Pricing Credit Derivatives with a Copula-Based Actuarial Model for Credit Risk

MICOCCI, MARCO;MENZIETTI M;MASALA, GIOVANNI BATISTA

2008-01-01

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Abstract

Credit derivatives are financial contracts whose pay-off are contingent on the creditworthness of some counterparts. As was pointed out in some recent works (Mashal & Naldi (2002), Meneguzzo & Vecchiato (2002)), they have become in recent years the main tool for transferring and hedging credit risk. The most complicated of such instruments are the multinames ones. Indeed, these instruments are not quoted (market prices are not available). Besides, we do not posses closed forms for their pricing: we must necessarily set up a Monte Carlo simulation procedure. The key to perform this task consists in modelling correctly multiple defaults. A dependence structure using copulas methods was first set up by Li (2000). In this paper, Li considers time-until-default for each obligor and model their dependence structure through a Student t-copula. Li describes a default for a single obligor through the so-called survival function. This model has been resumed by Mashal & Naldi with the intent to price particular multinames credit derivatives such as nth-to-default baskets. Their model is a hybrid of the well-known structural and reduced form approaches for modelling defaults. After simulating a large number of multivariate times-until-default, one deduces pay-off for our derivative. Finally, the pricing is estimated using standard risk-neutral pricing technology. In the model proposed in this paper, we adopt a more general credit risk framework already developed in Masala, Menzietti & Micocci (2004): hazard rates are random variables whose values follow gamma distributions coherently with Credit Risk Plus; recovery rates themselves are supposed to be stochastic and follow a Beta distribution, moreover credit migrations are allowed. This feature is specific of our model and becomes very important when we treat credit derivatives whose payoff depends on credit spread. Finally, pricing techniques follow the usual course. We conclude then with a numerical application.