We have seen up to now only instruments in one specific currency: foreign exchange (FX) forwards are, as one would suspect, cross currency instruments. An FX forward is in practice an agreement to exchange, at some point in the future, fixed (at the time the contract is entered upon) amounts in two different currencies: at some point in the future one party is going to pay N units of currency X and the other party is going to pay M units of currency Y. This type of contract implies that an exchange rate between X and Y in the future is almost always different from the exchange rate today, the spot exchange rate.

FX forwards can be quoted in two ways, as premia, as shown in Figure 2.4a, or outright, as shown in Figure 2.4b. Let us define the spot rate as FXt and the expected exchange rate at some point T in the future, the forward, as FWDT. An FX forward quoted outright, defined as FWDor, is meant to be the expected^{[1]} FX rate in the future itself, that is,

An FX forward quoted as premium, defined as FWDPP, is meant to represent the number of pips one has to add (or subtract) to the spot rate in order to obtain the exchange rate at time T, that is,

The great majority of FX forwards quoted as premia need to be divided by 10,000 however, since that number is driven by the number of significant

FIGURE 2.4 a) Russian Rubles FX forwards quoted in pips; b) Russian Rubles FX forwards quoted outright. Source: Thomson Reuters Eikon.

decimal places in the spot FX rate quote. For less liquid currencies we divide by other multiples of 10, usually smaller.^{[2]}

FFow can FX forwards be used for curve construction? They are used through the application of the interest rate parity, which states that, in principle, for two currencies X and Y we must have

where the FWD is quoted outright and where X/Y means the amount of X we obtain for one unit of Y and where, as before, Dj are the discount factors at time T (Dj in currency Y and Dj in currency X). Unless otherwise specified, all spot and forward exchange rates are quoted versus USD. If we assume that the discount factors in USD are known, we can easily obtain the discount factor in the foreign currency. By setting Y = USD we have

(2.3)

For those thinking that this seems a rather roundabout way of finding discount factors, the reply is that in many emerging countries the FX forward market is the first one to develop or the only one to offer a minimum of liquidity. There is no single reason why this is the case, but a few hypotheses can be formulated. Emerging economies face uncertainty in terms of credit and in terms of institutions. FX forwards are usually short dated, that is, one does not need to agree to a long contract in a risky environment, and they are very simple because they do not have some of the complexity of swaps agreements. Most importantly, FX forwards are fully collateralized in the sense that by exchanging principals simultaneously, the two parties essentially hold a collateral until maturity, and during the life of the trade only (and not always) pay margin calls, that is, amounts needed to correct the transaction should the realized FX rate at the expiration of the contract differ from the one expected at the beginning of the contract.

The attentive reader might have spotted two issues with this approach. The first is that, as we have stressed, interest rate parity works in principle and not always in practice. We shall address this when discussing currency basis swaps. The second is that we assume that the USD curve is known. Since, as we shall see later, there is no official way to construct a curve, two market participants–by building their respective USD curve in different ways–will necessarily obtain two different values for the discount factors in the foreign currency. This can be a very serious problem since, while most of the time the difference can be negligible (one hopes that two market participants agree fairly closely on such an important currency as USD), for some foreign currencies in some special cases it can lead to a large impact.

[1] One should not interpret the term expected as having probabilistic undertones. By expected forward foreign exchange rate, we mean the rate implied by the rates' differential. The rest of the chapter will describe the link between the foreign exchange and the interest rates in each currency.

[2] For example, in the case of NGN, the Nigerian Naira, one needs to divide by 100.

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