Re: Matching results between HW tree and simulation models

Posted by Peter Caspers-4 on May 06, 2015; 5:50pm
URL: http://quantlib.414.s1.nabble.com/Matching-results-between-HW-tree-and-simulation-models-tp16399p16539.html

Hi Goutham,

thanks for the reference to the paper, it is interesting.

I was only referring to the case zero bonds. I seem to remember that
Hull (in his OFOD-book) describes a procedure for tree building where
(even with the discrete time spacing) zero bonds are _exactly_ matched
(using Arrow-Debreu prices). That's what I meant by "carefully
implemented". If the tree is not carefully implemented, then yes,
you'd need to let \Delta t reach zero to converge to the initial yield
curves' zero bond prices. The HullWhite::tree(const TimeGrid&)
implementation seems to indicate that it is indeed "carefully"
implemented, so zero bonds should be exactly matched independent of
the grid spacing.

All kinds of option pricings are a different matter of course, but
that wasn't the initial question.

Best regards
Peter

On 6 May 2015 at 19:04, gouthambs <[hidden email]> wrote:

> Peter
>
> I think the grid size would determine how close the numbers will match the
> zero bonds in the tree implementation.
>
> On a side note, I have played with trees to price European options, and I
> have noticed that the fair option value from the trees oscillated about the
> theoretical value. And how much it differed from the fair value depended on
> the grid spacing in the trees.
>
> Check figure 2 in :
> http://www.scribd.com/doc/4108897/Options-Pricing-Using-Binomial-Trees
>
>
> I would expect a similar behavior here, though I haven't tried it myself.
>
> Goutham
>
>
>
>
>
> --
> View this message in context: http://quantlib.10058.n7.nabble.com/Matching-results-between-HW-tree-and-simulation-models-tp16399p16538.html
> Sent from the quantlib-users mailing list archive at Nabble.com.
>
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