多期企業短期信用風險評估模型

Academy Papers

61

93 61-86 a E-mail: [email protected] b E-mail: [email protected]

A Multi-period Corporate Short-term Credit Risk Model

(

) classical statistical models

stochastic intensity models

(stochastic solvency ratio)

(Industrial state dependent stochastic solvency ratio model)

a,*

Hsien-hsing Liao

Associate Professor, Department of finance,

National Taiwan University

b,**

Tsung-kang Chen

Ph.D Student, Department of finance, National

Taiwan University

c l a s s i c a l

statistical models

stochastic intensity models

Probability of Liquidity Crisis

Abstract

Due to the fast development of corporate financing techniques and applications of derivative instruments, corporate credit risk evaluation becomes an important issue. Corporate credit risk can be roughly classified into two categories---short-term and long-term credit risk. A company's short-term credit depends upon its capability to meet its payment obligation. While a company's long-term credit relies upon the growing potential of its future net worth (asset value minus debt). In current short-term credit risk literature, liquidity crisis prediction model is the major research area. However, within this research field, neither classical statistical models nor stochastic intensity models can obtain probability of liquidity risk and ratio of insufficient liquidity at the same time. It is therefore that this line of research has its limitations in credit rating and in the valuation of related derivates. In addition, within the above two frameworks, few studies apply stochastic solvency ratio models to predict corporate liquidity crisis. Basing upon the two significant characteristics of solvency ratio -- mean-reversion and non-negative value and the concept of varying coefficient model, the study develops an Industrial state-dependent stochastic solvency ratio model . To consider future industrial economic state changes' impacts on a firm's solvency ratio, we also construct a stochastic model of industrial economic state. The information forecasted from the state model is used as the base for adjusting the parameters of the industrial economic-state dependent solvency ratio model. The solvency ratio model can simulate many solvency ratio paths and then the solvency ratio distributions of each future period. With the information of solvency ratio distribution and the criteria of insolvency (when solvency ratio is less than one), we can obtain the probability of a company's both short-term credit risk and ratio of insufficient liquidity in future periods. To perform a multi-period firm's short-term credit risk analysis, this solvency ratio model needs only publicly available information of corporate finance and the industrial economic state (i.e. the industrial cyclicality information).

Key Words: Solvency ratio, multi-period short-term credit risk model, State-dependent stochastic model, Short-term credit rating

Academy Papers

63

PLC

Ratio of

Insufficient Liquidity

RIL

PLC

1

Beaver

1966

,

Beaver

1968a,1968b

, and Altman

1968

Ohlson

1980

,

logit and probit

Altman

1968

Ohlson

1980

duration analysis

Lee and Urrutia

1996

, Shumway

2001

, Donald & Van de Ducht

1999

,

Kavvathas

2001

, Chava and Jarrow

2002

, and Hillegeist, Keating, Cram, and

Lundstedt

2003

Litterman and Iben

1991

, Madan and Unal

1995

, Jarrow

and Turnbull

1995

, Jarrow, Lando and

Turnbull

1997

, Lando

1998

, Duffie

and Singleton

1999

, Duffie

1998

and

Duffee

1999

. The latter covers Wilson

1997a and 1997b

, Guption, Finger and

Bhatia

1997

, McQuown

1997

,

Crosbie

1999

1 _{recursive partitioning analysis}

O-U

stochastic solvency ratio

2

Industrial state

dependent stochastic solvency ratio model

structural-form

2 _A1

Academy Papers

65

3

---2.1.

---3 _{distance-to-default} (Merton, 1976; KMV,1998)

1

1

SR

_t

t

OCIF

_tMA

_t

E B I T

4

n o n

-operating-related adjustment items

NOR Adj. item

operating-related adjustment items

OR

Adj.item

5

2

OCIF_tMA _{= MA (EBIT} t+NOR Adj.itemst + OR Adj.itemst + Increase on APt )

2

AP

OCOF

_tMA

t

accrual expenses

EBIT

C

_t-1

, SI

_t-1

t

DA

_t

t

t

6

Int

_t

, Tax

_t

t

4 _{EBIT ( )}

5 _{Chen, Tsung-Kang and Hsien-Hsing, Liao, 2004, A Cash}

Flow Based Multi-period Credit Risk Model , Working paper, A Paper presented in the 12th Conference on the Theories and Practices of Securities and Financial Markets.

