs expériences et des exemples concrets, nos interlocuteurs apportent des réponses précises sur les meilleures pratiques tant en France qu’à l’international.
www.au-group.fr
Modelling the expected loss of bodily injury claims using gradient boostingGregg Barrett
This document summarizes an effort to model the expected loss of bodily injury claims using gradient boosting. Frequency and severity models are built separately and then combined to estimate expected loss. Gradient boosting is chosen as the modeling approach due to its flexibility. Tuning parameters like shrinkage, number of trees, and depth must be selected. The goal is predictive accuracy over interpretability. Performance is evaluated on a test set not used for model selection.
More Information:
https://flevy.com/browse/business-document/business-case-template-excel-683
DOCUMENT DESCRIPTION
For individuals who are fairly new at developing business cases, the Business Case Template Excel file provides a step-by-step methodology for developing a high level business case.
This Template Excel is also a companion document of the "How to Develop a Business Case" presentation which guide business leaders make investment decisions by helping them understand the financial impact of those decisions throughout the planning stage of a project to help justify a strategic direction and operating strategy
This Excel template includes the following sections:
- Instruction Guide
- Step 1. Input Variables
- Step 2. Generate Baseline Data
- Step 3. Input Benefit Estimate
- Step 4. Review Benefit Calc
- Step 5. Enter Investment
- Step 6. Review Cap Ex
- Step 7. Review Cash Flow Result
- Step 8. What-If Analysis
- Financial Summary
- Example Charts
Got a question about the product? Email us at support@flevy.com or ask the author directly by using the form to the right. If you cannot view the preview above this document description, go here to view the large preview instead.
The document summarizes key changes in the Basel Committee's revised market risk framework, known as Fundamental Review of the Trading Book (FRTB). It introduces more complex capital calculations under the internal models approach, with requirements for multiple scenario analyses and risk factor combinations that significantly increase processing needs. It also requires clearer position classification and metadata for regulatory capital calculations. Banks will need enhanced data management and risk aggregation capabilities to integrate information across business units. The substantial technology impacts suggest a long-term, flexible implementation approach rather than short-term minimum compliance.
This document discusses using attribute reduction to increase the efficiency of credit card fraud detection using decision trees. It analyzes a credit card transaction dataset containing attributes like credit usage, employment status, and purpose. Attribute statistics show some attributes have a single dominant value. The paper performs tests removing these attributes and finds the correctly classified instances increases from 70.5% to 72.9%, showing attribute reduction improves efficiency. By removing unnecessary attributes that don't contribute useful information, decision trees can more accurately classify transactions as fraudulent or genuine.
"Multilayer perceptron (MLP) is a technique of feed
forward artificial neural network using back
propagation learning method to classify the target
variable used for supervised learning. It consists of multiple layers and non-linear activation allowing it to distinguish data that is not linearly separable."
Pillar III presentation 2 27-15 - redacted versionBenjamin Huston
This document provides an overview of a market-based indicators approach to stress testing financial institutions in the United States. It describes using a systemic risk dashboard to monitor risks, a contingent claims analysis model to estimate institutions' default probabilities, and generalized additive models to project default probabilities under stress scenarios. Historical results are also recapped. Key findings on macroeconomic contributions and inter-sector spillovers are presented. Annexes provide details on modeling methodologies.
In this paper I compare a conventional classification regression method with the state of the art machine learning technique XGBoost. This results in a major performance gain in terms of classification and expected loss.
This document provides specifications for a new payroll system for Tyler R Us. The current system is outdated and inadequate for the company's future needs. The new system needs to be modular, flexible to accommodate growth, easy to use, and comply with all legislative requirements. It must store historical payroll data for 7 years and have robust security. Each requirement is assigned a priority level of 1) essential, 2) optional but beneficial, or 3) additional/future need. The document then provides detailed specifications for key payroll modules including employee master files, payments/deductions, pensions, data input, statutory payments, taxes, loans, orders and reports.
