In this work we define a multivariate semi-Markov process. We derive an explicit expression for the transition probability of this multivariate semi-Markov process in the discrete time case. We apply this multivariate model to the study of the counterparty credit risk , with regard to correlation in a CDS contract. The financial crisis has stressed the importance of the study of the correlation in the financial market . In this regard, the study of the risk of default of the counterparty in any financial contract has become crucial in the credit risk . Many works has been done to trying to describe the counterparty risk in a CDS contract, but all this work are based on the Markovian approach to risk. In the our opinion this kind of model are too restrictive, because they require that the distribuction function of the waiting times has to be exponential or geometric, for discrete time. In the our model, we describe the evolution of credit rating of the financial subjects like a multivariate semi-Markov model, so we allow for arbitrarily distributed sojourn time. The age state dependency, typical of the semi-Markov environment, allow us to insert the correlation in a dynamical way. In particular, suppose that A is a default-free bondholder and C is the relative firm. The bondholder buy protection against C's default by another defaultable subject, say B the protection seller. Our model describe the evolution of the credit rating of the couple B and C. We admit for simultaneus default of C and B, the single default of C or single default of B .
We consider the problem of constructing an appropriate multivariate model for the study of the counterparty credit risk in credit rating migration problem. For this financial problem different multivariate Markov chain models were proposed. However the markovian assumption may be inappropriate for the study of the dynamic of credit ratings which typically show non markovian like behaviour . In this paper we develop a semi-Markov approach to the study of the counterparty credit risk by defining a new multivariate semi-Markov chain model. Methods are given for computing the transition probabilities, reliability functions and the price of a risky Credit Default Swap .
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In this work we define a multivariate semi-Markov process. We derive an explicit expression for the transition probability of this multivariate semi-Markov process in the discrete time case. We apply this multivariate model to
We consider the problem of constructing an appropriate multivariate model for
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, with regard to correlation in a CDS contract. The financial crisis has stressed the importance of
in credit rating migration problem. For this financial problem different multivariate Markov chain models were proposed. However the markovian assumption may be inappropriate for
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correlation in the financial market
dynamic of credit ratings which typically show non markovian like behaviour
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regard,
paper we develop a semi-Markov approach to
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risk of default of the counterparty in any financial contract has become crucial in the credit risk . Many works has been done to trying to describe the counterparty risk in a CDS contract, but all this work are based on the Markovian approach to risk. In the our opinion this kind of model are too restrictive, because they require that the distribuction function of the waiting times has to be exponential or geometric, for discrete time. In the our model, we describe the evolution of credit rating of the financial subjects like a
counterparty credit risk by defining a new
R
model, so we allow for arbitrarily distributed sojourn time. The age state dependency, typical of the semi-Markov environment, allow us to insert the correlation in a dynamical way. In particular, suppose that A is a default-free bondholder and C is the relative firm. The bondholder buy protection against C's default by another defaultable subject, say B the protection seller. Our model describe the evolution of the credit rating of the couple B and C. We admit for simultaneus default of C and B, the single default of C or single default of B
chain model. Methods are given for computing the transition probabilities, reliability functions and the price of a risky Credit Default Swap