Explanation:
Continuous compounding:
Spot * exp(rate_domestic * T) = Forward * exp(rate_foreign * T), such that:
rate_foreign = LN[Spot * exp(rate_domestic * T) / Forward] * 1/T =
LN[1.40 * exp(1% * 1.5) / 1.35] * 1 / 1.5 = 3.4245%.
In the same way, we can use the cost of carry model:
Forward = Spot * exp[(rate_domestic - rate_foreign) * T], such that:
rate_foreign = rate_domestic - LN(Forward / spot) * 1/T = 1.0% - LN(1.35 / 1.40) * 1 / 1.5 = 3.4245%
Annual compounding:
Spot * (1 + rate_domestic)^T = Forward * (1 + rate_foreign)^T, such that:
rate_foreign = [Spot * (1 + rate_domestic)^T / Forward]^(1/T) - 1. In this case,
rate(EUR) = [1.40 * (1.01)^1.5 / 1.35]^(1/1.5) - 1 = 3.478%
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Q-194.3. The spot exchange rate EUR/USD is $1.40. The 18-month forward exchange rate is EUR/USD $1.35. If the short-term US interest rate is flat at 1.00%, what is the 18-month Eurozone interest rate implied by (covered) interest rate parity (IRP) if we assume continuous compounding? As a bonus, also solve under an assumption of (discrete) annual compounding.
A
0.87%
B
1.45%
C
2.38%
D
3.42%
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