Fast and Robust Monte Carlo Cdo Sensitivities and Their Efficient Object Oriented Implementation

32 Pages Posted: 1 Jun 2005

See all articles by Marius G. Rott

Marius G. Rott

Independent

Christian P. Fries

Ludwig Maximilian University of Munich (LMU) - Faculty of Mathematics; DZ Bank AG

Date Written: May 31, 2005

Abstract

In this paper we present a simple yet generic method for fast and robust Monte-Carlo calculation of sensitivities of Collateralized Debt Obligations (CDOs). The method is product independent and only relies on four pricings against modified models. From a modeling perspective the method is also fairly general as it only relies on the availability of a conditional cumulative distribution function for the default time. In our presentation we concentrate on conditional independent loss models as given in [Li2000].

The method we propose in this paper is generic and allows for an equally generic object oriented implementation which is highly efficient with respect to calculation performance and coding time (time to market). We present the design pattern of a stochastic iterator, the default time iterator, to create a highly flexible product implementation framework in which any product may become the underlying of any other product. Our benchmark calculations indicate that our method improves calculation time by a factor of around 1000 compared to brute force finite differences. The coding of a new product still remains on a plug-and-play level with very short development time.

Keywords: Monte Carlo, CDO, Sensitivities, Greeks, Li Model, Likelihood Ratio, OO

JEL Classification: C63, G13

Suggested Citation

Rott, Marius G. and Fries, Christian P., Fast and Robust Monte Carlo Cdo Sensitivities and Their Efficient Object Oriented Implementation (May 31, 2005). Available at SSRN: https://ssrn.com/abstract=732564 or http://dx.doi.org/10.2139/ssrn.732564

Christian P. Fries

Ludwig Maximilian University of Munich (LMU) - Faculty of Mathematics ( email )

Theresienstrasse 39
Munich
Germany

DZ Bank AG ( email )

60265 Frankfurt am Main
Germany