- 200 - 978-1-4673-3014-5/12/$31.00 ©2012 IEEE

Study on Credit Risk Contagion Model Based on Filter Theory

YIN Qun-yao1，CHEN Ting-qiang1，HE Jian-min 1，WU Ya-li1,2 1 School of Economics and Management, Southeast University, P.R.China, 211189

2 China Construction Bank Branch in Jiangsu Province, P.R.China, 210012

Abstract: By using filter theory, we propose a credit risk contagion model with the features of credit default sequence, the structure of probability density of credit default time and the distribution function of company’s conditional survival probability. By introducing a two-dimensional Gumbel Copula function, we carry out simulation experiment and comparative analysis of the influencing factor of the company’s conditional survival probability distribution. We find that the impact of the sequentiality, correlation and intensity of credit defaults on the contagion effect of credit risk and the company’s survival probability is significant.

Keywords: credit risk contagion model, conditional survival probability, Gumbel Copula functions, simulation experiment 1 Introduction

Credit risk, defined as the degree of value fluctuations in debt instruments and derivatives due to the changes in the underlying credit quality of borrowers and counterparties, is a complicated and important issue for financial institutions especially for banking sectors. After some financial crises, where the downfall of a small number of firms had an economy-wide impact, such as Asian financial crisis and US Subprime Mortgage crisis, the contagion effect of credit risk has attracted widely attentions from financial institutions and regulatory departments. The earliest literature about the credit risk contagion may date back to the work of Davis et al. (2000; 2001), who present that the result of one debtor’s default can easily result in the default intensities of other debtor's rise. Recently, there has been a flurry of developments in the field of credit risk contagion modeling; most of them are based on the reduced-form models. A number of literatures consider intercompany credit risk contagion by generalizing existing reduced-form models. Jarrow and Yu (2001) present a reduced-form model that jointly describes defaultable

Supported by the National Natural Science Foundation of China (71071034), the National Basic Research Program of China (973 Program, 2010CB328104-02), and Funding of Jiangsu Innovation Program for Graduate Education (CXZZ12_0134, 0131).

bonds issued by many firms, where a counterparty relationship among these firms could affect their default probabilities. Frey and Backhaus (2003) consider intensity-based dynamic models for dependent defaults using Markov process techniques. The previous literatures all constructed models depending on the information in the underlying filtration with the property that credit default time must be totally inaccessible (Cetin and Jarrow, 2004; Elliott et al. 2000; Giesecke, 2004, 2006; Jarrow and Protter, 2004), and they all implied that credit default times be ordered. Both Giesecke (2003) and El Karoui et al. (2010) have proved the effectiveness of the analysis of ordered default times in defaultable bonds. However, Schönbucher (2003) and Collin-Dufresne (2010) show the highly correlation between the information-based default contagion and the highly misleading conclusions, which induced by using the analysis of ordered default times, that is, one firm’s default affecting beliefs about defaults of other firms and inducing jump in default intensity consequently. Kchia and Larsson (2011) extend reduced-form and filtration expansion framework in credit risk to the case of multiple, non-ordered defaults, and find that the effect is significant in the context of risk management.

The existing models of credit default intensity cannot reflect the companies’ risk characteristics, inter-company correlation, the impact of the market information on the company’s credit default risk and its contagion. Based on the filter theory and the theoretical research of credit risk contagion, we construct a credit risk contagion model with the features of credit default sequence, the structure of probability density of credit default time and the conditional survival probability distribution function. Through simulation experiment, we make comparative analysis of the impact of the sequentiality, correlation and intensity of credit defaults on the contagion effect of credit risk and the company’s survival probability.

The rest of the paper proceeds as follows. Section 2 develops a credit default intensity model of two firms and investigates their conditional survival probability distribution. Section 3 carries out simulation experiment and comparative analysis of the influencing factor of the conditional survival probability distribution. Section 4 contains concluding remarks.

