Suppose continuously compounded changes in the spot rate St$/ are independently and identically distributed (iid) as normal.

Question:

Suppose continuously compounded changes in the spot rate St$/¥ are independently and identically distributed (iid) as normal. The relation between the variance 2 of continuously compounded iid normal returns over a single period (e.g., one year) and the variance of return T2 over T periods is given by T2 = T2.
a. If the standard deviation of continuously compounded spot rate changes is 40% per year, what is the standard deviation of three-month (T = 0.25) changes in the spot rate in continuously compounded returns? If the current spot rate is $0.0100/¥, find the exchange rates that are plus or minus three standard deviations from this after one year.
b. Suppose you collect 52 weeks of spot exchange rates S$/SFr. The standard deviation of continuously compounded spot rate changes is 1.5% per week.
b-1. Assuming instantaneous (continuously compounded) spot rate changes are normally distributed with constant variance, what is the annual standard deviation of continuously compounded spot rate changes?
b-2. The current spot rate is SSFr/$ = SFr1.50/$. What spot rates are ±2( after one year?
b-3. What are the prices for ±2( stated in terms of the S$/SFr spot rate? Exchange Rate
The value of one currency for the purpose of conversion to another. Exchange Rate means on any day, for purposes of determining the Dollar Equivalent of any currency other than Dollars, the rate at which such currency may be exchanged into Dollars...