Furthermore, currency options’ implicit volatilities do appear to forecast future exchange rate volatility reasonably well in general — in contrast to those from stock or stock index options.6 Consequently, setting implicit forward variances
equal to the probability-weighted average of the zero value expected conditional upon currency union, and a higher estimated value conditional upon EMU not occurring, would appear a natural and direct way of assessing the probability of EMU transpiring fully.

The major difficulty with this approach is data availability. Interbank options on pound/DM, DM/FF, and DM/lira are actively traded, but primarily only for maturities of up to one year. International convertible bonds such as those studied by Jennergren and Naslund (1990) often contain longer-maturity intra-European cross-rate options, but extracting implicit option prices is severely complicated by the plethora of bond-specific features. Consequently, the effective absence until 1998 of data on actively traded options maturing after January 1, 1999 has precluded the construction of EMU calculators based upon intra-European currency options. Some studies have, however, used such options to assess developments in the run-up to the currency union; notably Campa, Chang, and Reider (1997), Butler and Cooper (1997), and Adao, Cassola, and Luiz (1998).

Even if the data were available, implicit volatility-based EMU calculators would suffer from many of the difficulties of the interest rate-based calculators discussed below. The major issue is estimating what cross-rate volatility would be conditional upon a specific country failing to join the EMU. If, for instance, non-members nevertheless fix their exchange rates against the Euro-bloc countries (Butler and Cooper’s ERM-2 scenario), the EMU and non-EMU cross-rate volatilities are virtually identical and EMU probability computations are infeasible. Nevertheless, using currency options to assess shifts in exchange rate regimes is a more direct approach than inferring shifts in regimes from bond yields, and it is regrettable that the data are not readily available.

Term structure-based EMU probability calculators

Theoretical foundations

The equilibrium approach to bond pricing exemplified by Cox, Ingersoll, and Ross (1985a,b) identifies zero-coupon bond prices of maturity T as
Equivalently, the forward rate ft,T contractible now for instantaneously depositing or borrowing T periods hence is given by
The basic EMU probability calculator approach implemented inter alia by De Grauwe (1996), J.P. Morgan (1997) and Favero, Giavazzi, Iacone, and Tabellini (1997) uses the interest rate forecasts inferred from intra-European forward rates to assess the probability of any two countries entering into a currency union. For instance, if both Germany and Italy enter into a permanent currency union, the elimination of currency risk implies that DM and lira Italian money market deposits and loans become perfect substitutes, with identical interest rates. By contrast, a failure to achieve currency union implies a gap, presumably positive, between Italian and German interest rates. The Marshallian expectations hypothesis ftT 9 Et(rt+T), combined with a particular estimate of the expected future interest rate spread conditional upon EMU not occurring (NEMU), yields a method of inferring the probability of EMU occurring from observed forward rate differentials: