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

HTML
DOWNLOAD

Μέγεθος: px

Εμφάνιση ξεκινά από τη σελίδα:

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

Φιλομήλα Γούναρης
6 χρόνια πριν
Προβολές:

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,,,.,,.,, ;,, ;.,,.

9 5 : 583,. : [1] Boss M, Elsinger H, Suer M, et al. The networ topology of the interban aret[j]. Quantitative Finance, 2004, 4(6): [2] Garlaschelli D, Loffredo M I. Structure and evolution of the word trade networ[j]. Physica A, 2005, 355(1): [3],,. [J]. :, 2012, 14(2): Li Hao, Chen Tingqing, He Jianin. The interban aret networ structure evolution odel based on the coplex networ theory[j]. Journal of Beijing Institute of Technology: Social Sciences Edition, 2012, 14(2): (in Chinese) [4] Jarrow R A, Lando D, Turnbull S M. A arov odel for the ter structure of credit ris spreads[j]. Review of Financial Studies, 1997, 10(2): [5] Zhou Chunsheng. An analysis of default correlation and ultiple defaults[j]. Review of Financial Studies, 2001, 14(2): [6],. [J]., 2009, 23(3): Chen Lin, Zhou Zongfang. A research based shareholding ratio on default contagion between parent and subsidiary copany in an enterprise group[j]. Journal of Industrial Engineering and Engineering Manageent, 2009, 23(3): (in Chinese) [7],,. : [J]., 2012, 32(3): Chen Jianxin, Luo Weiqi, Pang Sulin. The ris infection for the ban of et population odel: Based on the dynaic siulation of the cellular autoata[j]. Systes Engineering: Theory & Practice, 2012, 32(3): (in Chinese) [8],. [J]., 2012, 27(2): Ye Wuyi, Miao Baiqi. Analysis of financial contagion based on dynaic quantile regression odel[j]. Journal of Systes Engineering, 27(2): (in Chinese) [9] Heisea S, Kühn R. Derivatives and credit contagion in interconnected networs[j]. The European Physical Journal: B, 2012, 85(4): [10] Nier E, Yang J, Yorulazer T, et al. Networ odels and financial stability[j]. Journal of Econoic Dynaics and Control, 2007, 31(6): [11] Filiz I O, Guo X, Morton J, et al. Graphical odels for correlated defaults[j]. Matheatical Finance, 2012, 22(4): [12] Gai P, Kapadia S. Contagion in financial networs[j]. Royal Society of London Proceedings Series A, 2010, 466: [13] Cont R, Moussa A, Santos E B. Networ Structure and Systeic Ris in Baning Systes[EB/OL]. 2010, sol3/papers.cf?abstract id= [14] Mastroatteo I, Zarinelli E, Marsili M. Reconstruction of financial networs for robust estiation of systeic ris[j]. Journal of Statistical Mechanics: Theory and Experient, 2012(3): [15],. [J]., 2011, 24(2): Long Quan, Ding Yongsheng. Credit contagion of retail credit portfolio[j]. Journal of Manageent Science, 2011, 24(2): (in Chinese) [16],,,. [J]., 2011, 25(2): Li Shouwei, He Jianin, Zhuang Yaing, et al. Stability of inter-ban arets based on coplex networs[j]. Journal of Industrial Engineering and Engineering Manageent, 2011, 25(2): (in Chinese) : (1978 ),,,,, :, Eail: yonguili@aliyun.co; (1950 ),,,,, :,,, Eail: zhouzf@uestc.edu.cn.

Σχετικά έγγραφα

Correction of chromatic aberration for human eyes with diffractive-refractive hybrid elements

$Correction of chromatic aberration for human eyes with diffractive-refractive hybrid elements$ 5 5 2012 10 Chinese Optics Vol. 5 No. 5 Oct. 2012 1674-2915 2012 05-0525-06 - * 100190-14 - - 14. 51 μm 81. 4 μm - 1. 64 μm / O436. 1 TH703 A doi 10. 3788 /CO. 20120505. 0525 Correction of chromatic aberration