Valuation of credit default swaps via Bessel bridges

A credit default swap (CDS) is a financial contract in which the holder of the instrument will be compensated in the event of a loan default. When available, CDS's are used to monitor the credit risk of countries and companies. In this work we develop a closed form procedure to value a CDS in the case in which the so-called "credit rate index" is modelled as a Bessel bridge of arbitrary order. In particular, these processes seem to capture the nature of a defaultable asset in the sense that they remain strictly positive before default, and thus enrich the existing literature in this field.