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Analytic results and weighted Monte Carlo simulations for CDO pricing

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  • Marcell Stippinger
  • B\'alint Vet\H{o}
  • \'Eva R\'acz
  • Zsolt Bihary
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    Abstract

    We explore the possibilities of importance sampling in the Monte Carlo pricing of a structured credit derivative referred to as Collateralized Debt Obligation (CDO). Modeling a CDO contract is challenging, since it depends on a pool of (typically about 100) assets, Monte Carlo simulations are often the only feasible approach to pricing. Variance reduction techniques are therefore of great importance. This paper presents an exact analytic solution using Laplace-transform and MC importance sampling results for an easily tractable intensity-based model of the CDO, namely the compound Poissonian. Furthermore analytic formulae are derived for the reweighting efficiency. The computational gain is appealing, nevertheless, even in this basic scheme, a phase transition can be found, rendering some parameter regimes out of reach. A model-independent transform approach is also presented for CDO pricing.

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    File URL: http://arxiv.org/pdf/1105.5416
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1105.5416.

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    Date of creation: May 2011
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    Publication status: Published in EPJ B 85(2):51 11p (2012)
    Handle: RePEc:arx:papers:1105.5416

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    Web page: http://arxiv.org/

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