2012 International Conference on Management Science & Engineering (19th) September 20-22, 2012 Dallas, USA

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2 The model Let the uncertainty in the economy on time interval

[0, T*] be described by the filtered probability space *0( , , , )T

t t =Ω 0 0 , where *T=0 0 ， *0 T

t t =0 is a filtration based on 0 and is an equivalent martingale measure under which discounted bond prices are martingales. We assume the existence and uniqueness of , so that bond markets are complete and priced by arbitrage, as shown in discrete time by Harrison and Kreps (1979) and in continuous time by Harrison and Pliska (1981). 2.1 The credit default intensity model

In this section, we focus on the impact of the sequentiality of credit default times on the contagion effect of credit risk in economical system. First, let iτ denote the default time of firm i ( 1,2i = ), respectively. According to literatures Jeanblanc et al. (2009) and El Karoui et al. (2010), we assume the existence of the density 1 2( , )tf θ θ conditional on the filtration t0 , generated by the credit default times, that is, for θ +∈ , we have

1 2 1 2 1 1 2 2( , ) ( , )t tf d d d dθ θ θ θ τ θ τ θ= ∈ ∈ 0

Suppose 1 2= ( , )t uu t

G u uσ τ τ>

∨ ∧ ∧10 , then the filtration

0=( )t tG ≥ is generated jointly by 0 and the trivial σ − field of 1τ and 2τ . According to Doob−Meyer decomposition, for given filtration , there exist a continuous credit default intensity process tλ , which

makes 01

t

t sdsτ

τ λ∧

≤ − ∫ uniformly ( , ) -martingale

integral, where 0t ≥ , -stopped time τ denotes credit default time and 1 tτ ≤ is characteristic function of credit default with the value 1 1tτ ≤ = , if the event of credit default has happened before time t , otherwise,

1 0tτ ≤ = . Actually, 0 01

t t

s s sds dsτ

τλ λ∧

>=∫ ∫ is the

compensator of the credit default function. Based on the reduced-form model and the Cox process, it is well-known that, given the filtration 0=( )t tG ≥ ,

0inf :

t

st ds Eτ λ= ≥∫ , where E is unit exponential

random variable and independent of the common economic state variables. So, τ is the stopped time accompanied with the intensity tλ of credit default.

To firm i ( 1,2i = ), its process of credit default intensity satisfies the algebraic form a-s follow:

2 2

2 21 2

1 2 2 1 1 2 1

( , ) ( , )1 1

( , ) ( , )

tt tt t t

t tt t t

f t d f t

f d d f dτ τ

θ θ τλ

θ θ θ θ θ τ θ

∞

< ≥∞ ∞ ∞= +∫∫ ∫ ∫

(1)

1 1

1 12 1

1 2 1 2 1 2 2

( , ) ( , )1 1

( , ) ( , )

tt tt t t

t tt t t

f t d f t

f d d f dτ τ

θ θ τλ

θ θ θ θ τ θ θ

∞

< ≥∞ ∞ ∞= +∫∫ ∫ ∫

(2)

Equation (1) and (2) describe how some firm’s default to impact on other local firms, the-y are the typical model of information-driven credit risk contagion. Indeed, the two equations reveal that the first firm’s default affecting beliefs about default of the second firm indirectly and triggering contagion spread consequently. Proposition: For given equations (1) and (2), the process of credit default intensity satisfies

2

2 2

2

21

2

( , )( , )1 1

( , ) ( , )t tt t

t t tt t

F tF t tF t t F t

ττ τ

τ

τλ

τ< ≥

∂ ∂−∂= +

−∂ (3)

2

2 2

2

21

2

( , )( , )1 1

( , ) ( , )t tt t

t t tt t

F tF t tF t t F t

ττ τ

τ

τλ

τ< ≥

∂ ∂−∂= +

−∂ (4)

Proof: According to literatures (El Karoui et al. 2010; Kchia et al. 2011), with the assumption that the existence of the density 1 2( , )tf θ θ conditional on the filtration t0 , generated by the credit default times, for Martingale process of random variables

1 2 1 2, ( , )dθ θ θ θ +∈ , we have the following joint distributions of pairs of default times 1τ and 2τ

1 2 1 1 2 2( , ) ( , )t tF Fθ θ τ θ τ θ= > > 0 Note that

1 21 1 2 2 1 2 2 1( , ) ( , )t tF f x x dx dx

θ θτ θ τ θ

∞ ∞> > = ∫ ∫0

Then，we have

1 21 2 1 1 2 2 1 2 2 1( , ) ( , ) ( , )t t tF F f x x dx dx

θ θθ θ τ θ τ θ

∞ ∞= > > = ∫ ∫0 .

