I want to calculate the expected rate cut/change given futures contracts on the basic interest rate, knowing when the rate cut occurs (resembling the FED's FOMC). Consider compound rates and a 252 workday-year.
-DI1 is the interest rate's futures contract due to 7 workdays with an annual rate of 11.16% per year; -DI2 is the interest rate's futures contract due to 27 workdays with an annual rate of 11.05% per year; -The committee meeting occurs within 20 workdays. So the daily rate is constant until day 20 and, at day 21, the rate drops to a given target and remains constant until the maturity of the DI2 contract.
How to calculate the expected rate cut? Market expectations are close to a 0,5% annual rate cut (to 10.65% per year). I can work with the reverse calculation, but now without knowing the market expectations' cut.
Daily rates are calculated from effective rates. Consider the example from 11.15% per year: $i_{daily}=(1+0.1115)^{1/252}-1$
I also tried to reverse the forward rates and isolating the $i_{newrate}$ as of: $(1+i_{DI2})^{27/252} = (1+i_{DI1})^{20/252} * (1+i_{newrate})^{7/252} $
However, I'm dealing with average rates over an interval. I need the point estimate of the rate for the second period (from day 21 to 27).