Hello,I have a question regarding FX Risk Reversals. Consider the currency pair USD/EUR (USD is domestic, EUR is foreign), with a call on EUR. The 25 delta risk reversal would then be:RR_eur = vol of 25D EUR call - vol of 25D EUR putSuppose we now want to look at a call on USD. The risk reversal would be RR_usd = vol of 25D USD call - vol of 25D USD put = - (vol of 25D USD put - vol of 25D USD call)The question is: Is RR_eur = - RR_usd?My intuition is saying no... I don't think the vol of EUR call is equal to the vol of USD put for 25 delta. Likewise, vol of 25D EUR put is not equal to vol of 25D USD call. So the only way for the above to be true is if the vol of the EUR call and USD put and the vol of the EUR put and USD call differred in just the right way, for all term structures and deltas, which seems improbable...Thoughts?Thanks.

carolpeople use RRs as a means of capturing the slope of the smile surface.it simple is used to make arguments such as....in currency pair x/Yputs on x are priced at an implied vol that is 1% higher than calls on x.in this light, it is unclear to me wht are you aiming at with your argumentcordiallyO.

a call on Euros in $s is the same as a put on $s in euros

I am trying to figure out the relationship between a RR on x calls (ie. vol of call on x - vol of put on x) and a RR on y calls (ie. vol of call on y -vol of put on y) for a currency pair xy.I checked in bloomberg- the relationship is indeed RR_eur = -RR_usd (as per the notation in my first post above).I still cannot figure out why though, mathematically.