Originally Posted by MSPeconomist

For most hotels in most countries, at least when you make a reservation directly with the hotel, the rate in local currency is definitive, not a rate converted to dollars that might be shown for your convenience. Thus, the hotel receives the same number of yen for the basic room rate for your stay regardless of when the credit card is charged, assuming the hotel doesn't do a dynamic currency conversion scam. Your contract with the hotel is denominated in yen, not dollars.