Considering a simple future as an example for what the ECL could be, we get the
following result: Using the cash flow notation introduced above, every clean cash
flow on day k can be written as: CF(d, k)óCFfix (d, k)òCFvar(d, k) with CFfix(d, k) ó0.
(We are not considering the initial margin in this example for the sake of simplicity.)
When we are looking for the ECL we try to determine the value of the CF(d, k).
Assuming that we are trying to make a forecast for a special day k in the future, we
have in general the possibilities:
either CFvar(d, k)[0
or CFvar(d, k)ó0
or CFvar (d, k)\0
Assume there is no arbitrage possible in this market and CFvar(d, k)[0. As the future
price is its own forward, one could enter into this instrument at a zero price and
generate a risk-free profit by simply selling it at CFvar(d, k)[0. For the complementary
reason the cash flow cannot be CFvar(d, k)\0. That means CFvar(d, k)ó0 must be the
ECL for a future cash flow (i.e. it is the most likely value of a forward ‘future’ cash
flow).
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