1-Base-CaseTool KitChapter 11112118Note Calculations are automaMartineMccracken314
1-Base-CaseTool KitChapter 1111/21/18Note: Calculations are automatic, including for tables. This will make the calculations take longer to complete. You can disable automatic calculations for tables by following the steps shown here.Cash Flow Estimation and Risk AnalysisWorksheet 1-Base-CaseThis worksheet contains the base-case model. It calculates an expansion project's cash flows and performance measures using base-case, or most likely, values for the input variables. It also includes the basic analysis but with straight-line depreciation and bonus depreciation.Go to the menu "Files" at the top left of the menu bar.Select "Options" from the items in the first column.This will give you the screen shown below:The second worksheet (2-Sens) extends the basic model to include sensitivity analysis using Data Tables (we include a brief tutorial on the use of Data Tables). Worksheet 2-Sens also illustrates special cases of sensitivity analysis, including breakeven analysis, one-way data tables with multiple outputs, and two-way data tables.Worksheet 3a-Sens extends the basic model to include scenario analysis. Worksheet 3b-ScenMgr shows how to use Excel's Scenario Manager for scenario analysis.Worksheet 4-Sim extends the basic model to include simulation analysis. Worksheet 5-Replmt illustrates the analysis for a proposed cost-reducing replacement investment. Replacement decisions differ from expansion decisions because most of the cash flows are found by subtracting the old project's cash flows from those of the new project to calculate incremental cash flows for use in the analysis.Worksheet 6-DecTree extends the scenario analysis to examine two decision trees in which the decision is made in stages. The first one simply shows the situation where the firm can abandon the project if things are not working out and cash flows are negative. The second one involves a marketing study and a prototype of the final product designed to learn more about demand before deciding to go into full production.Worksheet Appendix 11-A provides depreciation tables as described in Appendix A of the textbook. It also shows examples using straight-line depreciation and bonus depreciation.11-1 Identifying Relevant Cash FlowsA proposal’s relevant project cash flows are the differences between the cash flows the firm will have if it implements the project versus the cash flows it will have if it rejects the project. These are called incremental cash flows.Choose "Formulas" in the first column.11-2 Analysis of an Expansion ProjectThis will give you the screen shown below.The figure below shows the inputs and key results of Project L (one of the projects whose cash flows are used in the previous chapter); the actual analysis is conducted further below in the worksheet. The values in the Inputs section are linked to the model, as are the values shown in Key Results. If you change any of the values in the Input Section, the model recalculate almost instantly, causing ch ...
1-Base-CaseTool KitChapter 11112118Note Calculations are automaAbbyWhyte974
1-Base-CaseTool KitChapter 1111/21/18Note: Calculations are automatic, including for tables. This will make the calculations take longer to complete. You can disable automatic calculations for tables by following the steps shown here.Cash Flow Estimation and Risk AnalysisWorksheet 1-Base-CaseThis worksheet contains the base-case model. It calculates an expansion project's cash flows and performance measures using base-case, or most likely, values for the input variables. It also includes the basic analysis but with straight-line depreciation and bonus depreciation.Go to the menu "Files" at the top left of the menu bar.Select "Options" from the items in the first column.This will give you the screen shown below:The second worksheet (2-Sens) extends the basic model to include sensitivity analysis using Data Tables (we include a brief tutorial on the use of Data Tables). Worksheet 2-Sens also illustrates special cases of sensitivity analysis, including breakeven analysis, one-way data tables with multiple outputs, and two-way data tables.Worksheet 3a-Sens extends the basic model to include scenario analysis. Worksheet 3b-ScenMgr shows how to use Excel's Scenario Manager for scenario analysis.Worksheet 4-Sim extends the basic model to include simulation analysis. Worksheet 5-Replmt illustrates the analysis for a proposed cost-reducing replacement investment. Replacement decisions differ from expansion decisions because most of the cash flows are found by subtracting the old project's cash flows from those of the new project to calculate incremental cash flows for use in the analysis.Worksheet 6-DecTree extends the scenario analysis to examine two decision trees in which the decision is made in stages. The first one simply shows the situation where the firm can abandon the project if things are not working out and cash flows are negative. The second one involves a marketing study and a prototype of the final product designed to learn more about demand before deciding to go into full production.Worksheet Appendix 11-A provides depreciation tables as described in Appendix A of the textbook. It also shows examples using straight-line depreciation and bonus depreciation.11-1 Identifying Relevant Cash FlowsA proposal’s relevant project cash flows are the differences between the cash flows the firm will have if it implements the project versus the cash flows it will have if it rejects the project. These are called incremental cash flows.Choose "Formulas" in the first column.11-2 Analysis of an Expansion ProjectThis will give you the screen shown below.The figure below shows the inputs and key results of Project L (one of the projects whose cash flows are used in the previous chapter); the actual analysis is conducted further below in the worksheet. The values in the Inputs section are linked to the model, as are the values shown in Key Results. If you change any of the values in the Input Section, the model recalculate almost instantly, causing ch ...
