1. Comments on “Nonlinear Correlated Defaults with Copulas”
Discussed by Tan Lee
Department of International Business
Yuan Ze University

2. 1. Purpose of This Article
To explore the pricing of first-to-default Credit Default Swaps (CDS) by combining models derived by Finkelstein et. al. (2002) and Li (2000).
To apply the formula to the practice by using stock market data both in U.S. and Taiwan.

3. 2. Main Conclusions of This Article
The joint default probability decreases as these assets are highly positive correlated.
The empirical results support that the dependence among these assets are asymmetric and can be better described by the Archimedean copula functions.

4. 3. Major Suggestions (1)
This article may be improved if the authors can compare their results with those of the literature, or with the empirical data.
For example, the first conclusion of this article is just opposite to Li (2000, p. 21 and p. 29) and Jorion (2005, p. 536). It could be better if the authors can find an explanation for the difference.
Similarly, the second conclusion has been asserted without comparing with the empirical data. The authors may need to find a convincing explanation if the empirical data is not available.

5. 3. Major Suggestions (2)
This article may also be improved if the authors can give the reader stronger motivation for developing this paper.
For example, a finite-time formula for pricing first-to-default CDS is in need, etc.

6. 4. Minor Comments
To increase the “attractiveness” of this article, the authors may explain the deriving process more intuitively.
For example, the authors assume that μ in equation (1) equals zero without explanation. Actually Finkelstein et. al. (2002, p. 11) has already provided a reasonable explanation.
Similarly, the authors assume the recovery rate is uncertain because this can bring the model flexibility. Finkelstein et. al. (2002, p. 5) has also already provided the motivation.

7. 5. Some Confusions
The formula on p. 12. How do the authors amend the formula from 1 asset as in Finkelstein et. al. (2002) to that of 3 assets? Since the process of derivation is lacked, and all the notations in the formula on p. 12 haven’t been defined.
The empirical results on p. 12. The authors use the data drawn from only two companies to calculate the pricing for first-to-default CDS when T=480, while the formula is to price CDS of three companies?

8. 5. Some Confusions (continued)
The simulation results on pp and p. 23. The results of survival probability (S) on p. 23 are actually the same no matter the value of correlation coefficient (ρ) is. Is this because although the authors has changed the value of the correlation coefficient (ρ), they still substitute the empirical data of stock prices into the formula?