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There is no such thing as a "proper" interpolation of CDS spreads. The only criterium your interpolation must obey is the absence of arbitrage. Note that, assuming that $spread(3M) < spread(6M)$, $spread(4M)$ can take any value between $spread(3M)$ and $spread(6M)$ without creating an arbitrage opportunity (actually it can be even slightly less than ...

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I believe that your problem can be formulated as: Find PD matrix that is as close as possible to a given PD matrix (result of some previous calibration, or the matrix computed using average hazard rate, or any other "target", or the penalty on non-smoothness) subject to the following constraints: The values that are given must be matched exactly ...

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The typical approach is to try to fit a ratings migration matrix to available rating transition data. If default rates are all you have then that's going to be difficult. Instead, I might try to fit a separate reduced form credit model on survival probability $P_\ell$ for each rating $\ell$ by fitting the function  P_\ell(T) = \exp\left( -\int_0^T h(t) ...

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I worked for a company where we had a similar problem with a volatility surface. I tried applying LOESS to it, but it didn't work. The final result has to conform to some obvious monotonicity restrictions and if that is not built into the smoothing method there will always be some odd points in the end. Another problem is that smoothing typically allows the ...

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