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This paper reports the effect of the change in the credit status of debtors on investors as a result of the banks’ transferring of credit risk to investors in the credit risk transfer (CRT) market. Thus, an entropy spatial model is introduced, in which the spatial distance and nonlinear coupling between the banks and the investors, the transfer ability of credit risk of banks, and investor appetite for risk in the CRT network are considered. The contagion effects of the credit default of debtor on the default rates of investors in the CRT market are investigated using numerical simulation and sensitivity analysis.

The recent subprime credit crisis motivates the development of models in which credit risk contagion has repercussions on other investors in the financial market, particularly the credit risk transfer (CRT) market. The effects of the credit risk contagion induced by the credit default of a debtor on the credit risk of investors in the CRT market are therefore evaluated.

Different approaches have been proposed to analyze the credit risk contagion. Davis and Lo [

A number of recent studies have considered the credit risk contagion of the CRT market. Haworth and Reisinger [

Entropy has been widely applied in the study of spatial interaction theory as the uncertainty measurement of the system to form the entropy spatial interaction theory. Entropy spatial interaction models can disperse the agents from an origin to all destinations, instead of assigning all agents to the nearest one. Moreover, entropy models can be obtained as an optimal solution of a mathematical programming problem such that the dispersion of the origin-destination flows is maximized by maximizing the entropy of the system [

In this paper, several contributions to the study of credit risk contagion in the CRT network are reported. First, a new model of credit risk transfer is proposed, in which the spatial distance and the nonlinear coupling between banks and investors, the transfer ability of credit risk of banks, and investor appetite for risk in the CRT network are considered. This model mainly analyzes the liquidity ratios of credit risk through credit risk transfer from banks to investors. Second, a value contagion model of discrete time of a multiname credit derivative is built based on Basso and Barro [

The paper is structured as follows. Entropy spatial models of credit risk transfer and contagion in the CRT network are discussed in Sections

A model of credit risk transfer is introduced. This model considers the spatial distance and the nonlinear coupling between the banks and investors, transfer ability of credit risk of the banks, and investor appetite for risk in the CRT network. Spatial transfer of credit risk is characterized by an entropy spatial interaction model. The CRT network is assumed to be a tiered structure network with multi-origin-destination (e.g., Figure

A tiered structure network of credit risk transfer with multi-origin-destination in CRT market.

The notations used in this paper are summarized as follows:

In addition, the locations of banks and investors are assumed to be homogeneous. This condition will reduce the complexity and difficulty of the present study and promote understanding the effect mechanism of the spatial distance between bank

According to O’Kelly [

According to the above hypothesis and (

That is,

For the impedance function

Equation (

Therefore, the new impedance function

The model defined using (

In the proposed model (

In the CRT market, banks optimize and reorganize credit risks that are formed by the debtors and then transfer them to investors through the form of credit derivatives. This behavior reduces the financing cost and risk concentration, satisfies the regulatory capital requirements, and maximizes the banks’ own interests. If the credit status of the debtors changes or the debtors credit defaults, the value of credit derivatives that are associated with the debtors fluctuates and affects banks and investors. Moreover, when the loss rate caused by the fluctuation of the value of credit derivatives is greater than the given threshold value

In this paper, the effects of the credit status of the debtors on investors of the CRT market are primarily discussed. To describe the contagion effect of credit risk, a value contagion model of discrete time based on the discrete time is introduced on the basis of the discrete time model proposed by Basso and Barro [

Only the credit defaults of the major debtors are considered in (

The effect of the past credit defaults of the debtors included in the credit derivatives is interred to long-term memory characteristic on the current credit risk of banks, and the effect of long-term memory is assumed to present an exponential decay in time as an influence of the past credit default [

That is,

Equation (

That is,

In the absence of a large number of time series data of an empirical test, numerical simulation analysis is the most effective testing method. Thus, numerical simulation analysis that considers the different values of the parameters in the entropy spatial model is performed. The credit derivatives that are mainly constituted by the credit loans of medium-sized and small enterprises are considered. Let the number of banks

In Figure

Effect of spatial distance on credit risk contagion in the CRT network with different values of

Effect of the concentration of credit risk of investor

In this paper, an entropy spatial model of credit risk contagion that considers the effect of the change in the credit status of the debtors on investors as a result of the transfer of credit risk by banks to investor in the CRT market. The effects of the spatial distance and nonlinear coupling between banks and investors, ability of bank to credit risk transfer credit risk, concentration of credit risk of investor, and appetite for risk of investors on credit risk contagion are discussed. Moreover, we found that credit risk contagion exhibits significant spatial distance effect and inhibitory effect on the correlation between banks and investors in the CRT network through numerical simulations and the sensitivity analysis.

However, the present studies may also be applied in other areas such as the inhomogeneity of the different geographical areas, banks, and investors and the interactivity of credit risk contagion.

There is no conflict of interests regarding the publication of this paper.

The authors wish to express their gratitude to the referees for their invaluable comments. This work was supported by the National Natural Science Foundation of China (nos. 70932003 and 71301078), China Postdoctoral Science Foundation (2014M561626), and the Philosophy and Social Sciences Research Funded Projects in Colleges and Universities of Jiangsu (2014SJB081).