From Principle-Based Risk Management to Solvency ... - Scor

on the portfolio itself and on the allocation method selected. It will thus, in
general, not be unique. In fact, it is reasonable to require of the allocation
the property that the sum of the individual values is equal to the overall
value. However, this will normally not uniquely determine the allocation
method, and additional requirements will have to be imposed.
The view that the value is defined only with regards to a balance sheet
makes sense when considering the values of produced physical goods: The
price of a good has to take into account all assets of the producing factory
(such as machines, buildings, . . . ) required to produce the good, as well as
all other goods produced by the factory.
There are, however, two aspects not yet considered: perfect replication
may not be possible; and the asset side of the actual balance sheet might
not be equal to the (perfect or imperfect) replicating portfolio. Both aspects
introduce a mismatch between asset and liability side, and are relevant for
the SST.
2.1.2 Imperfect Replication – Optimal Replicating Portfolio,
Basis Risk, Law Replication
We now focus on the valuation of insurance and reinsurance liabilities. In
view of the preceding Section 2.1.1, the value of the whole liability side of an
economic balance sheet is derived by (perfect) replication, and the value of
an individual liability in the balance sheet is derived by allocation from the
value of the whole liability side. In the context of the pricing of reinsurance
contracts, the corresponding allocation methodology we use is described in
Section 8.3 (pp. 168). A comparison of the valuation approaches in the SST
and in (non-life) pricing is given in Section 2.3.3.
Note that the value of the whole liability side of an economic balance
sheet is not independent of whether additional liabilities are added to the
balance sheet in the future. The assumption underlying the calculation of
the value of the liabilities thus has to be that no such additional liabilities
are added in the future.
Typically, insurance and reinsurance liabilities cannot be perfectly replicated.
By definition, this means that the cash flows cannot be replicated
for every state of the world by a portfolio of deeply and liquidly traded
instruments.
An optimal replicating portfolio (ORP) denotes a portfolio of deeply and
liquidly traded instruments “best replicating” the cash flows of the liabilities.
We call the mismatch between the actual liability cash flows and the ORP
cash flows the basis risk. We keep open for the moment what exactly is
meant by “best” replication; the idea is to minimize the basis risk. Note that
the condition that the ORP instruments be deeply and liquidly traded is, of
course, essential; otherwise, one could just select the liabilities themselves
for the ORP and have no basis risk left.
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