the correlation between EURO and Yen is quite high, as you may see from the attached graph, the rate of change (ROC) of EUR (in pink) is declining FASTER than Yen's (in purple). If one thinks that either EUR or Yen is going to down, do you think pair trade strategy will work?
If EUR goes down, long EUR put (ROC is higher), short JPY put (lower ROC allows us to take advantage from theta).
If EUR goes down, long EUR put (ROC is higher), short JPY put (lower ROC allows us to take advantage from theta).