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I have a spot curve where the front-end points (1Y, 2Y) have a fixed/float frequency of 3M3M, while the rest of the points are 6M6M. I want to build a full 6M6M curve. My question is: How can I derive 6M6M IRS prices from the 3M3M prices for the 1Y and 2Y tenors, given that I don't have basis swap prices?

Any insights, formulas, or references to relevant literature would be greatly appreciated. Thank you!

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    $\begingroup$ You need basis prices. You cannot do this without them. If you don't have market prices you can guess the basis based on theoretical or historical averages. But if you do that then it will not necessarily align with the market. Ultimately what you are asking is simply impossible. As an analogy your question is equivalent to: "How do I calculate the price of gold from the price of silver given I don't know the silver-gold basis?" $\endgroup$
    – Attack68 ♦
    Commented Aug 6 at 8:38
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    $\begingroup$ From the current 6M IBOR rate (which I assume you can access) you can actually derive what is called the spot 6m 6s3s basis quite trivially for the given time of the publication of the IBOR. This at least gives a reasonable peg for the initial basis at the start of the curves. $\endgroup$
    – Attack68 ♦
    Commented Aug 6 at 8:40

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