Basic Insights in Pricing Basket Credit Derivatives

Basket credit derivatives are those financial contracts whose payout depends on the credit events ("failure to pay", "default", et cetera) characterising a portfolio of bonds or loans over a determined time horizon. We have two main categories of basket credit derivatives. The first is characterised by a payout depending on the temporal ranking of the credit events: first-to-default, second-to-default, et cetera. The second is characterised by a payout depending on the percentiles of the portfolio's loss distribution induced by the credit events. The latter is often embedded in securitisations of portfolios of bonds or loans, i.e. CDO. This paper proposes some basic insights in the pricing of these particularly complex credit derivatives. Whenever possible, we will try to find an analytical approximation to the exact pricing formula, if a closed form solution is not available. The complexity of modelling the loss distribution of a portfolio of assets has been simplified. Duffie and Singleton, among the others, have showed how to build multi-factor affine models for a credit curve. However, we will remain a step behind the state-of-the-art in analytical modelling. In fact, we haven't addressed the crucial problems of parameters' estimation and we are not sure of the way in which one should treat in practice the uncertainty surrounding those estimates. The reader should then be aware that the proposed solution, apart from being in many cases an approximate one, is just a starting point in the difficult task of assessing the fair value of a basket credit derivative