Aplicación de la Teoría de Cópulas en modelos de riesgo de crédito: Determinación y análisis del Valor en Riesgo y Pérdida Esperada en la Cola

Abstract

This paper is an application of the theory of copulas to a loan portfolio, to know its dependence structure and estimate financial risk indicators. For the application first, the univariate marginal distributions were estimated from the default rate and the amount of exposure based on historical information, then copulas were built. Finally with these two inputs Sklar's theorem was applied by means of the construction of models of Multivariate Copula Distributions and scenario generation. The results indicate that using 99.5% confidence level the portfolio can present a Maximum Loss of $ 21,423,543.99 over a period of 30 days. Under normal market conditions, within the same confidence level in onemonth period, the maximum loss that can present the portfolio is $ 18,649,516.91 (Credit VaR). Modifying some factors and market conditions worsen, once the maximum loss was overcome, the expected loss after the Credit VaR, ie. the Expected Shortfall can reach a value of $ 21,487,961.16 at 99.50% confidence. Comparing the results of the theory of copulas with other methodologies shows that the indicators do not use this theory underestimate the results and extreme events.