Academy Papers

67

1

2.2.

1-4

6 _{Max(0,Net decrease on debt ) debt}

( )

(

) (Payment Obligation)

1.

lognormal distribution

A2

5-8

lnSR

Dickey-Fuller Test

3. 4. 5. lnSR 6. lnSR

Academy Papers

69

7. lnSR 8. lnSR

2.3.

Gaussian process

Dickey-Fuller Statistics SR lnSR -3.613*** -5.129*** -4.537*** -4.917*** -5.793*** -4.927*** -3.899*** -3.668*** -4.552*** -3.843*** -5.119*** -3.848*** -3.355** -3.112** *** 99% ** 95% * 90% Mean-reverting I 1 trend

O-U

stochastic solvency ratio

3

,

3

d(lnSR

_t

)

t

lnSR

a (t)

t

lnSR

b (t)

t

lnSR

(t)

t

lnSR

3

a t

b t

t

3

a

t

7

b

t

t

lnSR

t

t

lnSR

2.4.

8 9

4

4

t

t

b

7 _{a (t)} 8 9 _A1

Academy Papers

71

A3

3

b

t

t

10

5

6

b

Maximum Likelihood Estimation

Chen

1996

AR

1

11

7

8

(t)

t

0 1 1

lnSR

(

1nSR

_t

=

₀

+

_{1 t}

+

)

₀ 1

lnSR

1

lnSR

₁

b

Maximum Likelihood Estimation

Chen

1996

AR

1

10 _A3

2.5.

4

4

b

Maximum Likelihood

Estimation

Chen

1996

AR

1

4

Ornstein-Uhlenbeck

O-U

s

9

10

unconditional distribution

Likelihood function

11

12

12

A R

1

AR

1

MSE

9

13

13

14

14

t + t

0

10

Academy Papers

73

t

AR

1

4

14

15

= b (1-

),

=e

- t

_a

15

3

16

16

3.1.

7

ˆ

t

5

6

7

8

lnSR

3

taking exponent

N

N

N

9

9

PLC

17

Probability of liquidity crisist

17

Expected

Ratio of Sufficient Liquidity

ERSL

18

Expected

Ratio of Insufficient Liquidity, ERIL

19

18

19

9.

10

10.

4.1.

7

SR ( ) ( lnSR ) SR lnSR

Academy Papers

75

TEJ

TRC

1998 - 2004 Q2

1995 - 2004

Q 2

NBER

1997

1998

4.2.

16

a, b,

lnSR

1

A4

A4

4.3.

TEJ , TRC TEJ S&P Moody 1 1 2 1 2

1. TEJ, Datastream 1. TEJ, Datastream

2. TEJ, Datastream 2. TEJ, Datastream

3. DRAM SEMI,

Bloomberg, Datastream

* _1,2 **

Model's

PLC

Model's ERIL

Model's PLC

S

P

1981-2002

Moody

1920-2001

one-year cumulative

default rate curve

Moody

Moody

global rating

local rating

TRC

a b Functional value 1 1.6325 3.2471 1.8557 -60.261 0.0142 0.1492 0.0023 0.0891 1.5769 3.6468 1.4361 -46.574 -0.0016 0.1205 0.0001 0.0591 1.7255 2.0849 1.5529 -48.082 0.0163 0.1591 0.0006 0.0763 1.5686 1.4772 1.4280 -31.083 0.0463 0.1319 0.0022 0.0634 0.8621 2.1258 1.2974 -51.487 0.0260 0.0314 0.0013 0.0258 0.8372 3.0126 1.5471 -58.709 0.0103 0.0284 0.0004 0.0291 0.5378 2.6758 1.1325 -51.189 0.0670 0.0135 0.0001 0.0158 1. 2. _{MLE Optimization} functional value

