by jige » Tue Aug 07, 2012 4:33 pm
Hello,
This is my first post here, so first let me thank you for all the details and time you took working on ADE and answering to people here and on wilmott.
After reading lot of posts and coding on my side, i successfully implemented an ADElike PDE solver in 1D for classic european/american options (plain vanilla, barrier, asian).
I also did a 2D version for spread options which seems to fully work.
My question , as i'm not from a research background come for the crossderivatives in 2D.
In the shepard thesis you find the expression for cross derivatives in the file attached.
I use this expression with W=0 which basicely is the explicit scheme.
As a consequence, because your method use two sweeps , one coming from downside and one coming from upside, with W=0 i use the EXPLICIT schemes for this crossed derivatives and don't see how to build an ADE like scheme.
Its not what for example you do with first order derivatives mixing u_n and u_n+1 (HERE n represent the time dimension) because neither u_n+1,i1,j+1 nor u_n+1,i+1,j1 is known when computing the U sweep or V sweep.
My question is, does the fact that for cross derivatives i use the EXPLICIT schemes but use ADE schemes for other derivatives make sense, does it break robustness, convergence or stability ? (i didn't remark it during my study on prices or greeks). Is ADE for cross derivatives equal to the Explicit schemes ?
Many thanks.[/img]
 Attachments

 Shepard Cross Derivatives
 070812 43752 PM.jpg (18.07 KiB) Viewed 41479 times