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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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Do you know the concept of duration? It is an approximation of how much the price of the bond changes if the interest rate (appropriate for the market in which the bond trades) changes. This is the interest rate is used to discount cash flows. It is common to all the bonds in the same market (e.g. German govis). For various reasons (liquidity, credit risk, ...



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