Pd Shock

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• sensitivity analysis (4)
• credit risk (3)
• percentage change (3)
• credit risk sensitivity (2)
• macroeconomic conditions (2)
• stress scenarios (2)
• combined shock (2)
• pd elasticity (2)
• elasticity coefficients (2)
• lgd elasticity (2)

1.Mitigating Credit Risk through Sensitivity Analysis[Original Blog]

One of the main challenges in credit risk management is to assess how sensitive the credit risk of a borrower or a portfolio is to changes in various factors, such as interest rates, exchange rates, macroeconomic conditions, or borrower-specific characteristics. Sensitivity analysis is a useful tool to measure and manage credit risk sensitivity, as it allows the analyst to estimate how the credit risk indicators, such as probability of default (PD), loss given default (LGD), or exposure at default (EAD), would change in response to changes in the input variables. Sensitivity analysis can also help to identify the most influential factors that affect credit risk and to design appropriate risk mitigation strategies.

There are different methods and approaches to conduct sensitivity analysis for credit risk, depending on the level of complexity, data availability, and the purpose of the analysis. In this section, we will discuss some of the common methods and their advantages and limitations. We will also provide some examples to illustrate how sensitivity analysis can be applied to different types of credit risk scenarios. The methods we will cover are:

1. Scenario analysis: This method involves defining a set of scenarios that represent different possible outcomes of the input variables and calculating the credit risk indicators for each scenario. The scenarios can be based on historical data, expert judgment, or simulations. The advantage of this method is that it can capture the joint effects of multiple factors and provide a comprehensive view of the credit risk sensitivity. The limitation is that it can be difficult to define realistic and consistent scenarios and to assign probabilities to them.

2. Elasticity analysis: This method involves estimating the percentage change in the credit risk indicators for a given percentage change in the input variables. The elasticity coefficients can be derived from empirical models, such as regression analysis, or from theoretical models, such as option pricing models. The advantage of this method is that it can provide a simple and intuitive measure of the credit risk sensitivity. The limitation is that it assumes a linear and constant relationship between the input and output variables, which may not hold in reality.

3. Stress testing: This method involves applying extreme or adverse changes in the input variables and evaluating the impact on the credit risk indicators. The stress scenarios can be based on historical events, hypothetical events, or regulatory requirements. The advantage of this method is that it can assess the resilience and solvency of the borrower or the portfolio under severe conditions. The limitation is that it can be subjective and arbitrary to define the stress scenarios and to interpret the results.

Example 1: Sensitivity analysis for a corporate loan

Suppose we want to conduct a sensitivity analysis for a corporate loan with the following characteristics:

- Principal amount: $10 million

- Maturity: 5 years

- Interest rate: 5% fixed

- PD: 2% per year

- LGD: 40% of the outstanding balance

We can use the scenario analysis method to evaluate how the credit risk indicators would change under different scenarios of the interest rate and the PD. We can define four scenarios as follows:

- Scenario 1: Base case (interest rate = 5%, PD = 2%)

- Scenario 2: Interest rate shock (interest rate = 7%, PD = 2%)

- Scenario 3: PD shock (interest rate = 5%, PD = 4%)

- Scenario 4: Combined shock (interest rate = 7%, PD = 4%)

We can then calculate the expected loss (EL), which is the product of PD, LGD, and EAD, for each scenario and compare them with the base case. The results are shown in the table below:

| Scenario | Interest rate | PD | EAD | LGD | EL |

| 1 | 5% | 2% | $10 million | 40% | $80,000 |

| 2 | 7% | 2% | $10.7 million | 40% | $85,600 |

| 3 | 5% | 4% | $10 million | 40% | $160,000 |

| 4 | 7% | 4% | $10.7 million | 40% | $171,200 |

From the table, we can see that the EL increases in all scenarios compared to the base case. The largest increase occurs in scenario 4, where both the interest rate and the PD increase. This indicates that the credit risk of the loan is more sensitive to the combined shock than to the individual shocks. The sensitivity analysis can help us to understand the potential losses under different scenarios and to design appropriate risk mitigation strategies, such as hedging, diversification, or loan restructuring.

Example 2: Sensitivity analysis for a credit card portfolio

Suppose we want to conduct a sensitivity analysis for a credit card portfolio with the following characteristics:

- Number of accounts: 100,000

- Average balance: $1,000

- average interest rate: 15%

- Average PD: 3% per month

- Average LGD: 60% of the outstanding balance

We can use the elasticity analysis method to estimate how the credit risk indicators would change for a given percentage change in the input variables. We can assume that the elasticity coefficients are as follows:

- PD elasticity with respect to interest rate: 0.2

- PD elasticity with respect to macroeconomic conditions: 0.5

- LGD elasticity with respect to interest rate: -0.1

- LGD elasticity with respect to macroeconomic conditions: 0.3

We can then calculate the percentage change in the EL, which is the product of PD, LGD, and EAD, for a given percentage change in the interest rate and the macroeconomic conditions. The results are shown in the table below:

| Percentage change in | Interest rate | Macroeconomic conditions | EL |

| 1 | 10% | 0% | 5.8% | | 2 | -10% | 0% | -5.8% | | 3 | 0% | 10% | 24.6% | | 4 | 0% | -10% | -24.6% | | 5 | 10% | 10% | 31.2% | | 6 | -10% | -10% | -31.2% |

From the table, we can see that the EL changes in the same direction as the interest rate and the macroeconomic conditions. The largest change occurs in scenario 5 and 6, where both the interest rate and the macroeconomic conditions change by 10%. This indicates that the credit risk of the portfolio is more sensitive to the combined changes than to the individual changes. The elasticity analysis can help us to measure and manage the credit risk sensitivity and to adjust the pricing and provisioning policies accordingly.

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