How Default Correlation Affects a First-to-Default Contract

Summary

The document poses a credit-derivatives question: with different hazard rates for two entities, how does correlation affect the price of a contract paying if entity A defaults before entity B? It offers an intuition that perfect positive correlation may minimize the contract’s value, since B has the higher hazard rate and would be more likely to default first when both default times move together.

The document does not derive the Gaussian copula result or provide a numerical answer. Its intuition is a starting hypothesis, not a demonstrated conclusion; pricing requires specifying how default times are coupled and calculating the probability that A defaults first under that dependence model. The stated hazard rates alone do not establish the minimizing correlation without further analysis.

Key ideas

• The contract pays according to which of two entities defaults first.
• The two entities have different stated hazard rates.
• The question asks which Gaussian copula correlation minimizes the contract price.
• The proposed intuition is that perfect positive correlation may favor the more rapidly defaulting entity B.
• The document gives no derivation or verified answer to its pricing question.

Tags

# Gaussian copula: contract price


# Gaussian copula: contract price












The hazard rates for A and B are 1% and 2% respectively. A contract pays you $1 if A defaults earlier than B. What is the correlation that minimizes the price of the contract?

I have not studied the Gaussian copula model yet, but intuitively I would say that the price of the contract is lowest (contract has the least value) when the correlation is 1 because in that case the defaults time for A and B will follow the same movements around the mean and B is more likely to default earlier than A because its hazard rate is higher.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.