With equations (1) and (2), it is then simple to acquire the conclusions. Q.E.D.

The proposition gives out the model of structure of probability distribution of credit default intensity. Through the structure of probability distribution, we describe the impact of the effect of information-driven credit default and the characteristic of company’s credit risk on the intensity of credit default more clearly, and we also acquire a more effective tool to study the effect of information-driven credit risk contagion.

2.2 The conditional survival probability distribution

Already known of the credit default intensity model with two companies, it will be a key element of the study of credit risk contagion that inspection of status of company survival in the context of credit risk contagion. Let 1 1 2ς τ τ= ∧ , 2 1 2ς τ τ= ∨ , there is no more than one event of credit default happening at time T ( [0 *]T T∈ , ). For the credit default events

1 2 t tτ τ> ∩ ≤ and 1 2 t tτ τ≤ ∩ > , they are non-ordered related to the given filtration 0=( )t tG ≥ . In order to capture the impact of ordered credit default times and non- ordered credit default times on the company’s survival probability, we define a new filtration 0=( )t tG ≥

, which is generated by the credit time 1 2( , )ς ς considered in filtration , where

1 2( , )t uu t

G u uσ ς ς>

= ∨ ∧ ∧ 10 . Obviously, we have

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⊂ . According to the filter theory, the credit default events 1 tς > and 1 2 t tτ τ> ∩ > are equivalent, and that, from the filtration tG perspective, the union set of the credit default events 1 2 t tτ τ> ∩ ≤ and

1 2 t tτ τ≤ ∩ > is 1 2tς ς≤ < , that is, the credit default event 1 2tς ς≤ < is ordered uniquely under the filtration tG . Theorem 1: For given time T , filtration 0=( )t tG ≥ and 1 1 2ς τ τ= ∧ , 2 1 2ς τ τ= ∨ , then, at time t ( 0 t T≤ ≤ ), the company’s conditional survival probability distribution is

2 1

1 2 1 2 1 2

2 1

2

2 1

2 1

( | )( , ) ( , )( , ) ( , ) ( , )

1 1 1( , ) ( , ) ( , )

t

t tt t tt t t t t t

t t t

T GF T F TF T t F t T F T T

F t t F t F tτ τ

τ τ τ τ τ ττ τ

ςτ ττ τ> ∩ > > ∩ ≤ ≤ ∩ >

>∂ ∂+ +

= + +∂ ∂

(5)

Proof: According to the assumptions above, then, the company’s conditional survival probability distribution affected by credit risk contagion at time t ( 0 t T≤ ≤ ) is

2 1 2 1 2 1 2( ) ( , ) ( , ) ( , )t t t tT G T T G T T G T T Gς τ τ τ τ τ τ> = > > + > ≤ + ≤ > By literatures (Harrison et al. 1979; Giesecke, 2003; El Karoui et al. 2010) and the formula of conditional probability, we have

1 2

1 2

1 2

1 2 2 1 1 2 2 1 1 2 2 1

1 2 2 1

( , | )

( , ) ( , ) ( , )1

( , )

( , ) ( , ) ( , )1

( , )

t

t t tT t t T T Tt t

tt t

t t tt t

t

T T G

f d d f d d f d d

f d d

F T t F t T F t tF t t

τ τ

τ τ

τ τ

θ θ θ θ θ θ θ θ θ θ θ θ

θ θ θ θ

∞ ∞ ∞ ∞ ∞ ∞

> ∩ >∞ ∞

> ∩ >

> >

+ +=

+ +=

∫ ∫ ∫ ∫ ∫ ∫∫ ∫

2 2

1 2 1 2

22

2 2 21 2

22 2

( , ) ( , )( , ) 1 1

( , )( , )

t tt t t t t

tt

f T d F TT T G

F tf t dτ τ

τ τ τ ττ

τ

θ θ ττ τ

τθ θ

∞

> ∩ ≤ > ∩ >∞

∂> ≤ = =

∂∫∫

1 1

1 2 1 2

11

1 1 11 2

11 1

( , ) ( , )( , ) 1 1

( , )( , )

t tt t t t t

tt

f T d F TT T G

F tf t dτ τ

τ τ τ ττ

τ

θ θ ττ τ

τθ θ

∞

≤ ∩ > ≤ ∩ >∞

∂≤ > = =

∂∫∫

This ends the Proof of Theorem 1. Lemma: Suppose that 1 2 1 1 2 2( , ) ( , )t tFθ θ ς θ ς θ= > > 0 , then, for 1 2φ θ θ= ∨ , we have

