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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