Analytic results and weighted Monte Carlo simulations for CDO pricing

TL;DR

This paper introduces analytic solutions and importance sampling techniques for efficient Monte Carlo pricing of CDOs, highlighting variance reduction and phase transition phenomena in a tractable intensity-based model.

Contribution

It provides the first exact analytic Laplace-transform solution and reweighting efficiency formulas for a compound Poissonian CDO model, enhancing computational efficiency.

Findings

Analytic Laplace-transform solutions for CDO pricing.

Importance sampling significantly reduces variance in Monte Carlo simulations.

Identification of phase transition regimes affecting model applicability.

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.