GARP.FRM.PQ.P1 No arbitrage FX market (garp13-p1-6)

[Bester]

Hi,

Can you please help me understand why the answer uses continuously compounded rates and not annual rate. In this question the answer is the same whether using continuosly or annual compounding, but may not always be the same.


Question

You are examining the exchange rate between the U.S. dollar and the euro and are given the following information regarding the USD/EUR exchange rate and the respective domestic risk-free rates:

Current USD/EUR exchange rate is 1.25

Current USD-denominated 1-year risk-free interest rate is 4% per year

Current EUR-denominated 1-year risk-free interest rate is 7% per year

According to the interest rate parity theorem, what is the 1-year forward USD/EUR exchange rate?

a. 0.78

b. 0.82

c. 1.21

d. 1.29

Correct answer: c

Explanation: The forward rate, FT, is given by the interest rate parity equation:

Ft =S0 * e(r-rf)T

where

S0 is the spot exchange rate, r is the domestic (USD) risk-free rate, and rf is the foreign (EUR) risk-free rate

T is the time to delivery

Substituting the values in the equation:

Ft = 1.25 * e(0.04-0.07) = 1.21

 

[ShaktiRathore]

Hi
There is difference when discrete rate is used
Ft=1.25*(1.04/1.07)=1.215~1.22(rounding)
Using continoues compounding Ft=1.25*exp(.04-.07)=1.213~1.21
Here continous compounded rates are given,not discrete rates. It should have been mentioned in the question that rates are continous or discrete.
Thanks