FX Options delta-neutral strike

[foges]

Hey guys, I'm hoping to get some help with a small problem I have. If you take a look at these slides on pg. 7 (http://faculty.baruch.cuny.edu/lwu/9797/Lec8.pdf), it states that the delta-neutral strike is K=F*exp(1/2*sigma^2*t), this however means that the delta-neutral strike for a currency pair (eg. EURUSD) does not correspond to the delta-neutral strike of the inverse pair (USDEUR). To me that doesn't make much sense.. Would appreciate it if someone could help me clear this confusion. Thanks!

 

[foges]

If anyone is interested, the error turned out to be my assumption that the delta neutral volatility is the same for a currency pair and the flipped currency pair.

 

[financeguy]

hmm shouldn't the volatility of EURUSD and USDEUR be the same? we're looking at the standard deviation of log returns, they should be equal since every return of EURUSD is just -1 times the return of USDEUR..
also what about the premium adjustment.. in fx the dns is computed such that you offset the premium you pay (which creates a delta) with a strike delta mismatch.. is that taken into account here?