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Register a new userOrdering the smallest claim amounts from two sets of interdependent heterogeneous portfolios
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Let $ X_{lambda_1},ldots,X_{lambda_n}$ be a set of dependent and non-negative random variables share a survival copula and let $Y_i= I_{p_i}X_{lambda_i}$, $i=1,ldots,n$, where $I_{p_1},ldots,I_{p_n}$ be independent Bernoulli random variables independent of $X_{lambda_i}$s, with ${rm E}[I_{p_i}]=p_i$, $i=1,ldots,n$. In actuarial sciences, $Y_i$ corresponds to the claim amount in a portfolio of risks. This paper considers comparing the smallest claim amounts from two sets of interdependent portfolios, in the sense of usual and likelihood ratio orders, when the variables in one set have the parameters $lambda_1,ldots,lambda_n$ and $p_1,ldots,p_n$ and the variables in the other set have the parameters $lambda^{*}_1,ldots,lambda^{*}_n$ and $p^*_1,ldots,p^*_n$. Also, we present some bounds for survival function of the smallest claim amount in a portfolio. To illustrate validity of the results, we serve some applicable models.
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Let $ X_{lambda_1},ldots,X_{lambda_n}$ be dependent non-negative random variables and $Y_i=I_{p_i} X_{lambda_i}$, $i=1,ldots,n$, where $I_{p_1},ldots,I_{p_n}$ are independent Bernoulli random variables independent of $X_{lambda_i}$s, with ${rm E}[I_{p_i}]=p_i$, $i=1,ldots,n$. In actuarial sciences, $Y_i$ corresponds to the claim amount in a portfolio of risks. In this paper, we compare the largest claim amounts of two sets of interdependent portfolios, in the sense of usual stochastic order, when the variables in one set have the parameters $lambda_1,ldots,lambda_n$ and $p_1,ldots,p_n$ and the variables in the other set have the parameters $lambda^{*}_1,ldots,lambda^{*}_n$ and $p^*_1,ldots,p^*_n$. For illustration, we apply the results to some important models in actuary.
Let $X_{lambda_1}, ldots , X_{lambda_n}$ be independent non-negative random variables belong to the transmuted-G model and let $Y_i=I_{p_i} X_{lambda_i}$, $i=1,ldots,n$, where $I_{p_1}, ldots, I_{p_n}$ are independent Bernoulli random variables independent of $X_{lambda_i}$s, with ${rm E}[I_{p_i}]=p_i$, $i=1,ldots,n$. In actuarial sciences, $Y_i$ corresponds to the claim amount in a portfolio of risks. In this paper we compare the smallest and the largest claim amounts of two sets of independent portfolios belonging to the transmuted-G model, in the sense of usual stochastic order, hazard rate order and dispersive order, when the variables in one set have the parameters $lambda_1,ldots,lambda_n$ and the variables in the other set have the parameters $lambda^{*}_1,ldots,lambda^{*}_n$. For illustration we apply the results to the transmuted-G exponential and the transmuted-G Weibull models.
Financial markets are exposed to systemic risk, the risk that a substantial fraction of the system ceases to function and collapses. Systemic risk can propagate through different mechanisms and channels of contagion. One important form of financial contagion arises from indirect interconnections between financial institutions mediated by financial markets. This indirect interconnection occurs when financial institutions invest in common assets and is referred to as overlapping portfolios. In this work we quantify systemic risk from indirect interconnections between financial institutions. Having complete information of security holdings of major Mexican financial intermediaries and the ability to uniquely identify securities in their portfolios, allows us to represent the Mexican financial system as a bipartite network of securities and financial institutions. This makes it possible to quantify systemic risk arising from overlapping portfolios. We show that focusing only on direct exposures underestimates total systemic risk levels by up to 50%. By representing the financial system as a multi-layer network of direct exposures (default contagion) and indirect exposures (overlapping portfolios) we estimate the mutual influence of different channels of contagion. The method presented here is the first objective data-driven quantification of systemic risk on national scales that includes overlapping portfolios.
We model hierarchical cascades of failures among banks linked through an interdependent network. The interaction among banks include not only direct cross-holding, but also indirect dependency by holding mutual assets outside the banking system. Using data extracted from the European Banking Authority, we present the interdependency network composed of 48 banks and 21 asset classes. Since interbank exposures are not public, we first reconstruct the asset/liability cross-holding network using the aggregated claims. For the robustness, we employ three reconstruction methods, called $textit{Anan}$, $textit{Hal{}a}$ and $textit{Maxe}$. Then we combine the external portfolio holdings of each bank to compute the interdependency matrix. The interdependency network is much denser than the direct cross-holding network, showing the complex latent interaction among banks. Finally, we perform macroprudential stress tests for the European banking system, using the adverse scenario in EBA stress test as the initial shock. For different reconstructed networks, we illustrate the hierarchical cascades and show that the failure hierarchies are roughly the same except for a few banks, reflecting the overlapping portfolio holding accounts for the majority of defaults. Understanding the interdependency network and the hierarchy of the cascades should help to improve policy intervention and implement rescue strategy.
In this paper, we propose a neural network-based method for CVA computations of a portfolio of derivatives. In particular, we focus on portfolios consisting of a combination of derivatives, with and without true optionality, textit{e.g.,} a portfolio of a mix of European- and Bermudan-type derivatives. CVA is computed, with and without netting, for different levels of WWR and for different levels of credit quality of the counterparty. We show that the CVA is overestimated with up to 25% by using the standard procedure of not adjusting the exercise strategy for the default-risk of the counterparty. For the Expected Shortfall of the CVA dynamics, the overestimation was found to be more than 100% in some non-extreme cases.
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