## Risk Modeling with Risk Management Toolbox

Risk Management Toolbox™ provides tools for modeling seven areas of risk assessment:

Consumer credit risk

Corporate credit risk

Market risk

Insurance risk

Lifetime models for probability of default

Loss given default models

Exposure at default models

### Consumer Credit Risk

*Consumer credit risk * (also referred to as
*retail credit risk*) is the risk of loss due to a
customer's default (non-repayment) on a consumer credit product. These products can
include a mortgage, unsecured personal loan, credit card, or overdraft. A common
method for predicting credit risk is through a credit scorecard. The scorecard is a
statistically based model for attributing a score to a customer that indicates the
predicted probability that the customer will default. The data used to calculate the
score can be from sources such as application forms, credit reference agencies, or
products the customer already holds with the lender. Financial Toolbox™ provides tools for creating credit scorecards and performing credit
portfolio analysis using scorecards. Risk Management Toolbox includes a Binning Explorer app for automatic or manual binning to
streamline the binning phase of credit scorecard development. For more information,
see Overview of Binning Explorer.

### Corporate Credit Risk

*Corporate credit risk* (also referred to as
*wholesale credit risk*) is the risk that counterparties
default on their financial obligations.

At an individual counterparty level, one of the main credit risk parameters is the probability of default (PD). Risk Management Toolbox allows you to estimate probabilities of default using the following methodologies:

Structural models:

`mertonmodel`

and`mertonByTimeSeries`

Reduced-form models:

`cdsbootstrap`

and`bondDefaultBootstrap`

using Financial ToolboxHistorical credit ratings migrations:

`transprob`

using Financial ToolboxStatistical approaches: credit scorecards using

**Binning Explorer**and the`creditscorecard`

object using Financial Toolbox, and a wide selection of predictive models in Statistics and Machine Learning Toolbox™

At a *credit portfolio* level, on the other hand, to assess
credit risk, to assess this risk, the main question to ask is, Given a current
credit portfolio, how much can be lost in a given time period due to defaults? In
differing circumstances, the answer to this question might mean:

How much do you expect to lose?

How likely is it that you will lose more than a specific amount?

What is the most you can lose under relatively normal circumstances?

How much can you lose if things get bad?

Mathematically, these questions all depend on estimating a distribution of losses for the credit portfolio: What are the different amounts you can lose, and how likely is it that you lose each individual amount.

Corporate credit risk is fundamentally different from market risk, which is the risk that assets lose value due to market movements. The most important difference is that markets move all the time, but defaults occur infrequently. Therefore, the sample sizes to support any modeling efforts are different. The challenge is to calibrate a distribution of credit losses, because the sample sizes are small. For credit risk, even for an individual bond that has not defaulted, you cannot collect direct data on what happens in the event of default because it has not defaulted. And once the issuer actually defaults, unless you can pool default information from similar companies, that is the only data point that you have.

For corporate credit portfolio analysis, estimating credit correlations so that you can understand the benefits of diversification is also challenging. Two companies can only default in the same time window once, so you cannot collect data on how often they default together. To collect more data, you can pool data from similar companies and under similar economic conditions.

Risk Management Toolbox provides a credit default simulation framework for credit portfolios
using the `creditDefaultCopula`

object, where the
three main elements of credit risk for a single instrument are:

The probability of default (PD) which is the likelihood that the issuer defaults in a given time period.

The exposure at default (EAD) which is the amount of money that is at stake. For a traditional bond, this is the bond principal.

The loss given default (LGD) which is the fraction of the exposure that would be lost at default. When default occurs, usually some money is recovered eventually.

The assumption is that these three quantities are fixed and known for all the
companies in the credit portfolio. With this assumption, the only uncertainty is
whether each company defaults, which happens with probability
PD*i*.

