Contagion delayed effects of associated credit risk based on scale-free network

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1 JOURNAL OF SYSTEMS ENGINEERING Vol.30 No.5 Oct ,2, 1 (1., ; 2., ) :.,. D-SIS,. :, ;,,. : ; ; ; ; D-SIS : F830 : A : (2015) doi: /j.cni.jse Contagion delayed effects of associated credit ris based on scale-free networ Li Yongui 1,2, Zhou Zongfang 1 (1. School of Econoic and Manageent, University of Electronic Science & Technology of China, Chengdu , China; 2. School of Econoics, Southwest University of Political Science & Law, Chongqing , China) Abstract: The associated credit ris is a hotspot and a difficult proble in odern credit ris anageent field. Based on the average field theory of coplex networ and infectious diseases odel, the contagion delayed effects of associated credit ris between associated subjects in the case of the associated assets are studied. Through the establishent of a D-SIS odel, i.e., a scale-free networ based associated credit ris contagion odel, the equilibriu state of the associated credit ris contagion between the associated credit subjects in this networ is analyzed. Researches show that the assets correlation between associated credit subjects contributes to ris sharing, thus delaying the outbrea of the relative credit ris. The contagion of correlation credit ris has the delayed effect, and the longer the delayed tie, the stronger the contagion intensity of the associated credit ris. Key words: associated credit subjects; associated credit ris; delay effect; scale-free networs; D-SIS odel 1,,.,, : ; : : ( ); ( ).

2 , 2007, ; 2009, ; 2011,.,,,. 1.,,.,,.,,, 2.,,,. [1,2],,, ;, [3] BA.,,.,. T,.,,,., [4 5]. [6], ; [7], ; [8]., Heisea [9], CDS,, ; Nier [10] ; Onur [11],, copula ; Gai [12] ; Conty [13] , ; Mastroatteo [14],,,, ; [15], ; [16],.,,,.,,??.,., D-SIS, 1,. 2 (scale-free networs)., ER WS Possion,,.

3 5 : 577.,,,, ; ;.,, BA.,. 2 N,,., P()., η., : 1) S, ; 2) I,.,,.,,. t,, s(t), ρ(t), ρ(t) + s(t) = 1. t,,, ρ. t,, t + 1, γ, γ. SIS, t I,, t+t +1, δ S, p = γ/δ.,, δ = 1, γ p..,,,.,. t, ρ (t), ρ.,,,,, ṡ (t) = ρ,t (t) γη θ(ρ(t))s (t) ρ,0 (t) = ρ,0 (t) + γη ρ (t)s (t) ρ,1 (t) = ρ,1 (t) + ρ,0 (t) (1). ρ,t (t) = ρ,t (t) + ρ,t 1 (t), ρ,τ (t) t τ, T ρ (t) = ρ,τ (t), (2) τ=0

4 θ(ρ(t)), θ. (1) T, S ; t,. (1), ρ,τ (t)., D-SIS., θ(ρ(t)) <> θ(ρ(t)) = P()ρ (t), (3) s sp(s) <>= P(). (4) t, ρ(t) = P()ρ (t), (5), ρ,t η γ(1 ρ )θ = 0. (6) ρ η γ T, θ η,γ T. ρ,τ,τ = 0,1,...,T ρ,τ (t). D-SIS,, ρ,τ (t) = 0, ρ,0 = ρ,1 = = ρ,t, (2) ρ,t = ρ T + 1, ρ,t (6) ρ T + 1 η γ(1 ρ )θ = 0, ρ = (T + 1)γθη. 1 + (T + 1)γθη, (3) (4) θ = P()ρ s sp(s) = 1 <> (T + 1)γθη P(). (7) 1 + (T + 1)γθη,θ = 0 (7),. ( ), (7), θ 0, d 1 (T + 1)γθη P() dθ <> 1 + (T + 1)γθη 1. θ=0 η P()(T + 1)γ 1. <>,, γ C = <> < 2 > η (T + 1), (8) < 2 >= 2 P(). (8), T = 0,,,.,.,,, ;,, ;

