Kth default time distribution and basket default swap pricing

Abstract

We propose an alternative method of finding the kkth default time distribution in a portfolio with dependency. Analyzing order statistics of independent and identically distributed random variables, we explicitly derive probability distribution function of the kkth default time based on a one factor copula model with the Gaussian copula and the tt copula. Moreover we consider the pricing of portfolio credit derivatives such as the kkth to default swaps and mm out of nn default swaps within our framework. In particular we show the price of a nn out of nn default swap is equivalent to the price of a single-name CDS. In order to test efficiency and accuracy we compare the theoretical prediction between Gaussian quadrature and Monte Carlo simulation.