Assessing interbank contagion using simulated networks

This paper presents a new approach to randomly generate interbank networks while overcoming shortcomings in the availability of bank-by-bank bilateral exposures. Our model can be used to simulate and assess interbank contagion effects on banking sector soundness and resilience. We find a strongly non-linear pattern across the distribution of simulated networks, whereby only for a small percentage of networks the impact of interbank contagion will substantially reducoe average solvency of the system. In the vast majority of the simulated networks the system-wide contagion effects are largely negligible. The approach furthermore enables to form a view about the most systemic banks in the system in terms of the banks whose failure would have the most detrimental contagion effects on the system as a whole. Finally, as the simulation of the network structures is computationally very costly, we also propose a simplified measure—a so-called Systemic Probability Index—that also captures the likelihood of contagion from the failure of a given bank to honour its interbank payment obligations but at the same time is less costly to compute. We find that the SPI is broadly consistent with the results from the simulated network structures.     

Sensitivity analysis of the Eisenberg-Noe model of contagion

We use linear programming to provide a sensitivity analysis of Eisenberg and Noe’s one-period model of contagion via direct bilateral links. We provide a formula for the sensitivities of clearing payments and the terminal wealth of each node to initial wealth of each node.     

On spatial contagion and multivariate GARCH models

We propose a method for defining and measuring spatial contagion between two financial markets via conditional copulas. Some theoretical results on monotonicity and asymptotic properties of Gaussian copulas with respect to conditioning are presented. Next, we combine the spatial contagion approach with time series models. We investigate which model from a large family of multivariate GARCH is the best tool for modelling spatial contagion. In an empirical study, we show that among models designed for general fit, a two‐step model fitting procedure reduces the ability to describe the contagion effect. This is a feature of copula‐GARCH models. Copyright © 2013 John Wiley & Sons, Ltd.     

A contagion model with Markov regime-switching intensities

We consider a two-dimensional reduced form contagion model with regime-switching interacting default intensities. The model assumes the intensities of the default times are driven by macro-economy described by a homogeneous Markov chain as well as the other default. By using the idea of ＇change of measure＇ and some closed-form formulas for the Laplace transforms of the integrated intensity processes, we derive the two-dimensional conditional and unconditional joint distributions of the default times. Based on these results, we give the explicit formulas for the fair spreads of the first-to-default and second-to-default credit default swaps （CDSs） on two underlyings.     

Optimal advertising policy with the contagion model

This paper considers an optimal control problem for the dynamics of a contagion model, the optimal control being the rate of advertising expenditure that maximizes the present value of net profit streams over an infinite horizon. By using a Green's theorem approach, it is shown that there are multiple optimal stationary equilibria and that the optimal path from any given initial condition is a nearest feasible path to one of these equilibria.This work was partially supported by the National Research Council of Canada, Grant No. A4619.     

Credit contagion in a network of firms with spatial interaction

This contribution studies the effects of credit contagion on the credit risk of a portfolio of bank loans. To this aim we introduce a model that takes into account the counterparty risk in a network of interdependent firms that describes the presence of business relations among different firms. The location of the firms is simulated with probabilities computed using an entropy spatial interaction model. By means of a wide simulation analysis we investigate the behavior of the model proposed and study the effects of default contagion on the loss distribution of a portfolio of bank loans.     

Markov regime-switching quantile regression models and financial contagion detection

In this paper, we propose a Markov regime-switching quantile regression model, which considers the case where there may exist equilibria jumps in quantile regression. The parameters are estimated by the maximum likelihood estimation (MLE) method. A simulation study of this new model is conducted covering many scenarios. The simulation results show that the MLE method is efficient in estimating the model parameters. An empirical analysis is also provided, which focuses on the detection of financial crisis contagion between United States and some European Union countries during the period of sub-prime crisis from the angle of financial risk. The degree of financial contagion between markets is subsequently measured by utilizing the quantile regression coefficients. The empirical results show that in a crisis situation, the interdependence between United States and European Union countries dramatically increases.     