5 5 : 579,.,,,. 3 BA 3.1 BA 3 BA. BA, t, P(), P() = 2 2 3,., < >= + P()d = 2. BA K C, K C +,< 2 > 2 2 ln(k C /), (8) γ C 1 η (T + 1)ln(K C /). (9) BA, γ C η, T, K C. K C BA N,, K C N 1 2 (9), γc N γ C 2 η (T + 1)ln(N). (10) (10), γ C T η N.,,, ;, ;,,.,, BA., γ > γ C,,. η, P() <> (7), 1 = + (T + 1)γθη (1 + (T + 1)γθη ) d = η θγ(t + 1)ln P() (5) ρ = 2 2 (T + 1)γθη (Aln + B 1 + A = η γθ(t + 1),B = 1,C = η 2 γ 2 θ 2 (T + 1) 2. ( 1 + (T + 1)γθη C + γθη (T + 1) ln (1 + (T + 1)γθη ) ). (11) + ), (12) A,B,C (14) (11) ρ = 2 2 (T + 1)γθη (γθη (T + 1)ln + 1 ) = 2(T + 1)γθ(1 θ)η, (13) 1 + (T + 1)γθη θ (11). (11) (13), BA,. BA,. 3,, ;,.

6 BA BA, MATLAB 2012b,,. BA, = 2, θ = 1 2, η = N 1 = 10,N 2 = 30,N 3 = 50,. 2 T 1 = 5,T 2 = 10,T 3 = 20,., ;, ;,.,.,,,,.,,,, N 1 = 1 0 N 2 = T 1 = 5 T 2 = 1 0 N 3 = 5 0 T 3 = γ 0. 4 γ T N 1 N, γ T 2 T, γ N Fig. 1 Given N, the relation between γ and T Fig. 2 Given T, the relation between γ and N 3 4,., 1 3,,,.,,,., 3 4,,., 3 4,.,,.,,,. [7], γ 1 = 0.01,γ 2 = 0.03,γ 3 = 0.06, 5 6,.,,, ;.,,. 5 6, 4.

7 0 T 0 1 T 5 : 581.,,. 3 γ N, T Fig. 3 The relation between γ, N and T in considering directly related assets ratio 4 γ N, T Fig. 4 The relation between γ, N and T without consideration directly related assets ratio γ1 = γ1 = γ2 = γ3 = γ2 = γ3 = ρ ρ ρ T 6 ρ T Fig. 5 The relation between ρ and T in Fig. 6 The relation between ρ and T without considering directly related assets ratio consideration directly related assets ratio 7 8 T 1 = 3,T 2 = 6,T 3 = 15,.,,,.,,.,,. 7 8,,., , 9 10,,,.,,,.,.

0 0 1 582 30 0. 3 5 T 1 = 3 T 1 = 3 T 2 = 6 T 2 = 6 T 3 = 1 5 0. 8 T 3 = 1 5 0. 2 5 0. 6 ρ ρ 0. 1 5 0. 4 0. 2 0. 0 5 0. 0 1 5 0. 0 3 0. 0 4 5 0. 0 6 0. 0 1 5 0. 0 3 0. 0 4 5 0. 0 6 γ γ 7 ρ γ 8 ρ γ Fig.

8 T 1 = 3 T 1 = 3 T 2 = 6 T 2 = 6 T 3 = T 3 = ρ ρ γ γ 7 ρ γ 8 ρ γ Fig. 7 The relation between ρ and γ in Fig. 8 The relation between ρ and γ without considering directly related assets ratio consideration directly related assets ratio 9 ρ γ,t Fig. 9 The relation between ρ,γ and T in considering directly related assets ratio 10 ρ γ, T Fig. 10 The relation between ρ, γ and T without consideration directly related assets ratio,,.,,, ;,, ;,,,.,,. 4,,,.,,.,, ;,, ;.,,.

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