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Assuming I have a USDJPY put option at strike 100 (1USD = 100Yen) and the delta is D1. What is the delta of a corresponding JPYUSD call option at strike 0.01 (1Yen = 0.01USD) with the same maturity? Would it be related to D1?

Thank you very much!

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  • $\begingroup$ The two deltas add up to one. Just like the deltas of a put and a call with same strike add up to one. The call on JPYUSD can be seen as a put on USDJPY. $\endgroup$ – Alex C Oct 15 '16 at 19:42
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Since I'm not a FX guru I need to prove the comment of @alex c

A USDJPY 100 call on one dollar has payoff:

max(0, FX-100) Yen

where FX=USDJPY at maturity. A JPYUSD 0.01 call on one Yen has payoff

max(0, 1/FX - 0.01) Dollars = 0.01/FX * max(0,100 - FX) Dollars = 0.01 * max(0,100 - FX) Yen

which is the same as a USDJPY 100 put on 0.01 dollars, as suggested.

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