I have obtained a Ibor-6Months curve using bootstrapping techniques. For the short-term of the curve I used spot, for the middle-term FRAs and for the long-term IRS.
The curve that I have obtained is given in discount factors...(using the configuration detailed above). The question is, how can I now obtain the zero rate curve once the discount factors are known?
Shall I use equation (1):
Or shall I use equation (2):
where $\alpha$ refers to the year fraction and $r$ is the zero rate, $t$ is the actual time and $T$ is the maturity time.
Is the equation the same for any tenor (taking into account that the instruments involved are different)? I would say IRS tenors follow the equation (2) while spots or FRA tenors follow the equation (1).
Any comments are welcome! Thank you very much in advance.