8. When an institution purchases protection from a counterparty in a credit default swap, the resulting credit risk is minimized if the correlation between the event of default of the counterparty and the event of default of the underlying asset is

A. 0

B. 1

C. -1

D. Any positive value

Correct answer is C

A is incorrect.  When an institution purchases protection from counterparty in a credit default swap, the purchaser of the credit protection will experience a credit loss only if the underlying asset and the counterparty in the credit derivative transaction both default.  If only one defaults, there is no credit risk.  So credit risk decreases as the correlation between the event of default of the counterparty and the event of default of the underlying asset decreases.

B is incorrect.  When an institution purchases protection from counterparty in a credit default swap, the purchaser of the credit protection will experience a credit loss only if the underlying asset and the counterparty in the credit derivative transaction both default.  If only one defaults, there is no credit risk.  So perfect correlation between the event of default of the counterparty and the event of default of the underlying asset (i.e., correlation equal to 1) is undesirable.

C is correct.  When an institution purchases protection from counterparty in a credit default swap, the purchaser of the credit protection will experience a credit loss only if the underlying asset and the counterparty in the credit derivative transaction both default.  If only one defaults, there is no credit risk.  So credit risk is minimized when the event of default of the counterparty and the event of default of the underlying asset are as negatively correlated as possible.  Formally, the purchaser of the credit protection has exchanged the risk of default of the underlying asset for the joint risk of default of both the underlying asset and the counterparty, which is calculated by the following equation:

Prob(A and B) = Corr(A,B) * (Prob(A) * (1 - Prob(A)))^(1/2) * (Prob(B) * (1 - Prob(B)))^(1/2) + Prob(A) * Prob(B),

where A is the event of default of the counterparty and B is the event of default of the underlying asset.  This probability is minimized when the correlation between A and B is as small as possible; that is, Corr(A,B) = -1.

D is incorrect.  When an institution purchases protection from counterparty in a credit default swap, the purchaser of the credit protection will experience a credit loss only if the underlying asset and the counterparty in the credit derivative transaction both default.  If only one defaults, there is no credit risk.  So positive correlation between the event of default of the counterparty and the event of default of the underlying asset results in greater credit risk than negative correlation.

Reference: Caouette, Altman, Narayanan.  Managing Credit Risk, Chapter 20, page 314 - 315.

Type of Question: Credit Risk (Credit Derivatives)