Inflation Adjusted Cash Flow


Given a cash flow amount CF(t) at time t, the Inflation Adjusted Cash Flow is a cash flow CF'(t) that occurs at t and given by the formula:
CF'(t) = CF(t)Q(t)
Q(t) = I(t-lag)/I(t₀) is the index quotient ascribed to time t that is defined as the raw inflation index I(t-lag) that applies at time t-lag divided by the raw inflation index I(t₀) that applies at some fixed initial time t₀
This type of cash flows is used in the
Deriscope Types Inflation Swap and Inflation Bond
Effectively, Q(t) represents the raw inflation index at time t-lag in units of the raw inflation index at time t₀
Note that the raw inflation index I(t) is ascribed to time t but becomes known (published) with a certain delay delay at a later time t+delay
In order to know the index value Q(t) at time t, it must hold that lag >= delay

In most cases, the amount CF(t) is computed but never realized as a cash flow event, whereas the amount CF'(t) is the actually occurred cash flow.
The amount CF'(t) is referred as nominal because it is the number recorded in the corresponding transaction.
The CF(t) is referred as real because it expresses the nominal amount CF(t)Q(t) in real currency units RU that are imaginary units defined as follows:
At each time t, the real currency unit RU is assumed to be equivalent to Q(t) nominal (i.e. regular) currency units NU
So, by definition it holds:
RU = Q(t)NU for every time t
Therefore the nominal amount CF(t)Q(t) paid in nominal currency units NU can be written as CF(t)RU
In words, all this translates to the following two equivalent statements:
At time t CF(t)Q(t) units of the nominal currency NU are paid.
or equivalently
At time t CF(t) units of the real currency RU are paid.

Just like one talks about different economies associated with different currencies (eg the USD or EUR economy), one may also talk about the real and nominal economies associated with the real and nominal currencies.
Similarly, just like one may convert any price or rate from one currency to another, one may also convert a nominal price or rate to its equivalent real one and vice versa.
The corresponding real exchange rate is the ratio of the two currency units, i.e. RU/NU = Q(t)NU/NU = Q(t)
where we used the relation RU = Q(t)NU