At the credit portfolio level, however, the main question is, "What are the
default correlations between issuers?" For example, for two bonds with 10MM
principal each, the risk is different if you expect the companies to default
together. In this scenario, you could lose 20MM minus the recovery, all at once.
Alternatively, if the defaults are independent, you could lose 10MM minus recovery
if one defaults, but the other company is likely still alive. Default correlations
are therefore important parameters for understanding the risk at a portfolio level.
These parameters are also important for understanding the diversification and
concentration characteristics of the portfolio. The approach in Risk Management Toolbox is to simulate correlated variables that can be efficiently simulated
and parameterized, then map the simulated values to default or nondefault states to
preserve the individual default probabilities. This approach is called a
*copula*. When normal variables are used, this approach is
called a *Gaussian copula*. Risk Management Toolbox also provides a credit migration simulation framework for credit
portfolios using the `creditMigrationCopula`

object. For more
information, see Credit Rating Migration Risk.

Related to the `creditDefaultCopula`

and `creditMigrationCopula`

objects, Risk Management Toolbox provides an analytical model known as the Asymptotic Single Risk
Factor (ASRF) model. The ASRF model is useful because the Basel II documents propose
this model as the standard for certain types of capital requirements. ASRF is not a
Monte-Carlo model, so you can quickly compute the capital requirements for large
credit portfolios. You can use the ASRF model to perform a quick sensitivity
analysis and exploring "what-if" scenarios more easily than rerunning large
simulations. For more information, see `asrf`

.

Risk Management Toolbox also provides tools for portfolio concentration analysis, see Concentration Indices.

### Market Risk

*Market risk* is the risk of losses in positions arising from
movements in market prices. Value-at-risk is a statistical method that quantifies
the risk level associated with a portfolio. VaR measures the maximum amount of loss
over a specified time horizon, at a given confidence level. For example, if the
one-day 95% VaR of a portfolio is 10MM, then there is a 95% chance that the
portfolio loses less than 10MM the following day. In other words, only 5% of the
time (or about once in 20 days) the portfolio losses exceed 10MM.

*VaR Backtesting*, on the other hand, measures how accurate
the VaR calculations are. For many portfolios, especially trading portfolios, VaR is
computed daily. At the closing of the following day, the actual profits and losses
for the portfolio are known, and can be compared to the VaR estimated the day
before. You can use this daily data to assess the performance of VaR models, which
is the goal of VaR backtesting. As such, backtesting is a method that looks
retrospectively at data and refines the VaR models. Many VaR backtesting
methodologies have been proposed. As a best practice, use more than one criterion to
backtest the performance of VaR models, because all tests have strengths and
weaknesses.

Risk Management Toolbox provides the following VaR backtesting individual tests:

For information on the different tests, see Overview of VaR Backtesting.

*Expected Shortfall (ES) Backtesting* gives an estimate of
the loss in those very bad days when the VaR is violated. ES is the expected loss on
days when there is a VaR failure. If the VaR is 10 million and the ES is 12 million,
you know that the expected loss tomorrow, if it happens to be a very bad day, is
about 20% higher than the VaR.

Risk Management Toolbox provides the following table-based tests for expected shortfall based
on the `esbacktest`

object:

The following tools support expected shortfall simulation-based tests for the
`esbacktestbysim`

object:

For information on the different tests, see Overview of Expected Shortfall Backtesting.

### Insurance Risk

The ability to accurately estimate unpaid claims is important to insurers. Unlike companies in other sectors, insurers might not know the exact earnings during a financial reporting period until many years later. Insurance companies take in insurance premiums on a regular basis and pay out claims when events occur. In order to maximize profits, an insurance company must accurately estimate how much will be paid out on existing claims in the future. If the estimate for unpaid claims is too low, the insurance company will become insolvent. Conversely, if the estimate is too high, then the claims reserve capital of the insurance company could have been invested elsewhere or reinvested in the business

Risk Management Toolbox supports four claims estimation methods for actuaries to use with a
`developmentTriangle`

for
estimating unpaid claims:

For information on the estimation methods, see Overview of Claims Estimation Methods for Non-Life Insurance.

### Lifetime Models for Probability of Default

Regulatory frameworks such as IFRS 9 and CECL require institutions to estimate loss reserves based on a lifetime analysis that is conditional on macroeconomic scenarios. Earlier models were frequently designed to predict one period ahead and often with no explicit sensitivities to macroeconomic scenarios. With the IFRS 9 and CECL regulations, models must predict multiple periods ahead and the models must have an explicit dependency on macroeconomic variables.

