Hi.Is anyone here really really familiar with smile construction in fx markets? I mean someone who knows the difference between market bf and smile bf. I've seen two ways of constructing the smile and would like to discuss.First one is the one, where you match the bf in price terms and the rr in vol terms.Second one, where you match both in price terms, eg. atm+bf vol and atm +/- 0.5 rr vol for the rr.Which one to use? Also, any ideas which models are common?Thanks in advance!

Theoretically you'd want to match your (interpolated) value for each traded structure with the market price.So if on a broker the vols (and therefore the strikes) for the RR are determined using ATM + RR/2 + Mkt Bf (which seems the way brokers would see it, since they're not using your particular interpolation), your price for these options should be the same as the premium paid.How your interpolation method will fit those prices is another issue, though. There is a market RR and a smile RR too, but the difference might be within the spread of the RRs and not be so crictical for the interpolation as the Bf difference.

Thanks MCarreira,I know about the market bf, which is calculated with atm+bf as the vol. As far as I understand so far, the 25 delta put and calls arethen atm+ smile bf +/- 0.5 rr, so they're calculated with smile bf, not with market bf. Calculated in this way, their difference will bethe market rr vol quote. Is there any bias towards an interpolation scheme? Any recommendation? Thanks

QuoteOriginally posted by: LeonidasThanks MCarreira,I know about the market bf, which is calculated with atm+bf as the vol. As far as I understand so far, the 25 delta put and calls arethen atm+ smile bf +/- 0.5 rr, so they're calculated with smile bf, not with market bf. Calculated in this way, their difference will bethe market rr vol quote. Is there any bias towards an interpolation scheme? Any recommendation? ThanksWhat is the smile bf ? Do 2 different banks find always the same value ? Are brokers aware of it ? If the 2 banks can agree on the vols using a smile bf that is close enough to their interpolations, then all is well. If not, then you fall into the problem discussed below.

Leonidas,the market bf actually poses a problem, since it is not consistent with the way risk reversal (and also call or put spreads) are quoted. So basically you need an interpolation scheme capable to generate a smile using the three basic points (see my article with Mercurio, it has appeared in a magazine a couple of years ago but a version is available in Mercurio's web site or ssrn.comm under my name Castagna or Mercurio "Consistent Pricing of FX option"). Then by a numerical procedure you have to find out which is the "false" (since it is not the quoted one) bfly parameter you have to plug in your interpolation function (eg.: Castagna&Mercurio's Vanna Volga) so that it is perfectly fitting the R/R price (that is quoted in the market as a difference and not as two separate vols) and the market fly. In practice you have to move the "false" fly so as to match the market fly in price terms, not vol terms, by the interpolation function with the set of parameter vol atm, mkt rr, false fly.The procedure is described in details (also with examples) in my book on FX options that will be out in July, published by Wiley.

QuoteOriginally posted by: ancastThe procedure is described in details (also with examples) in my book on FX options that will be out in July, published by Wiley.What's the name of your book?

It might be "FX Options and Smile Risk", by Antonio Castagna.Cheers,Jordy

QuoteOriginally posted by: JordyIt might be "FX Options and Smile Risk", by Antonio Castagna.Cheers,JordyIndeed.Thank you, Jordy