JOURNAL OF SYSTEMS ENGINEERING 3., ) Uncertainty DE KMV model to measure credit risk of listed companies

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1 JOURNAL OF SYSTEMS ENGINEERING Vol.30 No.2 Apr DE KMV 1,2,3, 1,2, 1,2, 1,2 (1., ; 2., ; 3., ) : KMV, (DE), DE KMV., KMV, DE KMV,,., KMV,,. : ; KMV; ; ; : F830 : A : (2015) doi: /j.cnki.jse Uncertainty DE KMV model to measure credit risk of listed companies Zhang Dabin 1,2,3, Zhou Zhigang 1,2, Liu Wen 1,2, Jiao Peng 1,2 (1. School of Information Management, Central China Normal University, Wuhan , China; 2. Forecasting Science Research Center, Central China Normal University,, Wuhan , China; 3. Institute of Automation, Chinese Academy of Sciences, Beijing , China) Abstract: This paper focuses on the measurement of uncertainty KMV credit risk. Using differential evolution algorithm to optimize the coefficient of default point, we propose a uncertainty DE KMV model to measure the credit risk of public companies. Empirical results show that common KMV model often underestimate the value at risk of Chinese listed companies, but Uncertainty DE KMV model can get coefficient values very close to the actual risks considering the various risks of of China s listed companies. This model passes the quantile regression test, and the coefficient is significantly better in the confidence interval. The evidence above can prove the superiority of the uncertainty DE KMV model relative to common KMV models. Key words: differential evolution ; KMV; probability of default ; quantile regression; credit rating 1,,.,.,,, : ; : : ( ); (2012M510607); (CCNU14Z02016).

2 ;, ;,.,,, : 1) ; 2) ; 3) ; 4) ; 5) ; 6) [1].,.., ;,,., Merton [2],.. KMV, KMV,,., KMV,. [3 5]. Kealhofer [6],., KMV. Duffie [7],, KMV, [8] [9] KMV, KMV. [10] KMV 15,,, ST. [11],. [12] KMV EDF, EDF. [13] KMV,., KMV,, KMV,. Wang [14] KMV,, QR KMV KMV.,,,,,. KMV QR KMV. 2 DE KVM 1) KMV KMV Merton KMV 20 80,. KMV.,,.,, ;, [15]. Merton,,,, dv A = µv A dt + σ A V A dz, (1) V A, µ, σ A, Z Wiener. Merton.,

3 2 : DE KMV 167, Black Scholes Merton, Merton V E = V A N (d 1 ) De rt N (d 2 ), (2) V E, D, r, N( ), d 1 = (ln (V A /D) + (r + 0.5σ 2 A )T)/(σ2 A T),d 2 = d 1 σ A T. KMV, (2),. Merton,, Itô σ E = V ( ) A VE σ A. (3) V E V A Black Scholes Merton, V E V A = N(d 1 ), Merton, (2) (4), V A σ A. σ E = V A V E N (d 1 ) σ A, (4) KMV σ E ; ;,, (2) (5) V A σ A. PD = N DD = ln (V A/D) + (r + 0.5σA)T 2. (5) σa 2 T ( ( ln (VA /D) + (r + 0.5σ 2 A)T σ 2 A T )). (6) KMV,, ( DPT), DPT. DD ( DPT)/,,,. 2) KMV,,,, [16]. Knight [17] 1921,. Ellsberg Knight,,, [18]. KMV,,. KMV, Knight ( [16] ), KMV. : KMV ; KMV, ; Knight, Knight λ DD λ = ln (V A/D) + (r + 0.5σA 2 +λσ) T, (7) σa 2 T λ, λ ; λ KMV, ; λ,.

