Do we always use the Immunization Rate as a discount rate to calculate the PVL (present value of liability) and YTM as a discount rate to find out the Present Value of Asset?
In the example provided by the Kaplan Note for “Contingent Immunization” on page 225 if you have it.
They used 4% (immunization rate) in the fist example to discount the FVL to find out PVL (present value of liability)
In the second situation they mentioned on the same page, they used 3.9% (YTM) to discount the Future value of asset to find out the “Present value of asset”.
I know which rates to use but I dont understand why we semi-annualize the immunization rates. That doesnt make sense to me if the immunization rate is based off of a zero-coupon bond.