Credit Derivatives Papers

Analysis of new Regulatory Proposals for Capitalisation of Securitisations

Paper by Shalom Benaim, Dherminder Kainth and Manuel Losi (2013).

We explain and analyse the modelling and other assumptions behind the new regulatory proposals for capitalisation of securitisations, in particular the modified supervisory formula (MSFA) and the revised rating based approach (RRBA). We examine the impact of the different assumptions, and find that the underlying modelling approach is generally reasonable. However, we find that the additional overlays applied to the calculation, rather than the modelling assumptions per se, lead to excessively high estimates of the capital in many cases (in the sense that the requirement is significantly higher than any reasonable model would predict) and do not account for model risk in a risk sensitive way.

Fast CDO Tranche Pricing using Free Loss Unit Approximations

Paper by Douglas Muirden (2011).

Volatility in Credit Markets has highlighted that effective risk management of a CDO tranche trading book requires analysis across a wide range of potential scenarios. The Basel III Comprehensive Risk Measure (CRM) requires repricing a trading book over many thousands of simulations, while counterparty risk calculations such as Potential Future Exposure (PFE) are generally analyzed by revaluation across a wide range of future scenarios. Fast CDO tranche pricing has therefore become increasingly important. In many cases accuracy can be sacrificed for speed, but previously documented approximations are too inaccurate or are not applicable to the random recovery valuation models currently in use by most banks. This paper presents an approximation which retains high accuracy in extreme cases, and can be used efficiently with random recovery models and inhomogeneous portfolios.

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

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.