Earlier we outlined the VaR calculation for assets whose prices could be expressed
in terms of fundamental asset prices. Practical considerations limit the number of
fundamental assets that can be included as risk factors. In particular, it is not
feasible to include discount factors for every possible maturity. In this section, we
look at approximating assets not included in the set of fundamental assets by linear
combinations of fundamental assets. As a concrete example, consider the mapping
of future cashflows. The fundamental asset set will contain discount factors for a
limited number of maturities. For example, RiskMetrics datasets cover zero-coupon
bond prices for bonds maturing at 2, 3, 4, 5, 7, 9, 10, 15, 20, and 30 years. To
compute VaR for a real coupon-bearing bond, it is necessary to express the principal
and coupon payments maturities in terms of these vertices. An obvious approach is
to apportion exposures summing to the present value of each cashflow to the nearest
maturity or maturities in the fundamental asset set. For example, a payment of USD
1 000 000 occurring in 6 years might have a present value of USD 700 000. This
exposure might be apportioned to exposures to the 5- and 7-year discount factors
totaling USD 700 000.
In the example given in the preceding paragraph, the condition that the exposures
at the 5- and 7-year points sum to 700 000 is obviously insufficient to determine
these exposures. An obvious approach would be to divide these exposures based on
a simple linear interpolation. RiskMetrics suggests a more elaborate approach in
which, for example, the volatility of the 6-year discount factor would be estimated by
linear interpolation of the volatilities of the 5- and 7-year discount factors. Exposures
to the 5- and 7-year factors would then be apportioned such that the volatility
obtained from the VaR calculation agreed with the interpolated 6-year volatility. We
refer the interested reader to Morgan and Reuters (1996) for details.
Summary of mapping procedure
At this point, it will be useful to summarize the mapping procedure for asset flows
in a systematic way. We want to map a spot or forward position in an asset. This
position is characterized by an asset identifier, a credit quality, and a maturity. The
first step is to compute the present value (PV) of the position. To do so, we need the
following information:
1 The current market price of the asset in its native currency.
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