1 2 1 1( , ) ( , ) ( , ) ( , )t t t tF F Fθ θ θ φ φ θ φ φ= + − Proof: Let’s assume 1 2θ θ≤ , then we have

1 1 2 2 2 1 1 1 2 2

1 1 1 2 2 1 2 2

( , | ) ( , | )( , ) ( , ) ( , ) ( , )

t t

t t t t

F FF F F F

ζ θ ζ θ θ τ θ θ τ θθ θ θ θ θ θ θ θ

> ≤ = ≥ > < ≤= − − +

0 0

and we also have 1 1 1 1( ) ( , )t tF Fς θ θ θ> =0

Then

1 2 1 1 1 1 2 2

1 1 1 1 1 1

1 1

( , ) ( ) ( , )( , ) [ ( , ) ( , ) ( , ) ( , )]( , ) ( , ) ( , )

t t t

t t t t t

t t t

F FF F F F FF F F

θ θ ς θ ς θ ς θ

θ θ θ θ θ φ φ θ φ φθ φ φ θ φ φ

= > − > ≤

= − − − += + −

0 0

Q.E.D. Theorem 2: For given time T , filtration 0=( )t tG ≥

and

1 1 2ς τ τ= ∧ , 2 1 2ς τ τ= ∨ , then, at time t ( 0 t T≤ ≤ ), the company’s conditional survival probability distribution is

1 1

1 1 2

1 1

1 12

1 1

( , ) ( , )( , ) ( , ) ( , )( | ) 1 1

( , ) ( , ) ( , )t tt t t

t t tt t t

F T F TF T t F t T F T TT G

F t t F t F tς ς

ς ς ςς ς

ς ςς

ς ς> ≤ <

∂ + ∂+ +> = +

∂ + ∂

(6) Proof: Using Theorem 1 and the filter theory, also

substituting 1 2( , )τ τ with 1 2( , )ς ς , then simplified, we can get

1

1 1 2

1

12

1

( , )( , ) ( , ) ( , )( ) 1 1

( , ) ( , )t t t

t t t tt

TF T t F t T F T TT G

F t t tς

ς ς ςς

ςς

ς> ≤ ∩ <

∂+ +> = +

∂

By the Lemma, we have 1 1 1( , ) ( , ) ( , ) ( , )t t tT F T F T F T Tς ς ς= + −

and 1 1 1( , ) ( , ) ( , ) ( , )t t tt F t F t F t tς ς ς= + −

This ends the Proof of Theorem 2. 2.3 Commentary

For many documents of the credit risk of contagion, that investigating the companies’ survival probability distribution in the process of the contagion of credit risk tends to reduce the complexity of the real problem, and is quite different from the results which considered the complex market information and the credit default sequentiality. In fact, with constant innovation and development of the IT and financial instruments, credit risk management also gradually requires as much consideration as possible in which the local environment and the conditions of the specific market information, the contagion effect of credit default risk on the companies’ probability of survival and viability.

For the given filtration 0=( )t tG ≥ , Theorem 1 describes the effect of a company's credit default on the probability of survival of the other companies, by the credit default events 1 2 t tτ τ> ∩ ≤ and

1 2 t tτ τ≤ ∩ > . It is also more fully considered the company’s survival probability disorder of the impact of the credit event market environment information reflects the company's conditions of the survival probability distribution with the observed credit default sequentiality and credit default company's own characteristics are closely related.

For the given filtration , Theorem 2 gives out the distribution function of the company’s survival probability, which reveals the impact of ordering of the credit events and market information , on survival conditions and the viability.

Therefore, the two theorems describe the impact of the sequentiality of credit defaults on the company’s survival probability based on filtrations and , respectively. 3 Numerical simulations

To illustrate our results, we calibrate the model and

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simulate it numerically. In this section, we carry out simulation experiment and comparative analysis of the impact of the feature of credit default sequence and credit default intensity on the probability of survival of the two companies in the case that the two companies are positively related.

Let both of the credit default time 1 2( , )τ τ follow exponential marginal distribution with parameters 1λ and 2λ respectively. First, we introduce a two- dimensional Gumbel Copula function (Wei and Zhang, 2008), by which we joint the two marginal distributions of the credit default time 1 2( , )τ τ , and then we structure joint distributions of the credit default time 1 2( , )τ τ as follow,

1 1 2 21 2 1 1 2 2( , ) ( , ) ( , )t C e eλ θ λ θ

ρθ θ τ θ τ θ − −= ≤ ≤ = 0 (7)

Where, 1 1

[( ln ) ( ln ) ]( , ) x yC x y eρρ ρ

ρ− − + −= is a two-dimensional

Archimedean Copula Function, ρ is the correlation coefficient of the credit defaults and (0,1]ρ ∈ . While 1ρ = , random variables 1θ and 2θ are independent, and while 0ρ → , random variables 1θ and 2θ tend to be completely correlation.

Partially differentiating equation (7) with respect to 1θ and 2θ yield

1 11 1 1

1 1 2 2

1

1 [( ) ( ) ]( 1)1 2 1 1 1 1 1 2 2( , ) ( ) [( ) ( ) ] e

ρρ ρρ ρ ρ λ θ λ θρ

θ θ θ λ λ θ λ θ λ θ− − +−∂ = − +

and

1 11 1 1

1 1 2 2

2

1 [( ) ( ) ]( 1)1 2 2 2 2 1 1 2 2( , ) ( ) [( ) ( ) ] e

ρρ ρρ ρ ρ λ θ λ θρ

θ θ θ λ λ θ λ θ λ θ− − +−∂ = − + .

Let 1T = and 0.5t = through the whole simulation experiment. According to Theorem 1 and Theorem 2, also from the perspective of filtrations and , it is only the credit default event

1 2 t tς ς≤ ∩ > that has the impact of disturbance on company’s conditional survival probability distributions during the process of credit risk contagion. So, when simulating and making comparative analysis, we only consider these terms in 2( )tT Gς > and

2( )tT Gς > which containing the credit default event

1 2 t tς ς≤ ∩ > . It is seen based on the preceding analysis that the credit default events 1 2 t tτ τ> ∩ ≤ and 1 2 t tτ τ≤ ∩ > are non-ordered based on filtration , but based on filtration , the credit default event 1 2 t tς ς≤ ∩ > is ordered uniquely. However, by simulation experiment, not only to investigate the impact of the sequentiality of credit default on the company's survival conditions, but we also want to examine the impact of credit defaults on the probability of survival of the company. Therefore, under the established conditions and assumptions, we examine the impact of the correlation of credit defaults, which is shown in Figs. 1 and 2; and then examine the impact of credit default intensity which is shown in Figs. 3 and 4, on the conditional probability of survival of the company's.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.78

0.8

0.82

0.84

0.86

0.88

0.9

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0.35

0.4

0.45

0.5

0.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

λ1=0.1，λ2=0.2，ρ=0.2 λ1=0.1，λ2=0.2，ρ=0.4 λ1=0.1，λ2=0.2，ρ=0.6 λ1=0.1，λ2=0.2，ρ=0.8

Fig.1 Impact of the correlation between credit defaults on company’s survival probability

based on ordered credit default times

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0.76

0.77

0.78

0.79

0.8

0.81

0.82

0.83

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0.05

0.055

0.06

0.065

0.07

0.075

0.08

0.085

0.09

0.095

0.1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0.3

0.32

0.34

0.36

0.38

0.4

0.42

0.44

0.46

0.48

0.5

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0.56

0.58

0.6

0.62

0.64

0.66

0.68

0.7λ1=0.1，λ2=0.2，ρ=0.4λ1=0.1，λ2=0.2，ρ=0.2 λ1=0.1，λ2=0.2，ρ=0.6 λ1=0.1，λ2=0.2，ρ=0.8

