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I am just wondering if there is any way we could calculate a CDS Spread (not harzard rate) on a CDS curve. Most of the papers that I have come across so far discuss about interpolating the hazard rates using numerical root-finding algorithms by setting the break-even spread to 0. However can I assume that the hazard rates derived this way will give me a "proper" interpolation on the CDS spread? i.e., say if I have the 3 month and 6 month CDS spread, and I need to price the spread for a 4 month CDS, would it be OK if I simply assume the risky PV for the first 3 months is already 0 given the hazard rates that I have derived and just working on figuring out the final one month spread? Is there a direct, nice formula to compute for such a spread given hazard rate using piecewise constant hazard rate assumption between 3 month and 4 month?

Thanks!

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