multiperiod corporate default prediction a forward...

Multiperiod Corporate Default Prediction– A Forward Intensity Approach

Jin-Chuan Duana,b Jie Suna Tao Wangb

aRisk Management Institute, National University of SingaporebDepartment of Finance, National University of Singapore

2010 NTU International Conference on FinanceTaipei, December 2010

Duan, Sun, and Wang (NUS) Multiperiod Corporate Default Prediction December 2010 1 / 26

Research Question

Default/bankrutpcy prediction over different future periods

Term structures of default probabilitiesShort-term vs. long-term

A forward intensity approachReduced form model

Duan, Sun, and Wang (NUS) Multiperiod Corporate Default Prediction December 2010 2 / 26

Outline

1 Literature Review

2 A forward intensity approach to multiperiod default prediction

3 Data and covariates

4 Empirical results

5 Conclusion

Duan, Sun, and Wang (NUS) Multiperiod Corporate Default Prediction December 2010 3 / 26

Literature Review

Outline

1 Literature Review

2 A forward intensity approach to multiperiod default prediction

3 Data and covariates

4 Empirical results

5 Conclusion

Duan, Sun, and Wang (NUS) Multiperiod Corporate Default Prediction December 2010 4 / 26

Literature Review

Literature Review

Discriminat analysisBeaver (1966, 1968), Altman (1968), etc.Model output: credit scores

Binary response models: logit/probit regressionsOhlson (1980), Zmijewski (1984), etc.Model output: default probability in the next one period

Campbell, et al (2008): multiple logit models

Duan, Sun, and Wang (NUS) Multiperiod Corporate Default Prediction December 2010 5 / 26

Literature Review

Literature Review (Cont’d)

Recent development: duration analysisShumway (2001), Chava and Jarrow (2004), etc.

Duffie, et al (2007): intensity model with stochastic covariatesTwo Poisson processes

1 Default/bankruptcy2 Other exit: merger and acquisition, etc.

Instantaneous intensityInstantaneous rate of occurrenceFunctions of the covariates

Time-series dynamics of the covariates

Duan, Sun, and Wang (NUS) Multiperiod Corporate Default Prediction December 2010 6 / 26

A forward intensity approach to multiperiod default prediction

Outline

1 Literature Review

2 A forward intensity approach to multiperiod default prediction

3 Data and covariates

4 Empirical results

5 Conclusion

Duan, Sun, and Wang (NUS) Multiperiod Corporate Default Prediction December 2010 7 / 26

A forward intensity approach to multiperiod default prediction

Model Setup

Spot combined exit intensity: "average" rate of exitoccurrence

it (�) ≡ − ln(1 − Fit (�))

�= −

ln Et

[exp

(−∫ t+�

t (�is + �is)ds)]

�

Fit (�): the time-t conditional distribution function of the combinedexit time evaluated at t + � .�is: instantaneous intensity for default.�is: instantaneous intensity for other exit.

Duan, Sun, and Wang (NUS) Multiperiod Corporate Default Prediction December 2010 8 / 26

A forward intensity approach to multiperiod default prediction

Model Setup (Cont’d)

Forward exit intensity: forward rate of exit occurrence

git (�) ≡F ′it (�)

1 − Fit (�)= it (�) + ′it (�)�

Forward default intensity: forward rate of default occurrence

fit (�) ≡ e it (�)� limΔt→∞

Pt (t + � < �Di = �Ci ≤ t + � + Δt)Δt

= e it (�)� limΔt→∞

Et

[∫ t+�+Δtt+� exp

(−∫ s

t (�iu + �iu)du)�isds

]Δt

�Di : default time of the i-th firm.�Ci : combined exit time of the i-th firm.The default probability over [t , t + � ] becomes∫ �

0e− it (s)sfit (s)ds

Duan, Sun, and Wang (NUS) Multiperiod Corporate Default Prediction December 2010 9 / 26

A forward intensity approach to multiperiod default prediction

Model Setup (Cont’d)

Model fit (�) and git (�) directly as functions of state variablesavailable at time t and the horizon of interest, � .git (�) ≥ fit (�)

