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Given that you have swap rates and Cap prices (ATM, I assume), you can back out the IVs for the time periods using by bootstrapping. Strictly speaking, you would need Caplet prices for the given strikes. In such a case, You would look at the shortest dated cap and (assume) it is made up of only one caplet. You can then use black's formula and back out ...


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Thanks to my research leader, I found what I missed. $V_{0,1}$ is vol of swaption that matures at $T_0$ which is not 0 (as I thought), rather it is maturity of the first libor. So $V_{0,1}$ is the closest available point on market. And now this is all clear with table on page 323 in section 7.4. $V_{0,2}$ is realy vol of swaption that matures at $T_0$=1y ...



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