Academy Papers

77

Model's PLC Model's ERIL Model's rating Model's rating Model's rating Actual rating One-Year) (One-Year) (PLC) (ERIC) (Short-term) (Short-term)

1* 0.00% 0.0000% AAA / Aaa Aaa twA-1 twA-1

2* 0.00% 0.0000% AAA / Aaa Aaa twA-1 twA-1

3* 0.00% 0.0000% AAA / Aaa Aaa twA-1 twA-1

4* 0.04% 0.0074% A / A3 A2 twA-1 twA-1

5* 0.24% 0.0464% BBB+ / Baa2 Baa1 twA-1 twA-1

6* 0.04% 0.0136% A / A3 A2 twA-1 twA-1

7* 0.54% 0.1775% BBB- / Baa3 Baa3 twA-2 twA-2

* 1.

2. _{Model's PLC, ERIC: 15000}

( )

3. _{Model's rating(PLC) PLC S&P Moody (S&P/Moody)}

Model's rating(ERIC) ERIC Moody

4. _{Model's rating(short-term) Model's rating(PLC,ERIC) Global & Local rating}

a

b

Functional value 0.340310 0.032201 0.036594 75.13 0.007586 0.000071 0.000432 0.475810 0.010758 0.019298 101.08 0.012212 0.000036 0.000263 0.97626 0.000621 0.029346 77.72 0.040117 0.000032 0.000656 0.57584 0.032241 0.031241 84.85 0.015094 0.000017 0.000455 1. 2. MLE Optimization functional value

jump diffusion model

11-16

11. 1 12. 13. 1 14. 15. 1

Academy Papers

79

classical statistical models

stochastic intensity

models

jump diffusion model

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1 9 9 5 ~

2004Q2

A1-1

A1-4

A1-1. A1-2.

A2

A2-1

A2-4

Anderson-Darling statistics (Ralph and Stephens, 1986)

A1-3

A1-4

A2-1.

Academy Papers

83

A3

3

,

3

d

lnSR

t

t

lnSR

a

t

t

lnSR

b

t

t

lnSR

t

t

lnSR

.

3

a t

b t

t

3

a

t

12

b t

t

lnSR

A2-3. A2-4. 12 _a(t)

t

t

lnSR

(Maximum Likelihood

Estimation)

lnSR

a

b

b

(lnSR)

A3-1

lnSR

b

lnSR

b

b

t

A3-1

lnSR

A3-2

lnSR

(b)

A3-1

A3-3

A3-3

A3-4

A3-3

A3-4

1

A3-5

1

A3-6

∆

t

∆

1nSR_{t ∆} t ∆ 1nSRt 1 13 13 _{A3-5 A3-6 ( ) (} t) ` 1 (1nSRt) ( t) 1 (1nSRt) t t-1

Academy Papers

85

∆ 1nSRt ∆ t

∆

t

∆

InSR_t

A3-5

A3-6

lnSR

∆

t

∆

1nSR_t

t

_t

A3-2

t

lnSR

b

A3-7

t+1

_t+1

A3-2

t

lnSR

b

A3-8

A3-8

A3-7

∆

t

∆

1nSRt

A3-9

b

∆

t

∆

1nSRt

A3-10

A 3 - 1 0

l n S R

A 3 - 4

A3-5

_{∆ 1nSR} t ∆ t ∆1nSRt

∆

t

∆

1nSRt

A3-11

t

0

A4-2 AR 1

a

b

0.3146 0.0315 0.0377 0.4490 0.0106 0.0199 1.0737 0.0013 0.0317 0.5570 0.0310 0.0322 A4

Chen

1996

AR

1

A4-1 AR 1 a b 1 1.1051 3.4084 1.7321 0.0142 1.5635 3.6302 1.4791 -0.0016 1.7491 2.0516 1.5767 0.0163 1.4379 1.4758 1.4342 0.0463 0.8626 2.0822 1.3340 0.0260 0.8318 3.0624 1.5904 0.0103 0.5268 2.7353 1.1643 0.0670 *