An Efficient Algorithm for Basket Default Swap Valuation

Efficient algorithms for basket default swap pricing with multivariate Archimedean copulas

“…Applying the hierarchical property of the nested copula, we establish the dependence structure to inner copulas and an outer copula of the underlying portfolio which is composed of several subportfolios. Using sampling methods in Marshall and Olkin (1988) and Joe (1997) for exchangeable and nested Archimedean copulas, we build new algorithms with importance sampling for extreme events such as the kth default before maturity, which extend the results in Chiang et al (2007) to Archimedean copulas and the nested Gumbel copula. The proposed algorithms are simple to implement and guarantee variance reduction via appropriate choices of the importance sampling distributions.…”

“…Our goal is to select L which ensures the kth default event τ k to take place on every generated sample thus reducing the variance. In Chiang et al (2007) a new probability measure is introduced to compute Eq. (7) when the joint distribution (τ 1 , .…”

“…Their method depends on the order in which the default times are generated, which was improved by Chen and Glasserman (2008). Chiang et al (2007) introduced a new algorithm for importance sampling. This paper is organized as follows: Section 2 provides sampling algorithms for exchangeable Archimedean copulas and nested Archimedean copulas.…”