The U.S. risk-free rate is 2.96%, the Japanese yen risk-free rate is 1.00%, and the spot exchange rate between the United States and Japan is $0.00757 per yen. Both rates are continuously compounded. The price of a 180-day forward contract on the yen and the value of the forward position 90 days into the contract when the spot rate is $0.00797 are closest to:
answer is $0.00764 $0.00037
not getting it right any one getting this answer?
For such small rates it makes little difference whether the compounding is continuous or not. It also makes little difference whether they use 360 days or 365 days per year. Finally, it’s unclear whether they mean that 2.96% and 1.00% are the continuously compounded rates or the effective annual rates; guess what? (You got it: it makes little difference.)
I’ll assume 360 days per year and that the rates given are the continuously compounded rates. To get the 180-day forward rate, we calculate:
USD0.00757/JPY1.0 × (e^(2.96% × (180/360))) / (e^(1.00% × (180/360)))
= USD0.007645/JPY1.0.
For the value to the JPY receiver after 90 days when the spot rate is USD/JPY 0.00797, we calculate:
(USD0.00797/JPY1.0) / (e^(1.00% × ((180 – 90)/360)))
– (USD0.007645/JPY1.0) / (e^(2.96% × ((180 – 90)/360)))
= USD0.000362/JPY1.0.
I thought currency forward/future are solved with 365 days a year
I didn’t recall off the top of my head, and was too lazy to look it up. As I say, it really doesn’t make a difference. I’d encourage you to redo my calculations using 365 days per year to see the effect.