EBA欧洲银行-SR-03-Estimating-the-distribution-of-total-default-losses-R.-Garcia-Cespedes2C2020M.-Moreno_54页_906kb

Summary of "Estimating the distribution of total default losses on the Spanish financial system"

Core Content

This paper introduces a Monte Carlo Importance Sampling (IS) approach to estimate the credit risk loss distribution of the Spanish financial system. It extends the traditional credit risk models by incorporating more realistic assumptions such as random recoveries and market valuation. The study also examines the variability of risk measures over the business cycle and due to uncertainty in model parameters.

Main Points

• Objective: To estimate the loss distribution and risk allocation of the Spanish financial system using a general Monte Carlo IS method.
• Model: The Vasicek (1987) model is used as the basis for the credit risk analysis. It assumes that the default of a client is driven by macroeconomic factors and an idiosyncratic term.
• Risk Measures: The paper focuses on computing Value at Risk (VaR) and Expected Shortfall (ES) for the portfolio, as well as risk contributions from individual institutions.
• Methodology: The IS method is employed to improve the accuracy and efficiency of estimating the loss distribution compared to the standard Monte Carlo method. The optimal sampling distributions are derived for both the conditional default probabilities and macroeconomic factors.
• Random Recoveries: The paper uses data from the U.S. FDIC to account for random recoveries, which affect risk allocation but not the portfolio’s 99.9% probability loss.
• Market Valuation: A market valuation approach is introduced, which has a more significant impact on the loss distribution than the random recovery model.
• Risk Allocation: The paper emphasizes the importance of correctly allocating risk across financial institutions and highlights that different models can lead to different risk contributions.
• Business Cycle and Uncertainty: The variability of loss distributions over the business cycle and due to uncertainty in model inputs is analyzed.
• Contributions: The study provides three main contributions: the estimation of the loss distribution using IS, the extension of the IS method to account for random recoveries and market valuation, and the analysis of risk variability over time and under different assumptions.

Key Information

Credit Risk Model

• The Vasicek (1987) model is used, which assumes that the default of a client is influenced by macroeconomic factors and an idiosyncratic term.
• The model is widely used in banking regulation and forms the basis of Basel II and III capital requirements.

Risk Measures

• VaR: The value at risk is defined as the loss level that is exceeded with a given probability.
• ES: Expected shortfall is the average loss given that the loss is above the VaR threshold.
• Risk Contributions: The paper computes both CVaR (VaR contribution) and CES (ES contribution) for individual clients.

Importance Sampling

• The IS method is used to improve the efficiency of estimating the loss distribution and risk contributions.
• The optimal sampling distribution is derived by adjusting the default probabilities and macroeconomic factors to focus on the tail of the distribution.
• The weight function for the IS estimator is given by $ W_{1,i} = e^{-L_i \theta + \psi(\theta)} $, where $ \psi(\theta) $ is the cumulant generating function of the loss distribution.

Random Recoveries and Market Valuation

• Random recoveries are modeled using data from the U.S. FDIC, which significantly affects risk allocation.
• Market valuation is incorporated using a model similar to that in Grundke (2009), which has a larger impact on the loss distribution than the random recovery model.

Portfolio Data

• The study considers 157 financial entities covered by the Spanish deposit guarantee fund (FGD) as of December 2010.
• The portfolio is concentrated, with the top 25 institutions accounting for 92.1% of assets and 92.8% of deposits.
• The Herfindahl index indicates a low number of effective counterparties, suggesting a highly concentrated financial system.

Loss Given Default (LGD)

• LGD is estimated using historical data and adjusted for potential biases.
• The average LGD for deposits is 20.73%, but after adjustments, it is estimated at 18.35%.
• LGD for assets is calculated by applying a multiplicative factor of 1.378 to the adjusted deposit LGD.

Factor Correlation (α)

• The correlation between macroeconomic factors is based on the Basel III framework.
• The correlation is calculated using the formula $ \sqrt{0.12\omega + 0.24(1 - \omega)} $, where $ \omega $ is a function of the default probability.
• The correlation is extended to include additional geographies for BBVA and Santander, based on their net interest income data.

Results and Implications

• The IS method is shown to be more accurate and computationally efficient than standard Monte Carlo methods.
• The risk allocation varies significantly depending on the valuation model used.
• The study highlights the importance of considering both macroeconomic and market factors in risk modeling.
• It suggests that a simple default mode model can underestimate the risk compared to a market mode model.
• The approach can be used to identify Systemically Important Financial Institutions (SIFI) and to determine the required capital surcharge for these institutions.

Conclusion

The paper contributes to the field of macroprudential supervision by introducing a more comprehensive and accurate method for estimating credit risk losses in the Spanish financial system. It provides a framework that can be used by banking supervisors to better understand systemic risk and allocate capital requirements accordingly.