Eur. Phys. J. B (2012) 85: 51
https://doi.org/10.1140/epjb/e2011-20429-x

Regular Article

Analytic results and weighted Monte Carlo simulations for CDO pricing

¹ Department of Theoretical Physics, Budapest University of Technology and Economics, 8 Budafoki út, 1111 Budapest, Hungary
² Department of Stochastics, Budapest University of Technology and Economics, 1 Egry J. u., 1111 Budapest, Hungary
³ Morgan Stanley Business and Technology Centre, 8 Lechner Ö. fasor, 1095 Budapest, Hungary

^a e-mail: racze@phy.bme.hu

Received: 5 June 2011
Received in final form: 29 August 2011
Published online: 8 February 2012

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.