Validation of the Merton Distance to the Default Model under Ambiguity
Abstract
:1. Introduction
2. Models
2.1. Naive Merton DD Model
2.2. Merton’s DD Model under Ambiguity
2.3. Default Probability under Ambiguity
2.4. Cox Proportional Hazard Model
2.5. Credit Default Swap Spread Regression
3. Data
Variable | Quantiles | ||||||
---|---|---|---|---|---|---|---|
Mean | SD | Min | 0.25 | Median | 0.75 | Max | |
E | 59,213.18 | 74,361.40 | 0.45 | 13,575.92 | 28,167.40 | 74,009.42 | 519,044.42 |
F | 41,562.61 | 57,808.95 | 684.97 | 17,509.28 | 23,839.00 | 38,574.00 | 761,203.00 |
r (%) | 2.29 | 2.00 | −0.02 | 0.21 | 1.72 | 4.04 | 6.39 |
CCI | 86.94 | 28.22 | 25.30 | 61.40 | 92.95 | 106.13 | 144.70 |
r spread (%) | 0.77 | 10.45 | −69.01 | −4.58 | 0.80 | 6.48 | 89.40 |
1/σ_{E} | 1.91 | 0.44 | 0.52 | 1.58 | 1.92 | 2.24 | 3.13 |
naive σ_{v} (%) | 37.00 | 10.03 | 17.92 | 29.84 | 35.38 | 42.43 | 76.44 |
π^{naive} (%) | 6.43 | 9.53 | 0.00 | 0.23 | 2.58 | 8.20 | 54.21 |
π^{CCI} (%) | 6.59 | 9.36 | 0.00 | 0.33 | 2.81 | 8.59 | 53.56 |
Corr(π^{naive}, π^{CCI}) = 0.994 |
4. Empirical Results
4.1. Hazard Model Results
Dependent Variable: Time to default | ||||||
---|---|---|---|---|---|---|
Variable | Model 1 | Model 2 | Model 3 | Model 4 | Model 5 | Model 6 |
π^{naive} | −0.183 * | 0.733 * (0.062) | 0.504 * | |||
(0.018) | (0.077) | |||||
π^{CCI} | −21.065 * | −97.848 * | −22.196 * | −76.093 * | ||
(1.981) | (7.726) | (1.879) | (9.071) | |||
CCI | 0.021 * | 0.015 * | 0.013 * | |||
(0.002) | (0.002) | (0.002) | ||||
ln(E) | −0.758 * | −0.721 * | −0.698 * | |||
(0.035) | (0.035) | (0.035) | ||||
ln(F) | 0.746 * | 0.938 * | 0.920 * | |||
(0.048) | (0.052) | (0.051) | ||||
1/σ_{E} | −2.208 * | −2.170 * | −2.177 * | |||
(0.168) | (0.167) | (0.164) | ||||
r spread | 0.814 | −3.800 * | −3.783 * | |||
(0.342) | (0.636) | (0.638) |
Variable | Quantiles | ||||||
---|---|---|---|---|---|---|---|
Mean | SD | Min | 0.25 | Median | 0.75 | Max | |
CDS spread | 134.01 | 405.39 | 10.00 | 43.28 | 61.00 | 102.50 | 10,255.00 |
π^{naive} | 5.07 | 11.86 | 0.00 | 0.00 | 0.03 | 2.77 | 68.63 |
π^{CCI} | 5.02 | 11.79 | 0.00 | 0.00 | 0.02 | 2.59 | 68.59 |
Variable | Dependent variable: log(CDS spread) | ||
---|---|---|---|
Model 1 | Model 2 | Model 3 | |
Constant | −1.8494 * (0.0011) | −1.6551 * (0.0169) | −1.3999 * (0.0776) |
log(π^{naive}) | 0.1478 * (0.0050) | −0.2025 * (0.0599) | |
log(π^{CCI}) | 0.1735 * (0.0058) | 0.4075 * (0.0695) | |
Obs. | 2107 | 2107 | 2107 |
R^{2} | 0.2919 | 0.2995 | 0.3033 |
4.2. CDS Spread Regressions
5. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
References
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Chen, W.-l.; So, L.-c. Validation of the Merton Distance to the Default Model under Ambiguity. J. Risk Financial Manag. 2014, 7, 13-27. https://doi.org/10.3390/jrfm7010013
Chen W-l, So L-c. Validation of the Merton Distance to the Default Model under Ambiguity. Journal of Risk and Financial Management. 2014; 7(1):13-27. https://doi.org/10.3390/jrfm7010013
Chicago/Turabian StyleChen, Wei-ling, and Leh-chyan So. 2014. "Validation of the Merton Distance to the Default Model under Ambiguity" Journal of Risk and Financial Management 7, no. 1: 13-27. https://doi.org/10.3390/jrfm7010013