Fig.2 Impact of the correlation between credit defaults on company’s survival probability based on non-ordered credit default times

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0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0.45

0.5

0.55

0.6

0.65

0.7

0.75

0.8

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0.45

0.5

0.55

0.6

0.65

0.7

0.75

0.8

0.85

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0.45

0.5

0.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0.45

0.5

0.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

λ1=0.1，λ2=0.1，ρ=0.5 λ1=0.1，λ2=0.2，ρ=0.5 λ1=0.1，λ2=0.3，ρ=0.5 λ1=0.1，λ2=0.5，ρ=0.5

Fig.3 Impact of the intensity of credit default on company’s survival probability

based on ordered credit default times

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0.45

0.5

0.55

0.6

0.65

0.7

0.75

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0.44

0.46

0.48

0.5

0.52

0.54

0.56

0.58

0.6

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0.43

0.44

0.45

0.46

0.47

0.48

0.49

0.5

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0.39

0.395

0.4

0.405

0.41

0.415

0.42λ1=0.1，λ2=0.2，ρ=0.5λ1=0.1，λ2=0.1，ρ=0.5 λ1=0.1，λ2=0.3，ρ=0.5 λ1=0.1，λ2=0.5，ρ=0.5

Fig.4 Impact of the intensity of credit default on company’s survival probability

based on non-ordered credit default times

Figs. 1 and 2 illustrate the impact of the ordering of credit default times and the correlation between credit defaults on the company’s survival probability. Based on the ordered event of the credit defaults, 1 2 t tς ς≤ ∩ > , Fig. 1 depicts the impact of the correlation coefficient of the credit defaults ρ on the company’s survival probability. The simulation shows that the impact of the parameter ρ on the company’s survival probability has tail characteristics obviously, with the correlation between credit defaults lower, company’s survival environment get of the credit defaults better and the survival probability gradually increased. To contrast based on the non-ordered events 1 2 t tτ τ> ∩ ≤ and

1 2 t tτ τ≤ ∩ > , Fig. 2 shows that with the parameter ρ changing, the impact of ρ on the company’s survival probability increased significantly, and the tail characteristics reflected more obvious than in the case of ordered credit defaults event. So, the results of simulation illustrate that the effect of the order of occurrence of the credit default events and the correlation coefficient of the credit defaults on the company’s survival probability is significant.

Figs. 3 and 4 describe the impact of the intensity of credit default on the company’s survival probability based on ordered and non-ordered credit default event, respectively. The simulation shows that when 1 2 0.1λ λ= = , the sequentiality of the credit default event has no effect on the company’s survival probability, but has impact on the threshold of company’s survival probability. Simultaneously, when the credit default is ordered, with the intensity of the credit default increases, the increase in the probability of the company survival is slowing, overall, however, is rising. When the credit defaults is non-ordered, with the intensity of the credit default increases, the decrease in the probability of the company

survival gradually increasing, and the probability of survival decrease quickly.

4 Conclusion

According to literatures about credit risk contagion, the credit risk contagion is not confined to the framework of the traditional definition. It has been gradually extended to the context of microeconomic factors, that is, microscopic individual credit default events’ occurrences, can easily leading local microscopic-individuals to having similar economic behavior. This developed the former assumptions that the financial credit risk be only affected by the macrofactors. For this reason, the changes in the correlation between company’s credit defaults and the sequence of credit defaults alter the company’s conditional survival probability distribution.

In this paper, on the basis of existing theoretical studies, we propose a credit risk contagion model with the structure of probability density of credit default time, considering the feature of the credit default sequence and local market information of the credit default. The advantage of the model is that it can clearly portray the company's credit risk characteristics and the effect of the market information on the credit risk contagion. Through theoretical analysis and experimental simulation, we investigate the effect of the correlation among credit defaults, the feature of credit default sequence, credit default intensity to the contagion effect of credit risk and the company’s survival probability. We find that, the impact on the company’s survival probability from the correlation among credit defaults, the feature of credit default sequence and credit default intensity is significant.

This research work can be further deepen, such as the pricing of credit derivatives when considering the

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sequentiality of the credit default event, the correlation between credit defaults and the changes in market information collection. It is also interesting to improve the two-dimensional connection function, introduced in the simulation, for future research.

References

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