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Numerical Tools: Basket Expansions

Chapter
Part of the Applied Quantitative Finance book series (AQF)

Abstract

In the next few chapters, we study some efficient numerical methods for the valuation of large basket credit derivatives. While the approaches are presented in the Marshall-Olkin copula model, most of the numerical techniques are generic and could be used with other copulas as well. The methods presented span a large spectrum of applied mathematics: Fourier transforms, changes of probability measure, numerical stable schemes, high-dimensional Sobol integration, recursive convolution algorithms.

References

  1. T. Bielecki, M. Rutkowski, Credit Risk: Modeling, Valuation and Hedging (Springer, New York, 2002a)Google Scholar
  2. T. Bielecki, M. Rutkowski, Intensity-based valuation of basket credit derivatives, in Mathematical Finance, ed. by J. Yong (World Scientific, Singapore, 2002b), pp. 12–27Google Scholar
  3. D. Duffie, J. Pan, Analytical value-At-Risk with jumps and credit risk. Financ. Stochast. 5, 155–180 (2001)CrossRefGoogle Scholar
  4. J.P. Laurent, J. Gregory, Basket default swaps, CDOs and factor copulas. J. Risk 7(4), 103–122 (2005)CrossRefGoogle Scholar
  5. F. Lindskog, A. McNeil, Common Poisson Shock models: applications to insurance and credit risk modelling. ASTIN Bullet. 33(2), 209–238 (2003)CrossRefGoogle Scholar

Copyright information

© The Author(s) 2017

Authors and Affiliations

  1. 1.LondonUK

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