The main output of the lifetime credit analysis is the lifetime expected credit loss (ECL). The lifetime ECL consists of the reserves that banks need to set aside for expected losses throughout the life of a loan. There are different approaches to the estimation of lifetime ECL. Some approaches use relatively simple techniques on loss data, with qualitative adjustments. Other approaches use more advanced time-series techniques or econometric models to forecast losses, with dependencies on macro variables. Another methodology uses probability of default (PD) models, loss given default (LGD) models, and exposure at default (EAD) models, and combines their outputs to estimate the ECL. The lifetime PD models in Risk Management Toolbox are in the PD-LGD-EAD category

Risk Management Toolbox provides the following lifetime PD models:

For information on the different models, see Overview of Lifetime Probability of Default Models.

### Loss Given Default Models

Loss given default (LGD) is the proportion of a credit that is lost in the event of default. LGD is one of the main parameters for credit risk analysis. Although there are different approaches to estimate credit loss reserves and credit capital, common methodologies require the estimation of probabilities of default (PD), loss given default (LGD), and exposure at default (EAD). The reserves and capital requirements are computed using formulas or simulations that use these parameters. For example, the loss reserves are usually estimated as the expected loss (EL), given by the following formula:

*EL* = *PD* * *LGD* *
*EAD*

Risk Management Toolbox provides the following LGD models:

For information on the different models, see Overview of Loss Given Default Models.

### Exposure at Default Models

EAD is seen as an estimation of the extent to which a bank may be exposed to a counterparty in the event of, and at the time of, that counterparty’s default. EAD is equal to the current amount outstanding in case of fixed exposures such as term loans. For example, the loss reserves are usually estimated as the expected loss (EL), given by the following formula:

*EL* = *PD* * *LGD* *
*EAD*

Risk Management Toolbox provides the following EAD models:

For information on the different models, see Overview of Exposure at Default Models.

## See Also

`varbacktest`

| `esbacktest`

| `esbacktestbysim`

| `mertonmodel`

| `mertonByTimeSeries`

| `concentrationIndices`

| `creditDefaultCopula`

| `creditMigrationCopula`

| `asrf`

| `developmentTriangle`

| `chainLadder`

| `expectedClaims`

| `bornhuetterFerguson`

| `Logistic`

| `Probit`

| `Cox`

| `Regression`

| `Tobit`

| `Beta`

| `Regression`

| `Tobit`

| `Beta`

## Related Examples

- Common Binning Explorer Tasks
- Bin Data to Create Credit Scorecards Using Binning Explorer
- creditMigrationCopula Simulation Workflow
- creditDefaultCopula Simulation Workflow
- Modeling Correlated Defaults with Copulas
- Stress Testing of Consumer Credit Default Probabilities Using Panel Data
- VaR Backtesting Workflow
- Expected Shortfall (ES) Backtesting Workflow with No Model Distribution Information
- Expected Shortfall (ES) Backtesting Workflow Using Simulation
- Expected Shortfall Estimation and Backtesting
- Value-at-Risk Estimation and Backtesting
- Basic Lifetime PD Model Validation
- Compare Logistic Model for Lifetime PD to Champion Model
- Compare Lifetime PD Models Using Cross-Validation
- Expected Credit Loss Computation
- Incorporate Macroeconomic Scenario Projections in Loan Portfolio ECL Calculations

## More About

- Credit Simulation Using Copulas
- Credit Rating Migration Risk
- Default Probability by Using the Merton Model for Structural Credit Risk
- Concentration Indices
- Traffic Light Test
- Binomial Test
- Kupiec’s POF and TUFF Tests
- Christoffersen’s Interval Forecast Tests
- Haas’s Time Between Failures or Mixed Kupiec’s Test
- Overview of Expected Shortfall Backtesting
- Overview of Lifetime Probability of Default Models
- Overview of Claims Estimation Methods for Non-Life Insurance