Moderation and Meditation conducting in SPSSOsama Yousaf
The document defines moderation and describes the process for testing moderation using hierarchical multiple regression. Moderation implies an interaction effect where a third variable changes the direction or strength of the relationship between two other variables. To test for moderation, regression is used to assess whether the interaction term between the predictor and moderator variables significantly improves the model's ability to predict the outcome variable above and beyond the main effects alone. The steps involve standardizing variables, including main and interaction effects in separate regression models, and interpreting a significant change in R-squared between the models as evidence of moderation.
This document discusses methods for estimating key inputs used to calculate the weighted average cost of capital (WACC) for a company. It evaluates different approaches to estimating beta, the risk-free rate, and equity market risk premium based on regression analysis of stock return data. For the company in question, CSR, it selects a beta of 1.15 based on 3 years of weekly return data. The risk-free rate is taken as the 10-year government bond yield of 3.37% geometrically averaged over 4 years. The equity risk premium is estimated to be 8.88% based on the accumulation index return over the same period. This yields an estimated cost of equity of 13.58% and overall WACC cannot be
Calculation contex in sap business objectsDmitry Anoshin
The document discusses how to control calculation context in SAP Business Objects by defining input and output contexts. By default, measures are aggregated to the level of dimensions displayed. To override this, input and output contexts can be specified. Operators like "In", "ForEach", and "Where" are used to define which dimensions should be included or excluded from calculations. Examples demonstrate how to use these operators to define contexts for calculations like finding the maximum sales revenue for a given state and year.
Automobile Insurance Claim Fraud Detection using Random Forest and ADASYNIRJET Journal
The document presents a study on detecting automobile insurance claim fraud using random forest and ADASYN. The researchers used the random forest classifier and the ADASYN data sampling technique to address the class imbalance in their dataset. They applied one-hot encoding to resolve issues with imbalanced data, trained the random forest model on the balanced data, and evaluated its performance. Experimental results found that the random forest model achieved over 97% accuracy, 94% recall, and 99.8% precision for fraud detection after applying ADASYN, outperforming other classifiers like SVM and Naive Bayes. Thus, the random forest model with ADASYN was effective for the task of automobile insurance fraud detection.
In Machine Learning in Credit Risk Modeling, we provide an explanation of the main Machine Learning models used in James so that Efficiency does not come at the expense of Explainability.
(Contact Yvan De Munck for more info or to receive other and future updates on the subject @yvandemunck or yvan@james.finance)
The document discusses code coverage from the perspective of DO178B certification. It explains that testing of code coverage is essential for safety-critical software certification. It describes the five levels of software criticality in DO178B from Level A to E, with A being the highest. The level of testing required varies according to the software's criticality level, from no structural testing needed for Level D to modified condition/decision coverage required for Level A.
Ch05 P24 Build a Model Spring 1, 201372212Chapter 5. Ch 05 P24 B.docxtidwellveronique
This document provides information about bond valuation and modeling bond prices using Excel functions. It includes examples of using the PRICE and PV functions to value a bond given its coupon rate, par value, maturity date, and market yield. It also shows how bond prices change over time as market interest rates change, rising to 15% or falling to 5% from the initial 10% rate. The document discusses modifications needed to the model for bonds that pay interest semiannually, such as dividing the coupon payment, years to maturity, and market yield by two.
I have done this analysis using SAS on a dataset with 5000 records. I have used CART and Logistic regression to build a predictive model to identify customers which are likely to shift to competitors network.
2. CreditRisk+
Model
2
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)
3. CreditRisk+
Model
3
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.
4. CreditRisk+
Model
4
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.
5. CreditRisk+
Model
5
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.
6. CreditRisk+
Model
6
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.
7. CreditRisk+
Model
7
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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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