Good day, I gave following inputs of Libor rates :
ON 0.3731 1W 0.3939 1M 0.4265 2M 0.5148 3M 0.6176 6M 0.8655 1Y 1.1336
How can I build zero-rate curve ?
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The short answer is - you need more data.
If you want to build a full zero-rate swap curve, typically these curves go out to 30 years.
In general, the front of the curve is made from LIBOR rates, which you have. Typically you don't see practitioners use anything past the 3M point but some will use up to the 6M point.
For the 2nd part of the curve, from 6M to at least 2-years, you will need to imply rates from Eurodollar futures. There are a few places to get contract prices for these (CME and Quandl being two of them).
The the final part of the curve you will need to imply zero rates using par (at the money) fixed-float swaps. I don't know of a great place to get these rates other than bloomberg, although Quandl (mentioned above) may have a datasource.
Once you have data, there are many answers to curve-building questions such as this.
To construct a zero rate curve the first step needed is to build a IR curve using Cash,FRAs/Future,Swap rates. Second step is to form a Discount factor curve from these rates which is continuous(as the IR curve built is non continuous due to Future). Third step is to compute Zero curve from this discount curve which will be continuous in nature and ca be used for generating cash flows.