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

[Peter C. <pca...@gm...>]

Hi Steve

the standard 1y cap on RFR has

0m 3m
3m 3m
6m 3m
9m 3m

caplets.

Best
Peter


Steve Hsieh <war...@gm...> schrieb am Do. 17. Aug. 2023 um 08:30:

> 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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