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Pricing basket default swaps using quasi-analytic techniques

Author

Listed:
  • Nneka Umeorah

    (North-West University)

  • Phillip Mashele

    (North-West University)

  • Matthias Ehrhardt

    (Bergische Universität Wuppertal)

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.

Suggested Citation

  • Nneka Umeorah & Phillip Mashele & Matthias Ehrhardt, 2021. "Pricing basket default swaps using quasi-analytic techniques," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 44(1), pages 241-267, June.
    • Handle: RePEc:spr:decfin:v:44:y:2021:i:1:d:10.1007_s10203-020-00310-x
    DOI: 10.1007/s10203-020-00310-x
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    4. Koziol, Philipp & Schell, Carmen & Eckhardt, Meik, 2015. "Credit risk stress testing and copulas: Is the Gaussian copula better than its reputation?," Discussion Papers 46/2015, Deutsche Bundesbank.
    5. Rüdiger Frey & Jochen Backhaus, 2008. "Pricing And Hedging Of Portfolio Credit Derivatives With Interacting Default Intensities," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 11(06), pages 611-634.
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