Benchmarking collateral of triple-a rated securities

ABSTRACT

This paper presents a simple method to estimate the collateral associated with a Aaa tranche. The method is similar to historical simulation in the sense that there are no specific distributional assumptions, and the data fully determine the characteristics of the distribution. Both the transparency and simplicity of our method provide a valuable benchmark to existent tail of the distribution modelling. As a benchmark, our method also serves to validate collateral estimates for Aaa-rated securities as well as to validate capitalization models of financial institutions.

KEYWORDS:

• Non-parametric estimator
• probabilities of default distribution
• collateral
• tail of the distribution

JEL CLASSIFICATION:

• C14
• C15
• C52
• G22

Disclosure statement

No potential conflict of interest was reported by the author.

Notes

¹ While rating agencies methodologies are proprietary, there are a myriad of methods that forecast default probabilities. Bharath and Shumway (2007) compare structural models (Merton type models) to forecast default probabilities, while Agarwal and Taffler (2008) compare structural versus reduced form methods.

² Lopez and Saidenberg (2000) examine the challenges in validating and backtesting credit models and propose evaluations methods. Benchmarking is, therefore, the most feasible tool to validate estimates at the fat off tail of the distribution.

³ For example, the empirical bootstrap is recommended as a benchmark for operational risk capital models in US Advanced Measurement Approach guidance – see Board of Governors of the Federal Reserve System (2014), Basel Coordination Committee Bulletin 14–1.

⁴ See https://www.moodys.com/sites/products/DefaultResearch/2007400000578875.pdf.