$2.$ The current EURJPY exchange rate is $150$ JPY per EUR. The EUR and JPY risk$-$free interest rates are $2\%$

and $1\%$ per annum, respectively.

$($a$-$b$)$ The market price of a $9-$month European call option on EURJPY with a strike price of $160$ is JPY $2.$

Calculate the implied volatility of the exchange rate.

$($c$-$d$)$ A company enters into a range forward contract by buying the call in part $($a$)$ and selling a $9-$month European put option on EURJPY. Determine the strike price of the put option. Use the volatility found in part $($a$).$

$($e$)$ What is the $9-$month forward price of EURJPY? How is the company$$s position in part $($c$-$d$)$ different compared to buying a forward contract on EURJPY? Draw the payoff for each position on a single graph. for what EURJPY exchange rates does the range forward give more profit $($or less loss$)$ then the forward