Re: [Quantlib-users] Gaussian short rate model + calibration

[Matthias S. <mat...@gm...>]

Hello Matthias,

Thank you for the pointer to Peter Caspers' blog.
Now ceased the attempts to calibrate mean reversion with Gsr.

Have been looking at the GeneralizedHullWhite implementation, too.
"Interesting" results when comparing to the regular one, but need further
investigation before it potentially bears another question.


Regards,

Matthias


On Sat, Jun 6, 2020 at 2:00 PM lungwitz <lun...@go...> wrote:

> Hi Matthias,
>
> Peter Caspers has written a quite detailed description on his Blog on his
> GSR implementation that I have found very helpful:
>
> https://quantlib.wordpress.com/2015/03/29/gaussian-models/
>
> For callable Bonds you can use a nonstandard swaption (including a rebate
> and a Credit Spread) as described there, through this does not capture the
> Credit Spread volatility related part of the option.
>
> Indeed the mean reversion has to be provided as an external input.
>
> Best regards
> Matthias
>
> -------- Ursprüngliche Nachricht --------
> Von: mat...@gm...
> Datum: 06.06.20 12:36 (GMT+01:00)
> An: qua...@li...
> Betreff: [Quantlib-users] Gaussian short rate model + calibration
>
> Dear QL users,
>
> I cannot say I have great familiarity with short-rate or market models, so
> please bear with me on this one:
>
> Trying to value a multi-callable swaption and bond using a Hull-White
> model with (piecewise) time-dependent volatility.
> As I understand, <ql/models/shortrate/onefactormodels/hullwhite.hpp> does
> not satisfy this condition:
>
> This class implements the standard single-factor Hull-White model defined
> by
>         \f[
>             dr_t = (\theta(t) - \alpha r_t)dt + \sigma dW_t
>         \f]
> where \f$ \alpha \f$ and \f$ \sigma \f$ are constants.
>
> I believe it was this ML's archive where I picked up Gsr as a recommended
> alternative and it looks fine (for some definition of "fine") for swaption
> pricing.
> There are two questions, however:
>
> 1) It is apparently not possible to calibrate both volatilities and
> reversion(s).
>
> While Gsr implements CalibratedModel, performing "joint" calibration like
> this
>
> // vector<bool> fixedParms = gsr->FixedReversions();
> vector<Real> modelVols(voldates.size() + 1, 0.01);
> fixedParms = vector<bool>(modelVols.size() + 1, false);
> gsr->calibrate(calibSet, lm, ec, NoConstraint{}, vector<Real>{},
> fixedParms);
>
> would not work, because only the first modelVols.size() number of
> calibration instruments are acknowledged, leaving the optimizer with an
> under-determined function.
>
> Likely there is a good reason for this. Market practice to have mean
> reversion as a given model parameter? Or that is just the way the model is
> supposed to work?
>
> 2) There is no pricing engine for callable bonds that can consume Gsr, if
> I am not mistaken. Gsr does not seem to implement ShortRateModel:
>
> Gsr <- {Gaussian1dModel, CalibratedModel, ...} <-
> {TermStructureConsistentModel, ...}
>
> Likely to do with the tree(const TimeGrid&) method in that interface.
> Alternatively, there is
> <ql/experimental/shortrate/generalizedhullwhite.hpp>. It sits in the
> "experimental" folder, but so does everything callable bond related. So I
> wonder whether the latter is more suitable for instrument/bond pricing
> while Gsr might be more model of choice for scenario generation purposes?
>
>
> Again, apologies for any incorrect terminology or confusing remarks. Happy
> to clarify further, if necessary (and possible for me).
>
>
> Thank you,
>
> Matthias
>
>
>
>
>
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