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A multivariate regime-switching mean reverting process and its application to the valuation of credit risk. (English) Zbl 1307.91186

The authors study counterparty risk on a credit default swap (CDS) and the valuation of a first-to-default basket on three underlyings in the frames of a common shock model with regime-switching intensities. In the model, the defaults are driven by shock events whose arrivals follow a multivariate regime-switching shot noise process. Using joint Laplace transform of the regime-switching shot noise processes, the authors provide explicit formulas for the spread of the CDS (with and without counterparty risk) as well as for the spread of the first-to-default basket swap on the three underlyings.

MSC:

91G40 Credit risk
60J27 Continuous-time Markov processes on discrete state spaces
91G20 Derivative securities (option pricing, hedging, etc.)
60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
60H30 Applications of stochastic analysis (to PDEs, etc.)
62P05 Applications of statistics to actuarial sciences and financial mathematics
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