QuantLib enhancement proposals

[Luigi Ballabio-4]

Greetings everybody,
        a new section was opened on the QuantLib site containing the QuantLib
Enhancement Proposals, a.k.a QuEP (I hope Python people will forgive us):

http://quantlib.org/quep.html

The first two proposals are currently available for peer review and feedback.

Bye,
        Luigi

[Nicolas Di Césaré]

En réponse à Luigi Ballabio <[hidden email]>:

>
> Greetings everybody,

Hi Luigi,

> The first two proposals are currently available for peer review and
> feedback.

I just have look to the boundary condition proposal. It is not clear for me how
do you treat time dependent or free boundary conditions with your design. Could
you give more details, please?

bye,

Nicolas


--
Nicolas Di Césaré
http://acm.emath.fr/~dicesare

[Luigi Ballabio-4]

Hi Nicolas,

At 02:01 PM 10/25/01 +0200, Nicolas Di Césaré wrote:
>I just have look to the boundary condition proposal. It is not clear for
>me how do you treat time dependent or free boundary conditions with your
>design. Could you give more details, please?

<cough> Well, as for the time dependence, I forgot it. <cough>
The way I would treat it would be to add a setTime(Time t) method to the
BoundaryCondition interface which would be implemented by the derived BC
classes and would be called by the evolver before calling the other
methods. It might make sense to give it a default implementation which does
nothing.
I'll be updating the QuEP as soon as I find time.

As for your second question, what do you mean by free boundary conditions?
If you mean "no particular boundary condition given", it would be exactly
that---one wouldn't give any particular boundary condition, either by
passing a null Handle<BC> or implementing a NullBC class whose methods do
nothing. Of course this wouldn't exactly mean "no boundary condition",
since as long as you have a first row and a last row in your operator you
have two corresponding boundary conditions... but I'm probably missing
something here. Could you give more details, please?

Bye for now,
                 Luigi

[Ferdinando M. Ametrano-2]

At 10:38 AM 10/26/01 +0100, Luigi Ballabio wrote:
>what do you mean by free boundary conditions? If you mean "no particular
>boundary condition given", it would be exactly that---one wouldn't give
>any particular boundary condition, either by passing a null Handle<BC> or
>implementing a NullBC class whose methods do nothing. Of course this
>wouldn't exactly mean "no boundary condition", since as long as you have a
>first row and a last row in your operator you have two corresponding
>boundary conditions... but I'm probably missing something here. Could you
>give more details, please?

Luigi already got my answer since we're in the same office, anyway for the
sake of this list discussion, here is a sketch. Please feel free to add,
correct and/or give more detailed discussion.

An example of free boundary condition is the American early exercise.
With trees you're used to roll back and then simply apply the non-arbitrage
(call) condition:
V=max(V, S-K),
that is you enforce the option value V to be greater or equal to the option
intrinsic value.

To use the same approach with finite difference is OK with explicit
methods, not with implicit methods, because each option value on the
fixed-time grid depends on all the others on the same fixed-time grid.
That is you cannot solve the equation system and then apply the
non-arbitrage condition (if you do that you lower the accuracy order of
your solution), instead you have to solve the system enforcing the
non-arbitrage condition as early as you can, at the same time as the values
are found.

This is usually accomplished solving the system with the "Successive
Over-relaxation" (SOR) technique instead of LU decomposition.

Has anyone other example of free boundary problems? I can only think of
passport option.

ciao -- Nando

[Nicolas Di Césaré]

Ferdinando Ametrano wrote:

>
> Has anyone other example of free boundary problems? I can only think
> of passport option.


Hi all,

Discretization model can introduce free boundary condition. By example,
the model intoduced by K. Tsiveriotis and C. Fernandes to price
convertible bonds (CB). They define a second unknow, the "cash only
convertible bond" price solution of an equation with a free boundary
condition.


cheers,

Nicolas