Income
Subtype of Job RequestThe income I received by holding the referenced tradable between the given spot date (denoted as 0) and the given horizon date T specified in Horizon Date
It is also part of the PnL Explain table PnLExplain Table that is produced in association with the key PnL Explain when a tradable is priced with the Advanced Pricing model input.
By default, the spot date equals the globally set trade date ( i.e. valuation date) that usually equals today's date.
But if the As Of entry to the function Price exists, the latter date is then regarded as the spot date.
Precisely, I represents an amount regarded as received at T and defined as the sum of the present values as of T of the tradable's cash flows CFᵢ occurring between 0 (excluded) and T (included).
Formally:
I = Σ(CFᵢ(Pᵢ/P))
where:
CFᵢ are all realized cash flows occurring at times Tᵢ such as 0 < Tᵢ <= T, as implied by the market information available at T.
Pᵢ are the respective funding discount factors, i.e. the discount factors seen at 0 with maturities Tᵢ, as implied by the curve associated with the issuer supplied in Fund Crv Issuer
P is the funding discount factor seen at 0 with maturity T, as implied by the curve associated with the issuer supplied in Fund Crv Issuer
This definition is very similar to that of Carry
The only difference is that the cash flows CFᵢ in the case here are NOT implied by the information available at 0, but represent the ACTUAL (i.e. realized) cash flows in the referred time interval.
It turns out, the calculation of I requires the prior knowledge of all fixings that affect the cash flows occurring at or before T.
These must be provided to the function Price as an input object of type Historical Values entered in association with the key Horizon Market
Note, the computation also depends on the setting for Accr Before Hor