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CIMDO Methodology Recovers Distribution that Minimizes Entropy Distance from Prior
A new approach to modeling multivariate densities has been proposed, which recovers the distribution that minimizes the probabilistic divergence, or “entropy distance,” from the prior distribution and is consistent with the information embedded in moment-consistency constraints. This methodology, known as CIMDO, provides a rationale for selecting the posterior distribution closest to the prior, thereby solving the under-identified problem of determining an unknown multivariate distribution from partial information provided by Point-of-Distress (PoD) observations.
Methodology Overview
The proposed procedure uses cross-entropy solutions to reconcile inconsistencies between the prior distribution and empirical observations. This approach converts a problem of deductive mathematics into one of inference involving an optimization procedure, making it possible to infer values for unknown probability densities using data information.
Key Features
- Recovers distribution that minimizes entropy distance from prior
- Consistent with moment-consistency constraints and empirical observations
- Automatic adjustment of dependence structure to economic cycle
CIMDO-Copula: A Key Feature
The CIMDO approach also recovers a copula function that describes the dependence structure embedded in the multivariate CIMDO-density. This feature allows for the automatic adjustment of the dependence structure to different stages of the economic cycle, making it more flexible and efficient.
Quantification of Systematic Losses and Marginal Contribution to Systemic Risk
The authors also propose a methodology for quantifying systematic losses and marginal contribution to systemic risk (MCSR). The MCSR indicator incorporates two important factors: the size of the institution and its interconnectedness with the system. The MCSR is based on the Shapley Value, which requires the estimation of losses at the systemic level.
Simulation and Estimation
To simulate these losses, a Monte-Carlo simulation is performed using the CIMDO-estimated Financial Systemic Margin Distribution (FSMD). Two cases are considered: default or non-default, and the authors also account for losses resulting from deteriorated risk quality.
Benefits of CIMDO
The proposed methodology provides a more flexible approach to modeling multivariate densities, making use of limited available information in a more efficient manner. Overall, the CIMDO methodology offers a powerful tool for analyzing financial systems and predicting potential risks. Its ability to reconcile inconsistencies between prior distributions and empirical observations makes it a valuable addition to the field of financial economics.
Conclusion
The CIMDO methodology provides a new approach to modeling multivariate densities, recovering the distribution that minimizes entropy distance from the prior and incorporating moment-consistency constraints and empirical observations. Its flexibility and efficiency make it a valuable tool for analyzing financial systems and predicting potential risks.