$**$ Using the binomial model$**$On January $11,$ the spot exchange rate for the U$.$S$.$ dollar is $$0\mathrm{.}70$ per Canadian dollar. In one year$$s time, the Canadian dollar is expected to appreciate by $20$ percent or depreciate by $15$ percent. We have a European put option on U$.$S$.$ dollars expiring in one year, with an exercise price of $1\mathrm{.}39$ CND$$/$US$$,$ that is currently selling for a price of $$2\mathrm{.}93.$ Each put option gives the holder the right to sell $10,000$ U$.$S$.$ dollars. The current one$-$year Canadian Treasury Bill rate is $2$ percent, while the one$-$year U$.$S$.$ Treasury Bill rate is $3$ percent, both compounded annually. Treat the Canadian dollar as the domestic currency.

a$.$ What is the estimated value of this put option by using the binomial model?

b$.$ Calculate the estimated value of this put option for U$.$S$.$ T$-$Bill rates of $0\%,1\%,2\%,4\%,5\%,$ and $6\%.$ Plot these values in a graph $($by hand or using Excel$),$ with put option values on the y$-$axis and U$.$S$.$ T$-$bill rates on the x$-$axis. What can we conclude about the relationship between foreign interest rates and foreign currency put option values?

c$.$ Calculate the estimated value of this put option for Canadian T$-$Bill rates of $0\%,1\%,2\%,4\%,5\%,$ and $6\%.$ Plot these values in a graph $($by hand or using Excel$),$ with put option values on the y$-$axis and Canadian T$-$bill rates on the x$-$axis. What can we conclude about the relationship between domestic interest rates and foreign currency put option values?