Evaluating Cross-Sectional CDS Hazard Rate Models for CVA
Summary
The document describes a proposed cross-sectional regression for estimating credit default swap spreads, or their implied hazard rates, when a counterparty has no liquid CDS. The setup uses liquid CDS observations at a given tenor, with the logarithm of hazard rates as the response and categorical characteristics such as geography, rating, and industry as explanatory variables. It suggests estimating coefficients by ordinary least squares, then applying the fitted relationship to illiquid cases.
The question focuses on assessing model quality, especially out of sample predictions, beyond significance, residual normality, multicollinearity, and goodness of fit. No validation procedure or results are supplied, so the text frames a modeling problem rather than presenting a tested solution. In particular, it leaves open how to evaluate predictive accuracy, data representativeness, or the suitability of the assumed error distribution for CVA use.
Key ideas
- A cross-sectional regression can proxy hazard rates for counterparties with illiquid CDSs.
- The proposed response is the logarithm of hazard rates for liquid CDSs at a specified tenor.
- Geography, credit rating, and industry are candidate explanatory variables.
- The document asks how to assess out of sample prediction performance beyond standard regression checks.
- No validation findings or recommended evaluation procedure are provided.
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Full text
# Assessment of cross-sectional regression model for CDS spreads of CVA calculations
# Assessment of cross-sectional regression model for CDS spreads of CVA calculations
For the purposes of the CVA calculation, someone might need to proxy the CDS spreads (and their associated implied hazard rates) for counterparty cases with illiquid CDSs.
A common approach (leaving outside the whole bootstrapping procedure) followed by the banking industry is a cross sectional regression of the following form, trained or estimated on a sample derived from liquid CDSs:
$$\boldsymbol{y_{\tau}}= \boldsymbol{X_{\tau}} \boldsymbol{\beta_{\tau}} + \boldsymbol{\varepsilon_{\tau}}, \quad \varepsilon_{\tau,i}\sim N(0,1)$$
where
- $\boldsymbol{y}$ is an $n \times 1$ vector containing the natural logarithms of the hazard rates of each liquid CDS $i$ for a specific tenor $\tau$.
- $\boldsymbol{X}$ is an $n \times k$ matrix containing instrumental/dummy variables like geographical location, rating or industry that correspond to the liquid CDSs. First columns of the matrix consists of ones (intercept).
- $\boldsymbol{\beta}$ is the $k \times 1$ vector of the coefficients, including the intercept, which should be estimated via OLS.
- Finally, the vector $\boldsymbol{\varepsilon_{\tau}}$ contains the error terms which follow the standard normal distribution.
My (open) question is, apart from the "usual" checks about the statistical significance of the parameters, the normality of the residuals, the multicollinearity, the goodness of fit, etc. are there any other aspects of such a regression model that can be assessed or checked (and how), especially about the performance of its out of sample "predictions" $\boldsymbol{\hat{y_{\tau}}}$?Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.