# Non-linear Gaussian sovereign CDS pricing models

*Marco Realdon*

*Quantitative Finance*, 2019, vol. 19, issue 2, 191-210

**Abstract:**
Prior literature indicates that quadratic models and the Black–Karasinski model are very promising for CDS pricing. This paper extends these models and the Black [J. Finance 1995, 50, 1371–1376] model for pricing sovereign CDS’s. For all 10 sovereigns in the sample quadratic models best fit CDS spreads in-sample, and a four factor quadratic model can account for the joint effects on CDS spreads of default risk, default loss risk and liquidity risk with no restriction to factors correlation. Liquidity risk appears to affect sovereign CDS spreads. However, quadratic models tend to over-fit some CDS maturities at the expense of other maturities, while the BK model is particularly immune from this tendency. The Black model seems preferable because its out-of-sample performance in the time series dimension is the best.

**Date:** 2019

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