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

[philippe h. <pha...@ma...>]

Makes sense thank you.
I was asking because I’m writing a MC swaption calculator and for some reason; the realized volatility of my forward swap rate does not match the volatility of the short term rate with zero mean reversion nor does it match the closed form Jamshidian engine pricing. So I was trying to eliminate possible reasons but the drift is not one of them as per your explanation.

Regards

Philippe Hatstadt
+1-203-252-0408
https://www.linkedin.com/in/philippe-hatstadt


> On 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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