PDF Ebook Double Default Correlation
Copula functions have become standard practice for pricing multi-name credit derivatives. Marginal default distributions are often chosen by using a simple deterministic intensity function. It is well known that this approach only generates default time correlation and, apart from jumps due to default events, does not generate correlation between the conditional default intensities, or the conditional spreads. In this paper we consider pricing multi-name credit derivatives taking both default time correlation as well as default intensity correlation into account. This is achieved by defining two common factors, one for each type of correlation.
Further, we derive a fast way to price conditional on default events or survival for the factor model. Default and survival information is translated to information on the common factor. This approach allows us to graph conditional default intensities, or conditional CDS spreads, for simulated scenarios. These simulations show that our model results in a more realistic behavior of the conditional CDS spreads as one can distinguish both credit spread correlation as well as jumps in case of correlated default events.
Over the last decades the credit derivatives market has shown tremendous growth. The latest developments in this market can often be found in products whose payout depends on the default behavior of a portfolio of bonds or loans. Some examples are structured products such as CDOs, CLOs and CBOs, but also n-th to default swaps have gained popularity. The latest developments are the single tranche CDOs, or STCDOs, which involve the sale of a single CDO tranche to an investor. Throughout this paper we will refer to these products as multi-name credit derivatives. These developments have increased the need for pricing models which take default dependencies into account. In order to model default dependencies, a good starting point is the reduced form model, as this has become market practice for modelling single name credit derivatives such as credit default swaps, CDS. One can distinguish two methods to expand these reduced from models to allow for default correlation. The first and most obvious way is to model correlation between the dynamics of the default intensities of obligors directly. However, correlated Brownian motions do not seem to generate much default correlation and thus approaches focussing on jumps in intensities have become popular. Models uing this latter approach are often referred to as infectious default models and examples can be found in Davis and Lo (1999) and Jarrow and Yu (2001).
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PDF Ebook Double Default Correlation
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