Get Implied Rate
Function Get Implied Rate within Infl Curvereturns the inflation rates implied by the inflation curve for the provided dates.
First, for a given input date T, the corresponding index observation date T' is calculated as foillows:
If the inflation curve has Interp Index = true then T' = T - Δt, where Δt is the supplied Observation Lag.
For example, if T = 20 July 2020 and Δt = 2 months, then T' = 20 May 2020.
If the inflation curve has Interp Index = false then T' is moved even more backwards in time to equal the date when the related inflation index applies.
In the example above, T' would be set to 1 May 2020, assuming the inflation index is set on the first day of each month.
Subsequently, the time t between the valuation date (typically today's date) and T' is calculated as year fraction using the inflation curve's daycount convention.
Finally the rate implied by the curve for the time t is returned.
If the inflation curve has Quote Type = Relative, each returned rate equals the zero inflation rate and is essentially the fair rate for the corresponding zero-coupon inflation swap.
The zero inflation rate r on a given time T is defined as:
I(T)/I(T₀) = (1+r)ᴸ⁽ᵀ⁻ᵀᵒ⁾
where T₀ is the base date of the inflation curve as given by _Base Date and L(T-T₀) is the year fraction of the time interval from T₀ to T
If Quote Type = YoY Rate, each returned rate is produced by the QuantLib function "yoyRate" and is the corresponding year-on-year inflation rate.
The year-on-year inflation rate YoY(T) on a given time T is defined as:
YoY(T) = I(T)/I(T-1Year) - 1
as described at Year-On-Year Inflation Swap