Fundamental assets

For the purposes of this exposition, it will be convenient to take certain asset prices
as risk factors. We will term these fundamental assets. In what follows, we will see
that this choice leads to an elegant formalism for the subsequent problem of
estimating the distribution of portfolio value.
We propose using three types of fundamental assets:
1 Spot foreign-exchange (FX) rates. We fix a base currency. All other currencies will
be termed foreign currencies. We express spot prices of foreign currencies as the
value of one unit of foreign currency in units of base currency. For example, if
the base currency were USD, the value of JPY would be in the neighborhood of
USD 0.008.
2 Spot asset prices. These prices are expressed in the currency unit that is most
natural and convenient, with that currency unit being specified as part of the
price. We term this currency the native currency for the asset. For example,
shares in Toyota would be expressed in JPY. Commodity prices would generally be
expressed in USD, but could be expressed in other currencies if more convenient.
3 Discount factors. Discount factors for a given asset, maturity, and credit quality
are simply defined as the ratio of the value of that asset for forward delivery at
the given maturity by a counterparty of a given credit quality to the value of
that asset for spot delivery. The most common example is discount factors for
currencies, but similar discount factors may be defined for other assets such as
commodities and equities. Thus, for example, we express the value of copper for
forward delivery as the spot price of copper times a discount factor relative to
spot delivery.
In the abstract, there is no essential difference between FX rates and asset prices.
However, we distinguish between them for two reasons. First, while at any given time
we work with a fixed base currency, we need to be able to change this base currency
and FX rates need to be treated specially during a change of base currency. Second,
it is useful to separate out the FX and asset price components of an asset that is
denominated in a foreign currency.