Intensity Gamma: a new approach to pricing portfolio credit derivatives

Paper by Mark S. Joshi and Alan Stacey (2005), published in Risk Magazine, Volume 19, July/August 2006.
Presentation given at Isaac Newton Institute, Cambridge UK, February 2005.

We develop a completely new model for correlation of credit defaults based on a financially intuitive concept of business time similar to that in the Variance Gamma model for stock price evolution. Solving a simple equation calibrates each name to its credit spread curve and we show that the overall model can be calibrated to the market base correlation curve of a tranched CDO index. Once this calibration is performed, obtaining consistent arbitrage-free prices for non-standard tranches, products based on different underlying names and even more exotic products such as CDO2 is straightforward and rapid.

Applying importance sampling to pricing single tranches of CDOs in a one-factor Li model

Paper by Mark S. Joshi (2004).

It is shown that importance sampling can be effectively applied to the pricing of a single tranche of a CDO. In particular, by shifting the mean of the common factor, it is demonstrated that the price can be estimated to an accuracy of approximately one percent with about ten thousand paths in a large range of cases.This is achieved at minimal extra computational complexity.

Rapid computation of prices and deltas of nth to default swaps in the Li Model

Paper by Mark Joshi and Dherminder Kainth (2003), published in Quantitative Finance, volume 4, (2004), pages 266 - 275
Presentation

A paper on computing prices and deltas of nth to default credit default swaps. The effective use of importance sampling is demonstrated. It is shown how to extend the pathwise and likelihood ratio methods to computing deltas in this model. In addition, it is shown that the pathwise method can be used even when the pay-off is discontinuous resulting in speed ups by factors of thousands.