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

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

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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