Hello,Tried this topic on the technical forum, but I guess it wasn't appropriate since I got no responseI was wondering if there was a resource (paper, book, etc) that does a nice job of explaining the step by step process of constructing a volatility cube that incorporates caps ATM and smile data with swaption ATM data. I have seen the cube referred to on several postings here, but keep in mind I do not have access to Bloomberg's cube creation functions. There is a paper by Liang Hsueh talking about the volatility cube, but it is not well written and it some points are unclear to me.Motivation: I'm writing financial software to support caps/swaptions and need a volatility model that would be accetable to most traders. I think the cube seems to be market practice once swaptions are thrown into the mix. Please correct this assumption if I am wrong. I don't have contact with traders, so getting any market practice information on how often the cube is used for pricing would be great.Thanks-Sean

Can you explain a bit more what you are looking for? A cube is just a 3d table of option volatilities. You interpolate and extrapolate to cover prices that are not on an exact node, but, other than that, it is just a lookup table.People are moving a way from a cube to a parameterization now, where you are effectively describing the cube with fewer variables, as it tends to be believed that the nodes are not independent, and so can be fitted with some simpler equations. However, these parameterizations will still very frequently be used to produce a cube again, so you can very happily work in a system where the cube is used for every single price.To use your table, just have a 3-d lookup function. Interpolate in strike, tenor, and maturity, and you will get the appropriate volatility for any swaption.Getting market data is another matter, of course, but the cube construction is not difficult once you have this.

here is what I am looking for: typical market data for the vanilla caps/European swaption market (please correct if I am wrong) is flat cap volatility with a possible smile for the most liquid instruments and ATM swaption volatility. Given those two inputs, one wants to construct a volatility model to price a variety of instruments.My understanding for caps is this can be done simply with the caplet bootstrapping algorithm. Is is true that caplet volatility should never mix with swaption volatility within a volatility cube? Is is true that if one only cared about pricing caps, then one would never need a cube assuming that you are already quoted the smile? since swaptions are only provided ATM, one must do a little more. My understanding is that what is usually done is construction of a cube. However, since you do not have any strikes other than ATM, you must do some kind of smile model. Is SABR the standard?to put this in one sentence, I am looking to transform the most typical volatility for caps/swaptions into an appropriate lookup structure after some messaging of data via bootstrapping, smile modeling, etc. My understanding was that cube was the convention, but maybe this is wrong-Sean

OK, many points to answer, so I will do each briefly. Cap volatility is not flat in any dimension. Swaptions are not only provided ATM, there is a liquid market in lots of strikes in the major currencies. Volatility for saptions and caps can indeed be "mixed". For example, a six month - six month swption is looking at the same rate as a one year cap vs 6m libor, so the description of this rate's evolution needs to be the same for each.A model is more about filling in gaps in the surface/cube, rather than creating one from only ATM vols. SABR is, in my trading experience, the most frequently used, but other parameterisations can work well, too.

what about non major currencies for which you only have ATM prices?Also, I have not seen any examples via Bloomberg or Tullett for away from the money swaption prices.I'm not a trader so I don't have direct access to these pages, so it's quite possible I'm not getting the whole picture.......but often I hear the phrase that swaptions are rarely traded away from the moneythanks-Sean