f you are interested in FX options market making and risk management, you may find useful my book just published by Wiley.http://eu.wiley.com/WileyCDA/WileyTitle ... 4192.htmlI will be glad to answer also to questions you may have.a.c.

ancast,Got your book today, it is a nice book, and I think the first one to discuss the market butterfly.A good thing is the topic about risk managing a portfolio.Do you have anything on typical behaviour of the term structure of the ATMs or the comovement of ATM, RR and VWB ?Thanks,MCarreira

MCarreira,from my experience the behaviuor of the smile can be summarized in the following points, assuming no news completely re-shaping traders' expectations occurs:1) the ATM vol follows the slope of the smile (eg.: if base currency calls are favoured, when spot up then atm vol up)2) The RR generally increases its absolute value if the spot moves accordingly. In other words, when the spot down with RR favouring base cur puts, then the RR becomes more negative. This is true when the trend is not lasting for a long period. When the trend is rather long, depending also on the expiry of the option, the RR may start declining in absolute value when the spot moves confirm the trend, although it is very difficult to identify when market believes the trend is over and the FX spot rate may begin a stale period or an opposite trend. Clearly the sensitivity of the RR is grater for shorter expiries (up to 2 months). Fast movements may cause a twist in the vol surface, with short RR negative and long RR still positive, as an example (this used to happen in EURUSD, where RR are not too big, it is less common on currency with large RR such as the USDJPY).3) Fly are rather stable, usually they move after long period of quite markets (when market maker need to sell volga, and huge amounts of flys are sold). On the reverse, when markets becomes very frantic, it increases rapidly. In Eurusd 25 flys declined from 2003 to 2006 from .30% fo .10%. In one year, after market turmoils, it started increasing again very fast, reaching .225% in a very short period.This is what I can say from what I experienced in the market. Hope it may be of some help.

What confused me in the book is the following: In the example describing the RR trade, you're saying that ATM+0.5RR and ATM-0.5RRare basically the vols for the wings used in the trade. On the other side, your market consistent smile will have ATM+0.5RR+FLYand ATM-0.5RR+FLY as the vol after performing the numerical calibration procedure you describe later in the book. How is this related? Thanks

Hey, what I enjoyed from the book is the insight into techniques "used in anger" by the author in real experience.I would also be interested to hear your take on using VV smile interpolation in extreme (USDJPY) skew scenarios.USDJPY Skew Breakdownregards

Leonidas,you are right: in the first example of chaptter 1, I did not introduced yet the fly so I considered it equal to zero. When it is not zero, definetly the traded vol for RR is atm+0.5rr+fly for call and atm -0.5rr+fly for puts. In the other chapters this is the formula always used.I will make it clearer (if I will have the chance).Thank you

Sacevoy,I never read the MX statement on Risk Magazine, but basically their model Tremor produces dVdS, dRRdS very similar to those I described in my previous post.The VV used to work very well also for 10 strikes on USDJPY, if the equivalent fly was properly computed (as explained in the book). At the moment I cannot tell you how it is performing. Clearly for those extreme skew currencies the model chosen is playing a big role for extreme wings. If you used a Sabr, as an example, you can have higher wings, but you are also likely to suffer from the flaws of the sabr analytical approximation and dealing with a non-arbitrage free smile (negative butterfly for extreme strikes). Heston and VV agree rather well on extreme wings when they are both matching the atm and 25D C and P. Since I like Heston more than sabr, I feel rather comfortable with VV being not unreasonable.

I would like to add some thoughts about the VV and its ability to match market prices. For steep smiles (eg USDJPY and exotic currencies) it is sensible to have an extra parameter commanding the extreme wings' behaviour, since it is there where the VV has more flaws.If you use formula 4.9 pag 104 of the book you just have the 3 vols and 3 strikes as inputs and you lack some flexibility.Actually, if one uses the more general fomula 4.12 pag 108, where weights x_i are computed with system 4.4 pag 100, then one have one extra parameter sigma that does not has to be necessairly set equal to the ATM volatility (sigma = sigma_2), as it has been assumed to derive all the results.So one safely inputs the three options (atm and 25d wings) with their market vols and uses a vol different from those ones to calculate the Vega and then the weights in 4.4.It easy to check that changing sigma has almost no effect in the range included among the three strikes (and plus it still guarantees the three main strikes' vols are recovered), but has a strong effect in raising of lowering the extreme strikes' vols.This feature has not been studied in the book but maybe it is a good way to improve the fitting.

ancast,I remember that VV using 25d was not a good fit outside the 25d when USDBRL was steep (RRs up to 20).THe relationships between 25d and 10d parameters did change, but I didn't try to work with something like a 15d input and recheck VV.

