Analytic results and weighted Monte Carlo simulations for CDO pricing
2012
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.
Keywords:
- Condensed matter physics
- Physics
- Mathematical optimization
- Dynamic Monte Carlo method
- Monte Carlo molecular modeling
- Monte Carlo methods for option pricing
- Hybrid Monte Carlo
- Quantum Monte Carlo
- Monte Carlo method
- Monte Carlo integration
- Monte Carlo method in statistical physics
- Importance sampling
- Variance reduction
- Applied mathematics
- Correction
- Source
- Cite
- Save
- Machine Reading By IdeaReader
21
References
0
Citations
NaN
KQI