Re: [Quantlib-users] Drift adjustment in Jamshidian Engine and HW Prcoess

[Philippe H. <phi...@ex...>]

Actually, I have a follow-up question on the drift issue.
I was experimenting with the Hull-White implementation from the QuantLib
Cookbook, and interestingly, in Chapter 15, they build a flat curve with a
forward rate of 5%, via:
spot_curve = ql.FlatForward(todays_date,
ql.QuoteHandle(ql.SimpleQuote(forward_rate)), day_count)

The HW parameters are sigma=10% and a=10%, and the HW engine is built via:

hw_process = ql.HullWhiteProcess(spot_curve_handle, a, sigma)

They then proceed to generate paths of the short term rate, and they
demonstrate that the simulated rate converges to the theoretical
expected forward rate f(0,t<T) but the graph of such expected forward is
not flat at 5%, instead it is monotonously increasing from 5% to as high as
50% after 30 years. So it very much looks like the paths of rates that they
show are not drift adjusted otherwise the expected path should be flat at
5%.
So I'm unsure what is going on? Is there an optional argument in the
hw_process call to do the drift adjustment or not?

Philippe Hatstadt


On Sun, Oct 25, 2020 at 9:09 AM Peter Caspers <pca...@gm...>
wrote:

> Hi Philippe,
>
> the Jamshidian engine uses a) discount bond prices conditional on the
> state of the model (i.e. the short rate in the case of the Hull-White
> model) and b) zero bond option prices in the model to come up with a
> model swaption price. It retrieves this information via the
> discountBond() and discountBondOption() methods in the
> OneFactorAffineModel interface. The methods account for the adjustment
> term theta(t) in the Hull-White model SDE already, there is nothing
> that the engine needs to do in addition to that. I don't know if that
> answers your question?
>
> The HullWhiteProcess also takes into account the adjustment to the
> initial curve already. To see that you can look into the
> implementation of HullWhiteProcess::drift()
>
>
> https://github.com/lballabio/QuantLib/blob/master/ql/processes/hullwhiteprocess.cpp#L38
>
> which coincides with e.g. Brigo Mercurio, Interest Rate Models, Theory
> and Practice, Formulas (3.33) and (3.34) observing that in this
> context
>
>
> https://github.com/lballabio/QuantLib/blob/master/ql/processes/ornsteinuhlenbeckprocess.hpp#L90
>
> level_ is zero, speed_ is the Hull-White mean reversion parameter and
> x stands for the short rate at time t.
>
> Does that make sense?
>
> Thanks,
> Peter
>
>
> On Sun, 25 Oct 2020 at 12:47, philippe hatstadt via QuantLib-users
> <qua...@li...> wrote:
> >
> > Is there any information about how the Jamshidian engine does the drift
> adjustment to match the initial curve for the Hull White model?
> > If I want to use the QL HW Process in a MC model, I assume II have to do
> the drift adjustment myself, or is there existing QL functionality to do
> that?
> >
> > Regards
> >
> > Philippe Hatstadt
> > +1-203-252-0408
> > https://www.linkedin.com/in/philippe-hatstadt
> >
> >
> >
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