Question: Suppose the dollar denominated interest rate is 5 the yen denominated interest

Suppose the dollar-denominated interest rate is 5%, the yen-denominated interest rate is 1% (both rates are continuously compounded), the spot exchange rate is 0.009
$/¥, and the price of a dollar-denominated European call to buy one yen with 1 year to expiration and a strike price of $0.009 is $0.0006.
a. What is the dollar-denominated European yen put price such that there is no arbitrage opportunity?
b. Suppose that a dollar-denominated European yen put with a strike of $0.009 has a premium of $0.0004. Demonstrate the arbitrage.
c. Now suppose that you are in Tokyo, trading options that are denominated in yen rather than dollars. If the price of a dollar-denominated at-the-money yen call in the United States is $0.0006, what is the price of a yen-denominated at-the-money dollar call-an option giving the right to buy one dollar, denominated in yen-in Tokyo? What is the relationship of this answer to your answer to (a)? What is the price of the at-the-money dollar put?

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