Optimal reinsurance-investment strategy for a dynamic contagion claim model

We study the optimal reinsurance-investment problem for the compound dynamic contagion process introduced by Dassios and Zhao (2011). This model allows for self-exciting and externally-exciting clustering effect for the claim arrivals, and includes the well-known Cox process with shot noise intensity and the Hawkes process as special cases. For tractability, we assume that the insurer’s risk preference is the time-consistent mean–variance criterion. By utilizing the dynamic programming and extended HJB equation approach, a closed-form expression is obtained for the equilibrium reinsurance-investment strategy. An excess-of-loss reinsurance type is shown to be optimal even in the presence of self-exciting and externally-exciting contagion claims, and the strategy depends on both the claim size and claim arrivals assumptions. Further, we show that the self-exciting effect is of a more dangerous nature than the externally-exciting effect as the former requires more risk management controls than the latter. In addition, we find that the reinsurance strategy does not always become more conservative (i.e., transferring more risk to the reinsurer) when the claim arrivals are contagious. Indeed, the insurer can be better off retaining more risk if the claim severity is relatively light-tailed.     

The loss given default of a low-default portfolio with weak contagion

In this paper we study the loss given default (LGD) of a low default portfolio (LDP), assuming that there is weak credit contagion among the obligors. We characterize the credit contagion by a Sarmanov dependence structure of the risk factors that drive the obligors’ default, where the risk factors are assumed to be heavy tailed. From a new perspective of asymptotic analysis, we derive a limiting distribution for the LGD. As a consequence, an approximation for the entire distribution, in contrast to just the tail behavior, of the LGD is obtained. We show numerical examples to demonstrate the limiting distribution. We also discuss possible applications of the limiting distribution to the calculation of moments and the Value at Risk (VaR) of the LGD.     

Measuring bank contagion in Europe using binary spatial regression models

The recent European sovereign debt crisis clearly illustrates the importance of measuring the contagion effects of bank failures. Indeed, to better understand and monitor contagion risk, the European Central Bank has assumed the supervision of the largest banks in each of the member states. We propose a measure of contagion risk based on the spatial autocorrelation parameter of a binary spatial autoregressive model. Using different specifications of the interbank connectivity matrix, we estimate the contagion parameter for banks within the Eurozone, between 1996 and 2012. We provide evidence of high levels of systemic risk due to contagion during the European sovereign debt crisis.     

Financial contagion: extending the exposures network of the Mexican financial system

Direct contagion has been widely studied in recent years and little evidence has been found to be relevant to the study of systemic risk. However, we argue that this limited contagion effect might be associated with a lack of relevant data. A common assumption for the estimation of the matrices of exposures is to apply the maximum entropy principle to deal with data gaps; such an assumption might lead to an underestimation of contagion risk. In this paper, there are no data gaps and the information set is extended from interbank exposures alone to exposures among most of the financial intermediaries in the Mexican financial system (we even include exposures to some international foreign banks). Naturally, the contagion risk of an extended network of exposures changes with respect to the interbank exposures network, as there are many more institutions which can be the source of contagion and there are more institutions which can fail due to contagion. The most important contribution of this paper is that it provides evidence on financial contagion with an extended exposures network under stressful conditions. The results presented here support the international efforts by the Bank for International Settlements, the International Monetary Fund and the Financial Stability Board to increase the amount of information available which can be used to assess systemic risk and contagion based on exposures and funding data.     

马氏调制强度的传染模型下CDS的CVA计算

本文考虑了具有马氏调制强度的传染模型下,信用违约互换(CDS)的双边信用估值调整(CVA).在我们考虑的模型中,利率、回收率以及CDS的买方、卖方和参照实体三方的违约强度均受宏观经济环境的影响,该经济状况由一连续时间状态的齐次马氏链所刻画.利用测度变换和累积强度的Laplace变换,我们给出了CDS合同的双边CVA的表达公式,该公式可以表示为线性常微分方程组的基本解的形式.利用所得到的公式,我们数值分析了马氏调制和违约相关性对双边CVA的影响.     