MCarreira,jut for my curiosity, did you try and fit a stoch vol model to USD BRL smile (e.g. Heston)?As for the VV performance, I just refer to my previuos post, where I briefly explain how to extend the VV apporach in a very simple way, giving the user some control on the smile's behaviour for extreme wings

I was looking for good models for deep OTM strikes, and figuring out what should happen there; it is somewhat difficult to get a good fit for stoch vols, because on the onshore case there's no market for the vols of the onshore USD curve, and offshore there's no market for the BRL rate implied by the NDF and LIBOR; therefore, building a 4-factor model (spot + spot vol + 2 rates) gets too complicated, and ignoring the stochasticity of the rates for longer maturities would lead to misleading conclusions.I'll look in detail at your proposal.Thanks for the comments.

Ancast,Let me say first that this is a great book. I'm a student and have been trying to understand various aspects of the fx options market for a while now. Your book has really clarified things for me.In regard to your comments above on the Vanna Volga method, I had 2 questions regarding implementing VV when you have 5 strikes available (the 10 delta puts and calls as well as the 25s).1. Would it be possible to interpolate the skew using VV in 2 different pieces, using the ATM volatility as the anchor rather than the midpoint in each case? For example, could one set sigma1 equal to the 10 delta put IV, sigma 2 equal to the 25 delta put IV and sigma 3 equal to the ATM IV and then use the aformentioned formula 4.12 on page 108 or one of the approximations to derive one half of the skew, then do the equivalent procedure using sigma1=sigma(ATM), sigma2=sigma(25call), sigma3=sigma(10call), and join these 2 lines to have the full skew?2. If this does not make sense, is it better to use the 10 delta call and put implied volatilities as sigma1 and sigma3 (and their corresponding strikes) when these are available in the vanna volga method rather than the 25 deltas, with sigma2 set equal to the ATM implied volatility?Thanks again for the great book.

Dear Rocs,thank you for appreciating the book. As for the first point, in theory you can use any three points, but in practice to get sensible smiles you need an atm (or some strike near the spot), a strike lower than the spot and a third strike higher than the spot. So the approach you are suggesting does not seem very promising to me. Plus, it is not really related to any financial rationale (ie.: building a portfolio to hedge all relevant risks).You could try to insert more strikes in the procedure and try and cancel out other greeks (higher order greeks), but in this case you should be careful to the cross derivatives and make some assumptions also. Moreover, when I tried to do so, I got extremely unstable smiles, since in practice you come up with a high order polynomial interpolation. the second point is more sensible to me. I mean, if you think that 10 D options should be perfectly matched, then it is better to use them in the VV approach, and derive the 25 D accordingly. As I explained in a previuos post, you can get an extra degree of freedom by setting the volatility sigma equal to some number and not to the atm vol. This will allow you to get some control on the curvature of the smile, and get some better fit to options. Hope it helps.

I have difficulties understanding section 8.4. I don't see what the charts for the model exposure represent. The right hand sidecharts always represent the BS greeks with flat vol. Ok. Now, what does the other stuff mean with the LMUV setup? Say we areconsidering the RR position. What do you mean by the ATM STDL exposure of the RR? E.g. what exactly is represented in Figure 8.8, left chart (and all others)? Also, the VWB in your analyses seems to include 25D options, if I see correctly. In particular insection 3.8. But the market butterfly (from section 4.9) calculated with smile consistent vols does not have 25D options. I'd be happy about any clarification.

Leonidas,my aim was to show the tight link between a Vega-Vanna-Volga hedging (in the BS world) and the scenario hedging in a stoch vol world. Scenario hedging is one of the approaches one can use to hedge the stoch vol, as explained in chapter 3. Basically you hedge the three basic movements of the smile by the three standard options (atm and two 25D options), which can be recombined in the three main market instruments (Atm straddle, RR and Vega Weighted Bfly).Now, if you are long a RR you may have an axposure to the parallel shift of the smile, which can be hedged by trading an ATM straddle. Hence, a RR may have an exposure in terms of ATM. I wanted to show that the exposure of the ATM strongly resembles the Vega exposure, and the same happens for the RR exposure with the Vanna and for the VWBfly exposure with the Volga. The resemblance keeps for all the options and strucures I have analysed.The market fly does have 25D, otherwise how can you build it? It does not include the RR in the price in vol terms, so there is a small difference if you build the VWB with the strikes derived via the formulae Sigma 25d = atm + fly +- 0.5 rr, and if you build it with Sigma 25d = atm + fly. In chapter 8 I analysed the differences one gets when considering the proper VWBfly definition and the more consistent (but not market standard) definition.One final remark: unfortunately in the editing process of the book there has been a switch in all figures between the BS exposures and the LMUV exposures. The mistake is constant throughout the entire section 8.4, so you simply have to read right- (left-) hand side everytime left- (right-) hand side is written.Hope it helps.