Limits of Gaussian Proxy Integration for CDO Expected Loss

Summary

The document concerns expected-loss calculations for a collateralized debt obligation using the proxy distribution algorithm from Shelton's “Back To Normal” paper. The questioner is unable to reconcile their results with the standard recursion method and asks for working code. The reply does not provide code; instead, it identifies limitations and an integration detail that affect the calculation.

Proxy integration is an approximation and can differ substantially from recursion for thin tranches or when loss variance is extremely small or large. The reply also says the Gaussian proxy integral should begin at negative infinity rather than at zero to obtain the correct portfolio expected loss. These points are implementation guidance, not a validation against specific data or a complete algorithm. Users applying the proxy method should compare it with recursion and take particular care when tranche thickness or loss variance makes approximation error more pronounced.

Key ideas

• Gaussian proxy integration approximates the standard recursion method for CDO loss calculations.
• The approximation can deviate substantially for thin tranches and at extreme loss variances.
• The proxy integral should begin at negative infinity to calculate portfolio expected loss correctly.
• The document provides cautions but no code example or empirical validation.

Tags

# Any example code implementing the Shelton CDO 'Back To Normal' Paper?


# Any example code implementing the Shelton CDO 'Back To Normal' Paper?












I'm having a hard time getting my expected loss calculations to tie out with the standard recursion method when implementing the proxy distribution algorithm described by the Back To Normal CDO paper by Shelton.

Anyone have working code examples for this?

## Answer by quant_dev (score 2)

https://quant.stackexchange.com/a/769

Proxy integration is just an approximation which can deviate pretty strongly from the recursion algorithm for thin tranches or extremely large/small loss variances. Proceed with caution.

Also: when you integrate the Gaussian proxy, do you start from $-\infty$ or from 0? Counter-intuitively, you should start from $-\infty$ to get the correct portfolio expected loss.

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