2012/04/10 by Jean‐David Fermanian, Fermanian, Jean-David, Olivier Vigneron +1
Economics, Econometrics and Finance · #Banking stability, regulation, efficiency #Credit Risk and Financial Regulations #FOS: Economics and business #Financial Risk and Volatility Modeling #Pricing of Securities (q-fin.PR) #Risk Management (q-fin.RM) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1204.2251
openalex publication_date 2012/04/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the pricing of European-style structured credit payoff in a static framework, where the underlying default times are independent given a common factor. A practical application would consist of the pricing of nth-to-default baskets under the Gaussian copula model (GCM). We provide necessary and sufficient conditions so that the corresponding asset prices are martingales and introduce the concept of "break-even" correlation matrix. When no sudden jump-to-default events occur, we show that the perfect replication of these payoffs under the GCM is obtained if and only if the underlying single name credit spreads follow a particular family of dynamics. We calculate the corresponding break-even correlations and we exhibit a class of Merton-style models that are consistent with this result. We explain why the GCM does not have a lot of competitors among the class of one-period static models, except perhaps the Clayton copula.