||After financial crisis in 2007, the credit risk management has became one of the important|
issues around the financial institutions. In Duffie (2011), there are several features of correlated default between each firm, namely co-movement, contagion, and information
release. Fuh and Kao (2017) use the commonly factor model to capture those features and proposed three types of multi-name Distance-to-Default. In order to study the correlation between each firm, we use factor model which propose by Fuh and Kao (2017) to capture the correlation and calculate the variance-covariance matrix. Using the US financial data, we calculate the variance-covariance matrix and multi-name Distance-to-Default. We also separate our data to observe the different of the correlation of between each firm before and after firm default.
From the correlation matrix based on empirical data, we can find that the firm with high firm-value is not easily influenced from other firm default and the firm with low firmvalue is easily influenced from other firm default. In addition, we also observe that we can easily distinguish the firm with high and low firm-value from the color of correlation matrix. Based on multi-name Distance-to-Default, we can discover that the default event have an impact on other firms in same industry sector. However, the default probability of other firms are also affected from the financial state of itself or the fluctuation of financial market.
|| Black, Fischer and John C Cox (1976). “Valuing corporate securities: Some effects of bond indenture provisions”. In: The Journal of Finance 31.2, pp. 351–367.|
 Das, Sanjiv Ranjan. et al. (2006). “Correlated Default Risk”. In: The Journal of FixedIncome 16.2, pp. 7–32.
 Duffie, Darrell (2011). Measuring corporate default risk. Oxford University Press.
 Duffie, Darrell and Nicolae Garleanu (2001). “Risk and valuation of collateralized debt
obligations”. In: Financial Analysts Journal 57.1, pp. 41–59.
 Duffie, Darrell, Leandro Saita, and Ke Wang (2007). “Multi-period corporate default prediction
with stochastic covariates”. In: Journal of Financial Economics 83.3, pp. 635–665.
 Duffie, Darrell and Kenneth J Singleton (1999). “Modeling term structures of defaultable bonds”. In: The review of financial studies 12.4, pp. 687–720.
 Fuh, Cheng-Der and Chu-Lan Michael Kao (2017). “Correlated Defaults with a Distanceto-Default”. In: Technical Report.
 Huang, Jimmy et al. (2012). “Modeling credit correlations an overview of the Moody’s Analytics GCorr Model”. In: Technical Report.
 Leland, Hayne E (1994). “Corporate debt value, bond covenants, and optimal capital structure”. In: The journal of finance 49.4, pp. 1213–1252.
 Longstaff, Francis and Eduardo Schwartz (1995). “Valuing risky debt: A new approach”. In: Journal of Finance 50.3, pp. 789–819.
 McNeil, Alexander J, Rudiger Frey, and Paul Embrechts (2015). Quantitative risk management:Concepts, techniques and tools. Princeton university press.
 Merton, Robert C (1974). “On the pricing of corporate debt: The risk structure of interest rates”. In: The Journal of finance 29.2, pp. 449–470.
 Shreve, Steven E (2004). Stochastic calculus for finance II: Continuous-time models.Vol. 11. Springer Science & Business Media.
 Zhou, Chunsheng (2001). “The term structure of credit spreads with jump risk”. In:Journal of Banking & Finance 25.11, pp. 2015–2040.