Re: [Quantlib-users] Understanding HullWhite::tree method

[Hong Y. <hy...@ho...>]

Hi.  I have read Hull’s “Options ...” book too, particularly the parts on H-W trinomial-tree building procedure.  Compared to the code, it seems that ‘value’ in each i-loop corresponding to the displacement function alpha(), ‘statePrices’ corresponding to Q(), ‘underlying()’ are initial interest-rate and interest-rate related computing parameters.  Do you intend to use H-W on real financial data?

Also, I have got H-W’s paper on numerical procedure (I) and 2001 version of F Mercurio’s book.  If you would be interested, I am happy to share a copy of the references.

Regards,

Hong Yu




From: Smith, Dale 
Sent: Monday, June 27, 2011 8:41 PM
To: Hong Yu 
Cc: qua...@li... 
Subject: RE: [Quantlib-users] Understanding HullWhite::tree method

Hi,

 

I don’t have Hull’s paper, nor do I have Hull’s “Interest Rate Derivatives”. I’ll take a look at Chapter 30 before I respond further.

 

Thanks,

Dale Smith, Ph.D.

Senior Financial Quantitative Analyst

Risk & Compliance

Fiserv.

107 Technology Park

Norcross, GA 30092

Office: 678-375-5315

Mobile: 678-982-6599

Mail: dal...@fi...

www.fiserv.com

 

From: Hong Yu [mailto:hy...@ho...] 
Sent: Monday, June 27, 2011 8:07 AM
To: Smith, Dale
Cc: qua...@li...; Yu Hong
Subject: Re: [Quantlib-users] Understanding HullWhite::tree method

 

 

Hi.  I can’t completely answer your questions yet; but have made some progress after going through the code and the suggested paper.  

 

The code looks a numerical implementation of Hull-White.  I have also referenced another book “Options, Futures, and Other Derivatives” by Hull; that book’s chapter 30 have some introductions to the H-W numerical procedure.  Do you have access to the book?

 

And, I guess we can again find helpful discussions in: Fabio Mercurio’s book “Interest Rate Models”, Hull’s paper “Numerical procedures for implementing term structure models I: Single-Factor Models”, and Hull’s book “Interest Rate Derivatives”.  Unfortunately I haven’t got access to those references.  Do you have them?  Look forward to more discussions.

 

Regards,

 

Hong Yu

 

 

 

From: Smith, Dale 

Sent: Friday, June 24, 2011 11:35 PM

To: qua...@li... 

Subject: [Quantlib-users] Understanding HullWhite::tree method

 

Hello,

 

I have questions about the implementation of HullWhite::tree. I’ve reproduced the code from hullwhite.cpp here for reference:

 

    boost::shared_ptr<Lattice> HullWhite::tree(const TimeGrid& grid) const {

 

        TermStructureFittingParameter phi(termStructure());

        boost::shared_ptr<ShortRateDynamics> numericDynamics(

                                             new Dynamics(phi, a(), sigma()));

        boost::shared_ptr<TrinomialTree> trinomial(

                         new TrinomialTree(numericDynamics->process(), grid));

        boost::shared_ptr<ShortRateTree> numericTree(

                         new ShortRateTree(trinomial, numericDynamics, grid));

 

        typedef TermStructureFittingParameter::NumericalImpl NumericalImpl;

        boost::shared_ptr<NumericalImpl> impl =

            boost::dynamic_pointer_cast<NumericalImpl>(phi.implementation());

        impl->reset();

        for (Size i=0; i<(grid.size() - 1); i++) {

            Real discountBond = termStructure()->discount(grid[i+1]);

            const Array& statePrices = numericTree->statePrices(i);

            Size size = numericTree->size(i);

            Time dt = numericTree->timeGrid().dt(i);

            Real dx = trinomial->dx(i);

            Real x = trinomial->underlying(i,0);

            Real value = 0.0;

            for (Size j=0; j<size; j++) {

                value += statePrices[j]*std::exp(-x*dt);

                x += dx;

            }

            value = std::log(value/discountBond)/dt;

            impl->set(grid[i], value);

        }

        return numericTree;

    }

 

My questions are

 

1.        What is the difference between numericTree->statePrices(i) and trinomial->underling(i,0)? Aren’t the values returned by underlying(…) the actual short rates obtained from the H-W model? What is returned by statePrices? What would value be just before the impl->set(…) statement?

2.       What should I expect in numericTree upon return? I would expect the actual short rates (or discount factors) simulated by the H-W model but I don’t think this is true. See question 1.

 

At first I thought tree(…) returned what I wanted – an actual array (Lattice) of interest rate paths with short rates (or discount factors) simulated by the H-W model. I could then use these rates to calculate cashflows. But perhaps I’m missing something.

 

Before sending this email, I read the HW paper “Using Hull-White Interest Rate Trees”, searched the Quantlib examples and testsuite, read the class module documentation, the source code, and documents on http://quantlib.org/docs.shtml. Please provide any additional pointers to docs I can use to understand this, or perhaps some pointers to sample code I missed that would help. Additionally, I can provide a summary back to the list for future reference.

 

Thanks,

Dale Smith, Ph.D.

Senior Financial Quantitative Analyst

Risk & Compliance

Fiserv.

107 Technology Park

Norcross, GA 30092

Office: 678-375-5315

Mobile: 678-982-6599

Mail: dal...@fi...

www.fiserv.com

 


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