Butterfly Volatility in Forex Markets

[boulala]

Hey there,

I am new in FX markets and I have a few questions regarding the volatility quotation for BF.

The first thing is, why does a butterfly measure the convexity of the smile?

Secon how can I get to the formula for the butterfly volatility?: (VolCall+VolPut)/2 -VolATM

kind regards
boulala

 

[Keith Tan]

the equations looks like it measures the change in volatility per unit delta. Do you have the reference materials?

 

[boulala]

do you mean by reference material, the literature?
f.e. http://www.fam.tuwien.ac.at/~sgerhold/pub_files/sem12/s_sibetz_nowak.pdf page 6.
I alwys thought about a butterfly, that it is build kind like: Long Call, Short 2Calls and long Call all at different strikes. but how does this match with the formula for the vol?
Maybe you can explain it to me

 

[financeguy]

The butterfly measures how far the strangles of a given delta (normally 25 delta) trade above ATM straddles, in vol terms. The actual structure it represents is buying a strangle and selling a straddle in vega neutral amounts (i.e. more notional of the strangle such that the whole package is vega neutral). It's not exactly the convexity of the smile, but intuitively you can see that the higher the butterfly, the higher strangles are marked above the ATM vol, which is sort of a measure of convexity. It's not quite the whole picture, because you need to see where the risk reversal of the same delta is marked to know exactly where the vols are for both 25 delta points.

 

[boulala]

yeah finance guy nice answer! thank you now I understand it. I was wondering how this can measure the "real" convexity... now its clear