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Economic Capital Assessment via Copulas: Aggregation and Allocation of Different Risk Types

by Marco Morone of Intesa-Sanpaolo,
Anna Cornaglia of Intesa-Sanpaolo, and
Giulio Mignola of Intesa-Sanpaolo

March 2, 2007

Abstract: The most common approach in estimating the inter-risk diversification effect is to aggregate the stand alone economic capital for each risk type through a variance/covariance Markowitz approach. In this paper we propose an alternative framework, still "ex-post" in the sense that marginal models for the loss distribution of each risk are independently developed and then merged to a joint distribution, but based on the simulation of a t-copula dependence structure; the Kendall's τs measure is used to correlate the risks. No assumption is then required on the marginal distributions, which depend in fact on the specific models used to describe each risk. The method is applied to calculate the economic capital for a hypothetical portfolio of risks typically faced by a commercial bank. A Window Conditional Expectation approach for allocating back the diversified capital has also been experimented.

JEL Classification: C15, G31, G21.

Keywords: copula, risk aggregation, stressed correlations, risk contribution, economic capital, capital allocation, expected shortfall, window conditional expectation, Basel II, Pillar II.

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