突发公共卫生事件对系统性金融风险的冲击及传染效应研究

首先基于面板向量自回归模型考察了突发公共卫生事件对系统性金融风险的冲击影响,接着综合考虑突发公共卫生事件的影响及其所导致的收益率的非对称性构建单指标非对称CoVaR模型,最后借助LASSO惩罚函数与局部估计法进行求解,以此构建有向网络分析金融机构间的传染效应.研究发现:(1)突发公共卫生事件冲击会使系统性金融风险水平短...     

A reduced-form model with default intensities containing contagion and regime-switching Vasicek processes

The contagion credit risk model is used to describe the contagion effect among different financial institutions. Under such a model, the default intensities are driven not only by the common risk factors, but also by the defaults of other considered firms. In this paper, we consider a two-dimensional credit risk model with contagion and regime-switching. We assume that the default intensity of one firm will jump when the other firm defaults and that the intensity is controlled by a Vasicek model with the coefficients allowed to switch in different regimes before the default of other firm. By changing measure, we derive the marginal distributions and the joint distribution for default times. We obtain some closed form results for pricing the fair spreads of the first and the second to default credit default swaps (CDSs). Numerical results are presented to show the impacts of the model parameters on the fair spreads.     

Measuring the subprime crisis contagion: Evidence of change point analysis of copula functions

In this paper, we first determine the existence of structural changes in the dependence between time series of equity index returns of two markets using the change point testing method. The method is based on Archimedean copula functions, which are able to comprehensively describe dependence characteristics of random variables. The degree of financial contagion between markets is subsequently estimated using the tail dependence coefficient of copula functions before and after the change point. We empirically test our method by investigating financial contagion during the subprime crisis between the US S&P 500 index and five Asian markets, namely China, Japan, Korea, Hong Kong and Taiwan. Our results show that a statistically significant change point exists in the dependence between the US market and all Asian stock markets except Taiwan. The upper tail dependence is larger after the time of change, implying the existence of contagion during the banking crisis between the US and the Asian economies. The degree of financial contagion is also estimated and found to be consistent with market events and media reports during that period.     

Spatial contagion between financial markets: a copula‐based approach

A method is proposed for defining and investigating spatial contagion between two financial markets X and Y by using the information contained in their copula. A practical illustration of the introduced method is also given by examining the presence of contagion among two European stock indices (namely, FTSE 100 and DAX). Copyright © 2009 John Wiley & Sons, Ltd.     

Spin Models of Index 2 and Hadamard Models

A spin model (for link invariants) is a square matrix W with non-zero complex entries which satisfies certain axioms. Recently it was shown that ^t WW ^–1 is a permutation matrix (the order of this permutation matrix is called the index of W), and a general form was given for spin models of index 2. Moreover, new spin models, called non-symmetric Hadamard models, were constructed. In the present paper, we classify certain spin models of index 2, including non-symmetric Hadamard models.     

Models of hysteresis

The concept ofhysteresis operator is introduced. Existence of a solution is proven for a parabolic differential equation containing a hysteresis operator. A collection of references of mathematical papers on hysteresis is also provided.     

Stochastic contagion models without immunity: their long term behaviour and the optimal level of treatment

In this paper we analyze two stochastic versions of one of the simplest classes of contagion models, namely so-called SIS models. Several formulations of such models, based on stochastic differential equations, have been recently discussed in literature, mainly with a focus on the existence and uniqueness of stationary distributions. With applicability in view, the present paper uses the Fokker–Planck equations related to SIS stochastic differential equations, not only in order to derive basic facts, but also to derive explicit expressions for stationary densities and further characteristics related to the asymptotic behaviour. Two types of models are analyzed here: The first one is a version of the SIS model with external parameter noise and saturated incidence. The second one is based on the Kramers–Moyal approximation of the simple SIS Markov chain model, which leads to a model with scaled additive noise. In both cases we analyze the asymptotic behaviour, which leads to limiting stationary distributions in the first case and limiting quasistationary distributions in the second case. Finally, we use the derived properties for analyzing the decision problem of choosing the cost-optimal level of treatment intensity.