Pricing basket default swaps using quasi-analytic techniques

Nneka Umeorah (), Phillip Mashele () and Matthias Ehrhardt ()
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Nneka Umeorah: North-West University
Phillip Mashele: North-West University
Matthias Ehrhardt: Bergische Universität Wuppertal

Decisions in Economics and Finance, 2021, vol. 44, issue 1, No 15, 267 pages

Abstract: Abstract This research work is based on the concept of the one-factor copula model together with the discrete Fourier transform, which is applied to reduce the dimensionality problems associated with the basket default swap pricing. We employ the Gaussian, the student-t and the Clayton one-factor copula to estimate the conditional probability of default. Incorporating the Fourier transform together with the distribution function of a counting process, we derive the quasi-analytical expression for the computation of the swap payment legs. We compute the conditional characteristic function for the corresponding portfolio loss distribution using the fast Fourier transform. Then, employ numerical integration with the aid of the inverse fast Fourier transform to retrieve the distribution function or the unconditional characteristic function. Our results show that in the absence of the trending simulation method, a semi-analytic method which involves the applications of the discrete Fourier transform can be utilized to price the basket credit default swaps.

Keywords: Discrete Fourier transform; Fast Fourier transform; Copulas; Convolution; Basket default swaps; Characteristics function; Probability distributions (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10203-020-00310-x

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