[Quantlib-dev] Re: [Quantlib-users] Ideas for two new classes

[Joseph W. <jo...@co...>]

Daniel J. Duffy wrote:

> I use the Bridge pattern for PDE concept (a PDE has many 
> implementations), and I use Template Method for FDM hierarchy. Betewen 
> PDE and FDM I use standardised interfaces.
>  
> Do Quantlibbers use UML to communicate design ideas, or how does it 
> work in this case?

There is a lot of UML in the quantlib web.  In this case, I wasn't 
thinking in terms of any basic change to the basic class hierarchy or 
structure.  Merely two fairly localized (but important changes).  One of 
the purposes of these two changes is to decouple the FDM code from the 
rest of the system more so and so that we can then think about more 
fundamental changes to the way that the FDM engines work.

The FDM hierarchy already uses the template pattern.  The problem is the 
that right now quantlib creates the FDM operators directly from the 
black scholes process.  This couples the FDM far too closely to 
Black-Scholes.

IMHO, the way that it should work is that the BS process creates a PDE 
object and this PDE object is what get finite differenced.  The other 
problem is that right now the FD pricing engines create a pricing curve 
which can be used to create a delta and a gamma curve, but all of that 
gets thrown away.  Having a sampled curve class will let the price curve 
available as a class which you can then process. 

One problem with the sampled curve class is that it is based on the 
quantlib Array class and Array is hard coded to use Real's.

As far as what the PDE object should look like....

I hear that someone wrote a book on "Financial Instrument Pricing Using 
C++" where he spends an several chapters on this topic.  Hmmmmm.... :-) 
:-) :-) :-)

>  
> Daniel
>
> ------------------------------------------------------------------------
> *From:* qua...@li... on behalf of Joseph 
> Wang
> *Sent:* Sat 01/10/2005 02:48
> *To:* qua...@li...; 
> qua...@li...
> *Subject:* [Quantlib-users] Ideas for two new classes
>
> math/SampledCurve - represents a curve which consists of n+1 arrays, one
> for the independent values and n dependent values.  Methods of this
> class will allow for interpolation and generating first and second
> derivative curves.
>
> PartialDifferentialEquation - represents a PDE
>
> The idea behind these new classes will be to clean up the finite
> differencing code a bit.  Instead of deal with raw arrays, the code will
> deal with SampledCurve's which will have facilities to allow
> interpolation, and the finite difference class will be able to pass the
> SampleCurve back up to the instrument where things can be done with it
> such as calculating delta curves and option curves.
>
> The idea behind a PDE class is to separate the processes from the finite
> differencing code.  For example the BlackScholes process will generate a
> PDE object and the fd code will generate the finite difference operators
> from the PDE object rather than the BlackScholes process itself.
>
> The idea behind this is to improve code clarity as well as to allow for
> PDE arithmetic.  Also, I suspect that there are some very clever things
> that one can do with Feymann-Kac once we have this in place.
>
>
>
>
>
>
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