4 ) (DE),,,,. (DE) (GA),,., DE., ;, [19]. : (a). X g i = ( x g i,1,x g i,2,,x g i,k),i = 1,2,,NP, (8) (8) g i, NP, K. (9) x o i,j x min,j + rand(0,1) (x max,j x min,j ), (9) x max,j,x min,j x i j, rand(0,1) [0,1]. (b). x g i, r 1,r 2,r 3 ( NP 4), (10),, v g i, F, F = 0.5. v g ij x g r 1j + F ( x g r 2j x g r 3j), (10) (c). v g i x g i u g i, vi,j, g r C j = r d u g i,j x g i,j,, r, r (0,1); r d, r d {1,2,...,K}. CR [0,1] ( 0.5),, v g i. (d). x g i ug i xg+1,,,, u g i, u g i, xg i, u g i, f (u g i) f (x g i) x g+1 i x g i,, f. (e). G max VTR,,,.,, DE/x/y/z, x, y, z. DE/rand/1/bin, DE/best/1/bin DE/best/2/bin (11) (12) v g i x g best + F ( x g r 1 x g r 2 ), (13) v g i x g best + F ( x g r 1 x g r 2 ) + F ( x g r 2 x g r 3 ), (14)

5 2 : DE KMV ST, ST,, ST,,,., DE KMV : 1 (V A ) (σ A ). (2) (4)., KMV,, ; 2 DD.,. KMV 1, 0.5., DPT KDE KMV = αld + βsd, (15) α β. 3 λ, (16), ( ( ln (VA /DPT) + (r + 0.5σA 2 PD = N +λσ) T )) T σ 2 A (16) 4, , 0.5,,. f(n) = 1 n N, (17) N, n. 5,,,., ST, 232,, 221, 1 ST. 1 Table 1 ST Percentage of listed companies ST treatment / ST / / % , , 2010,, ST,. 2, 200, 200, 0.5, 0.3, 1. 3,

6 ) 1 n (KMV=0.5), (KMV=1), , , , , 0.35, / a 1 ST Fig. 1 Number of listed ST companies 2 Table 2 Tableau for differential evolution algorithms n/N Table 3 3 DE KMV Results of differential evolution algorithms /min /221= (cut-off value=0.3) (114/221= ) (KMV=0.5) 85/221= (cut-off value=0.5) (136/221= ) /221= (KMV=1) (cut-off value=0.8) (174/221= ) f( n Fig. 2 Fitness of the uncertainty DE-KMV model Fig. 3 Sub-optimal results trend of the uncertainty DE-KMV model

7 2 : DE KMV 171 DE KMV,. QR,,. QR,., QR, Y X, [20]. DPT, θ, ε. DPT (q) QR KMV = θ + αld + βsd + ε, (18), QR KMV , ,,., R 2. Table 4 4 Estimation results of quantile regression model (τ) Statistics Constant α β R Coefficient e P value Coefficient e P value Coefficient e P value Coefficient e P value Coefficient e P value Coefficient e P value Coefficient e P value Coefficient e P value Coefficient e P value Coefficient e P value Coefficient e P value Coefficient e P value Coefficient e P value Coefficient e P value Coefficient e P value Coefficient e P value Coefficient e P value Coefficient e P value Coefficient e P value : P value R.

8 ,, (a) (b)., 95%., ( 0.8) ( 0.85), e 5 ( 0.8) e 5 ( 0.85)., 0.85,., 0.85, KMV DD. 4 4 x 1 0 O L S e s t i m a t e w i t h 9 5 % b a n d O L S e s t i m a t e s w i t h 9 5 % b a n d α β v 1 Q u a n t i l e e s t i m a t e w i t h 9 5 % b a n d 0. 5 t 2 Q u a n t i l e e s t i m a t e s w i t h 9 5 % b a n d r (a) ² τ (b) Fig. 4 4 α (a) β (b) Variation in the long-term debt coefficient α (a) and short-term debt coefficient β(b) over the conditional quantiles 5, QR KMV KMV, 0.3, ,,. Table 5 5 DE KMV, QR KMV KMV Comparing the results of DE KMV,QR KMV and KMV models Cut-off value/model DE KMV QR-KMV KMV KMV. KMV, ,.,,,,,.,. QR KMV KMV,, DE KMV.,. KMV,,.,,,,,.

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