Xit = (xit ,1, xit ,2, ⋅ ⋅ ⋅ , xit ,k ): the set of the state variables

fit (�) = exp(�0(�) + �1(�)xit ,1 + �2(�)xit ,2 + ⋅ ⋅ ⋅�k (�)xit ,k

)git (�) = fit (�) + exp

(�0(�) + �1(�)xit ,1 + �2(�)xit ,2 + ⋅ ⋅ ⋅�k (�)xit ,k

)Discretize the model for empirical implementation

Duan, Sun, and Wang (NUS) Multiperiod Corporate Default Prediction December 2010 10 / 26

A forward intensity approach to multiperiod default prediction

Model Setup (Cont’d)

Forward default probability

Cumulative default probability

Duan, Sun, and Wang (NUS) Multiperiod Corporate Default Prediction December 2010 11 / 26

A forward intensity approach to multiperiod default prediction

Estimating the Forward Intensity Model

MLE

Decomposable

Non-sequential, parallelizable

Duan, Sun, and Wang (NUS) Multiperiod Corporate Default Prediction December 2010 12 / 26

Data and covariates

Outline

1 Literature Review

2 A forward intensity approach to multiperiod default prediction

3 Data and covariates

4 Empirical results

5 Conclusion

Duan, Sun, and Wang (NUS) Multiperiod Corporate Default Prediction December 2010 13 / 26

Data and covariates

Data

Sample period: 1991-2009.

Database:CompustatCRSPBloomberg

12,196 U.S. public companies (both industrial and financial),1,030,305 firm-month observations.

Duan, Sun, and Wang (NUS) Multiperiod Corporate Default Prediction December 2010 14 / 26

Data and covariates

Covariates

3-month treasury rateTrailing 1-year S&P500 returnDistance to defaultCash and shor-term investments/Total assetsNet income/Total assetsRelative sizeMarket to book ratioIdiosyncratic volatility

Level and trend

Duan, Sun, and Wang (NUS) Multiperiod Corporate Default Prediction December 2010 15 / 26

Empirical results

Outline

1 Literature Review

2 A forward intensity approach to multiperiod default prediction

3 Data and covariates

4 Empirical results

5 Conclusion

Duan, Sun, and Wang (NUS) Multiperiod Corporate Default Prediction December 2010 16 / 26

Empirical results

Parameter Estimates

Duan, Sun, and Wang (NUS) Multiperiod Corporate Default Prediction December 2010 17 / 26

Empirical results

Parameter Estimates (Cont’d)

Duan, Sun, and Wang (NUS) Multiperiod Corporate Default Prediction December 2010 18 / 26

Empirical results

Aggregate Number of Defaults

Duan, Sun, and Wang (NUS) Multiperiod Corporate Default Prediction December 2010 19 / 26

Empirical results

In-Sample Accuracy

1 month 3 months 6 months 12 months 24 months 36 months93.41% 91.42% 88.37% 82.70% 72.09% 64.77%

Duan, Sun, and Wang (NUS) Multiperiod Corporate Default Prediction December 2010 20 / 26

Empirical results

Out-of-Sample (Over Time) Accuracy

1 month 3 months 6 months 12 months 24 months 36 months91.99% 90.21% 87.36% 83.42% 74.35% 68.53%

Duan, Sun, and Wang (NUS) Multiperiod Corporate Default Prediction December 2010 21 / 26

Empirical results

Term Structures of Default Probabilities(Lehman Brothers)

Duan, Sun, and Wang (NUS) Multiperiod Corporate Default Prediction December 2010 22 / 26

Empirical results

Term Structures of Default Probabilities (Cont’d)

Duan, Sun, and Wang (NUS) Multiperiod Corporate Default Prediction December 2010 23 / 26

Conclusion

Outline

1 Literature Review

2 A forward intensity approach to multiperiod default prediction

3 Data and covariates

4 Empirical results

5 Conclusion

Duan, Sun, and Wang (NUS) Multiperiod Corporate Default Prediction December 2010 24 / 26

Conclusion

Conclusion

A forward intensity approach for the prediction of corporatedefaults over different future periods is proposed.Maximum likelihood analysis is conducted on a large sample ofU.S. industrial and financial firms spanning the period 1991-2009.Several frequently used covariates are shown to be useful forprediction at both short and long horizons.The forward intensity model is amenable to aggregation, whichallows analysts to assess default behavior at the portfolio and/oreconomy level.

Duan, Sun, and Wang (NUS) Multiperiod Corporate Default Prediction December 2010 25 / 26