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Analytic results and weighted Monte Carlo simulations for CDO pricing

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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 ∼ 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 formulas 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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Authors and Affiliations

  1. Department of Theoretical Physics, Budapest University of Technology and Economics, 8 Budafoki út, 1111, Budapest, Hungary

    M. Stippinger & É. Rácz

  2. Department of Stochastics, Budapest University of Technology and Economics, 1 Egry J. u., 1111, Budapest, Hungary

    B. Vető

  3. Morgan Stanley Business and Technology Centre, 8 Lechner Ö. fasor, 1095, Budapest, Hungary

    Zs. Bihary

Authors
  1. M. Stippinger
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  2. É. Rácz
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  3. B. Vető
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  4. Zs. Bihary
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Correspondence to É. Rácz.

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Stippinger, M., Rácz, É., Vető, B. et al. Analytic results and weighted Monte Carlo simulations for CDO pricing. Eur. Phys. J. B 85, 51 (2012). https://doi.org/10.1140/epjb/e2011-20429-x

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  • DOI: https://doi.org/10.1140/epjb/e2011-20429-x

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