Replicating Americans a la Jaeckel - Rebonato

[FDAXHunter]

That's precisely what got me hooked on it. The nice thing about this is that you can precompute functions once and recycle these for any(!) option on the surface. This is not possible with trees/FD.



You can get rid of the jumping problem by trading multiple options at the same expiration.

[mj]

i looked at similar cases, i.e. a bermudan option, in my paper on replication, downloadable from www.quarchome.org

[AVt]

a lame procedure in Maple with some examples: [url=/User%20Files/66/JaeckelRebonato_proc_NP.pdf]Attached File: JaeckelRebonato_proc_NP.pdf[/url]



[u]Edited 05. May 2005[/u]: Peter Jaeckel confirmed that it was undone to mention the detail that in the

case that there is no intersection between the portfolio value and the intrinsic value no additional

optiolina is to be added.

[AVt]

For the question of approximating with europeans (with smiles) i switched

to Kim's integral respresentation (even being not quite sure about what is

the correct version with smiles - if anybody has is, let me know ...).



The point is: after starring at his integrand and starring and starring (ok,

i know i am slow) and reading (ok, it was more a looking to understand) it

writes as european put, vanilla + binary. So the usual rules for numerical

integration in their simpliest form (Riemann sum or trapez rule or better)

lets one approximate as Put_american = Put + sum( puts + digitals ) as an

discretization.



But this is better continued in another thread. And later. While now  Chug Beer