On Pricing Basket Credit Default Swaps

TL;DR

This paper introduces a fast, analytical method for calculating ordered default time distributions in basket credit default swaps, improving efficiency and accuracy over traditional Monte Carlo simulations.

Contribution

The paper develops a recursive, analytical approach for ordered default time distributions in both homogeneous and heterogeneous models, enhancing computational speed and precision.

Findings

Analytical formulas enable faster computation of default probabilities.

Method outperforms Monte Carlo in valuation accuracy.

Inclusion of decay and multistate processes improves model realism.

Abstract

In this paper we propose a simple and efficient method to compute the ordered default time distributions in both the homogeneous case and the two-group heterogeneous case under the interacting intensity default contagion model. We give the analytical expressions for the ordered default time distributions with recursive formulas for the coefficients, which makes the calculation fast and efficient in finding rates of basket CDSs. In the homogeneous case, we explore the ordered default time in limiting case and further include the exponential decay and the multistate stochastic intensity process. The numerical study indicates that, in the valuation of the swap rates and their sensitivities with respect to underlying parameters, our proposed model outperforms the Monte Carlo method.