Problem:

An exchange rate is currently 0.8000. The volatility of the exchange rate is quoted as 12% and interest rates in the two countries are the same. Using the lognormal assumption, estimate the probability that the exchange rate in 3 months will be

a) Less than 0.7000

b) Between 0.7000 and 0.7500

c) Between 0.7500 and 0.8000

d) Between 0.8000 and 0.8500

e) Between 0.8500 and 0.9000

f) Greater than 0.9000 Based on the volatility smile usually observed in the market for exchange rates, which of these estimates would you expect to be too low and which would you expect to be too high? Explain comprehensively and provide full explanations.