140 CHAPTER 4. UNDERSTANDING FORWARD EXCHANGE RATES FOR CURRENCY
of outcomes on the basis of after-tax returns could be very different from the ranking
on pre-tax outcomes. Beware!
4.4 The Market Value of an Outstanding Forward Contract
tract
In this and the next section, we discuss the market value of a forward contract at its
inception, during its life, and at expiration. As is the case for any asset or portfolio,
the market value of a forward contract is the price at which it can be bought or
sold in a normally-functioning market. The focus, in this section, is on the value of
a forward contract that was written in the past but that has not yet matured. For
instance, one year ago (at timet 0 ), we may have bought a five-year forward contract
fornokatFt 0 ,T =clp/nok115. This means that we now have an outstanding
four-year contract, initiated at the rate ofclp/nok115. This outstanding contract
differs from a newly signed four-year forward purchase because the latter would
have been initiated at the now-prevailing four-year forward rate, clp/nok110.
The question then is, how should we value the outstanding forward contract?
This value may be relevant for a number of reasons. At the theoretical level, the
market value of a forward contract comes in quite handy in the theory of options, as
we shall see later on. In day-to-day business, the value of an outstanding contract
can be relevant in, for example, the following circumstances:
- If we want to negotiate early settlement of the contract, for instance to stop
losses on a speculative position, or because the underlying position that was
being hedged has disappeared. - If there is default and the injured party wants to file a claim.
- If a firm wishes to “mark to market” the book value of its foreign-exchange
positions in its financial reports.
4.4.1 A general formula
Let us agree that, unless otherwise specified, “a contract” refers to a forward pur-
chase of one unit of foreign currency. (This is the standard convention in futures
markets.) Today, at timet, we are considering a contract that was signed in the past,
at timet 0 , for delivery of one unit of foreign currency to you atT, against payment
of the initially agreed-upon forward rate,Ft 0 ,T. Recall the convention that we have
adopted for indicating time: the current date is always denoted byt, the initiation
date byt 0 , the future (maturity) date byT, and we have, of course,t 0 ≤t≤T.
The way to value an outstanding contract is to interpret it as a simple port-
folio that contains afc-denominatedpnwith face value 1 as an asset, and ahc-
denominatedpnwith face valueFt 0 ,T as a liability. Valuing ahc pnis easy: just