Are these the same terms as in the pdf?
One of my quant students solved the Bermudan PDE using about 4 different FD methods in about 2 months before he heads off for UCB (PDE savvy mandatory to get in). I did a few FDM as well for comparison. The schemes are super fast. Next is to compute sensitivities.
This PDE is benign (compared to Heston etc.) because PDE coefficients are constant.
[size=100] boundary conditions
We took Dirichlet BC on truncated domain. ?[/size]
Other cases give strange BCs,
seems you truncated the domain at 0. If a normal model why did you do that? Did you estimate the error compared to moving the truncation point into the negative short rate domain?
No truncation at 0! Please see my post to @bearish. See the pdf again for the way we pose the PDE.
We use rmax = 0.2 and umax = 0.1 for the far fields only which seems to be OK (in truth, we are using 'heuristic/pragmatic' thinking for the truncation part:))
The tentative conclusion is that our FDM models (exact HW2, ADE*, MOL and Soviet Splitting) all give the same results. Now just the Bermudan part. Let's see.
Hi, apart from my question on you pdf. Your arguments given to bearish are true. If you allow for example the short rate to become infinitly negativ then there is no easy boundary condition for - inf.
I tried out the PDE given in PWQF (Vol2) for a defaultable Zero Bond under the assumption that default will not occur before payment. Found it interesting. In PWQF no boundary conditions where given and the model war apperantly a normal one (looking at the sde for the default spread p there). I solved the equation (btw with mol) but truncated at 0 to. Well in fact i did a domain transformation from x -> r mapping [0,1] to [0,+inf].
so i did the same thing and i didnt analyze what happens if i truncate at negative short rates (or in this case negative default spreads).
To my (or maybe out both) excuses i like to say the choice of the truncation point in PDE Methods for normal ir models is mostly treated heuritically in what i found in papers. A recent paper (dont have the link atm) just did a domain transformation r->ln(ar+b) without commenting this much. This results of course also in domain truncation. But this time somewhere in the negative r domain.
And i remember a thread here on the site where one of the conclusion was afaik "Just choose an empirical truncation point slightly negative".
So i kindof wondered if you got access to some new arguments....