Re: [Quantlib-users] Missing sabr interpolation for capfloor vols in both QuantLib and ORE

[Steve H. <war...@gm...>]

Hi Peter and Ioannis,
I am also interested in this discussion and have one question about the “
swaption exercising into a single-period swap.” I am confused by the option
tenor in IBOR and RFR world.

1. In a fixing in advance IBOR world:
Take one year cap for example, we only have 3 live caplets since first one
is fixing on trade day and actually no volatility at all.  Assuming the
payment frequency is 3m, then we have:
    Caplet2=3m*3m swaption
    Caplet3=6m*3m swaption
    Caplet4=9m*3m swaption

2. In a fixing in arrear RFR world:
we now have 4 caplets,  then we have:
    Caplet1=3m*3m swaption
    Caplet2=6m*3m swaption
    Caplet3=9m*3m swaption
    Caplet4=12m*3m swaption

Am I correct?

Regards,
Steve





On Mon, Jul 31, 2023 at 3:24 AM Peter Caspers <pca...@gm...>
wrote:

> Hi Ioannis,
>
> Yes that makes sense to me, a swaption exercising into a single-period
> swap is the same as a (single) caplet / floorlet.
>
> I am just not sure how practical this approach is, it depends on what
> exactly you intend to do.
>
> By the way - you want to make sure that the conventions of the
> swaption are set correctly, e.g. the day counter of the fixed leg of
> the swap should be the same as on the floating leg to mimic an
> optionlet (e.g. A360 for both sides in the EUR case). And the swaption
> should be physically settled.
>
> This also reminds me of extensions for RFR swaptions we did in
> ORE-QuantLib, e.g. the ATM rate calculations for swaptions which is
> correct here
>
>
> https://github.com/OpenSourceRisk/QuantLib/blob/116cf704bf6642de824aff035ce9849e1e621fce/ql/termstructures/volatility/swaption/swaptionvolcube.cpp#L91
>
> but not yet in the original QuantLib. We still have to harmonize that
> stuff.
>
> Thank you
> Peter
>
> On Thu, 27 Jul 2023 at 21:01, Ioannis Rigopoulos <qua...@de...>
> wrote:
> >
> > Thanks Peter for the quick response.
> >
> > I posed the question because I have received an inquiry from the rates
> > option desk of a big Chinese bank, to whom I have already told I am
> > using QuantLib and ORE for the analytics part.
> >
> > Therefore I am really looking forward to any advancement that you could
> > possibly make with regard to the SABR calibration in that area.
> >
> > If you allow me, I would like to draw on to your expertise in this area
> > by asking you one quick question:
> >
> > As you know, both libraries have the ability to use SABR in the context
> > of swaptions. Some time ago I had even published the blog
> > https://blog.deriscope.com/index.php/en/excel-quantlib-swaption-sabr
> > along with a spreadsheet that demonstrates the cubic vol calibration of
> > the SABR parameters. Perhaps my thinking is naive, but a capfloor
> > consists of optionlets, which in turn are trivial one-period swaptions.
> > Since we can imply the optionlet vols by stripping the available
> > capfloor market vols, I suspect that we may then treat these implied
> > optionlet vols as if they were given swaption vols. Obviously the vols
> > manifold in this case will be a surface rather than a cube since all
> > swaptions will reference an underlying swap consisting of a single
> > period. I am wondering what would happen if I nevertheless run the SABR
> > calibration on these swaption vols, just like in the link above.
> >
> > Do you think such an approach could make sense?
> >
> > Thanks again for your time and your advice.
> >
> > Ioannis
> >
> > On 7/27/2023 9:22 PM, Peter Caspers wrote:
> > > Hi Ioannis,
> > >
> > > I agree with you, SABR is a popular method to model volatility smiles,
> > > especially for rates and we should support it for both swaptions and
> > > cap / floors. It's on my personal short list for sure (since a while!)
> > > and also loosely on the ORE roadmap, clients keep asking for this.
> > >
> > > Actually, it is kind of supported already in QuantExt because you can
> > > use SABRInteprolation with the StrippedOptionletAdapter (the version
> > > of this class in QuantExt). I never tried this though, and we don't
> > > expose this in the OREData curve builder, for a reason:
> > >
> > > I think there is more work to do, since when you model a whole cap
> > > surface or swaption cube with SABR you want to make sure that the SABR
> > > parameters vary smoothly for different expiries (and swap lengths),
> > > otherwise your interpolated vols might be useless.
> > >
> > > We also definitely want to look into arbitrage-free flavours of SABR
> > > like we started here
> > >
> > >
> https://github.com/OpenSourceRisk/Engine/blob/master/QuantExt/qle/models/normalsabr.hpp#L37
> > >
> > > Anyway, we'll keep you posted.
> > >
> > > Thanks
> > > Peter
> > >
> > >
> > >
> > >
> > >
> > >
> > >
> > > On Thu, 27 Jul 2023 at 15:11, Ioannis Rigopoulos <
> qua...@de...> wrote:
> > >> Hi Peter,
> > >>
> > >> I am asking you directly regarding my recent QuantLib inquiry below
> > >> because I saw your name as being the last contributor to
> > >> strippedoptionletadapter.cpp and I have not received any response yet.
> > >>
> > >> Since you also are an expert in the ORE library, I would also like to
> > >> ask you if that library supports the SABR calibration of capfloors.
> > >>
> > >> Many thanks!
> > >>
> > >> Ioannis
> > >>
> > >> On 7/21/2023 9:25 PM, Ioannis Rigopoulos wrote:
> > >>> Does anybody know why sabr interpolation of capfloor volatilities
> > >>> seems to be unsupported in both quantlib and ore although it is
> > >>> apparently common practice in the industry?
> > >>>
> > >>> More specifically, in strippedoptionletadapter.cpp there is a
> > >>> commented out code segment starting with "strikeInterpolations_[i] =
> > >>> ext::shared_ptr<SABRInterpolation>(...)".
> > >>>
> > >>> Does anybody know why this segment has been commented out?
> > >>>
> > >>>
> > >> --
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