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Greeks for barriers on a tree
Posted: Wed Jan 16, 2008 3:53 pm
by pj
Are they stable? (I have impression not)
How could they estimated better?
Richardson extrapolation?
Greeks for barriers on a tree
Posted: Wed Jan 16, 2008 4:03 pm
by Graeme
As I recall not even greeks on a vanilla tree are very pleasant.
Greeks for barriers on a tree
Posted: Wed Jan 16, 2008 4:16 pm
by pj
> not even greeks on a vanilla tree are very pleasant
Ça va. But barriers...
And how to do them better without recalculating them
too much?
Greeks for barriers on a tree
Posted: Wed Jan 16, 2008 11:38 pm
by mj
how about using the likelihood ratio method?
Greeks for barriers on a tree
Posted: Thu Jan 17, 2008 9:08 am
by pj
> how about using the likelihood ratio method?
That's too cryptic to me. Please expand Worship
Greeks for barriers on a tree
Posted: Fri Jan 18, 2008 9:28 pm
by functor
If you want delta, gamma, or theta, what is wrong with using the method of using the first few nodes? E.g. for delta just take (C(1,1) - C(1,0))/(S(1,1) - S(1,0)) where C(1,1) is the value of the option at the second time step and going up once? Similarly for gamma, theta.
For others like rho, I guess you have to use one tree to compute C(0,0) then compute it for r+h and take the differences over h, which would be unstable even for vanillas, but for the above greeks I mentioned it should be stable no? When I tested delta for vanillas I got the answer correct to 2 decimal places with 100 steps.
Greeks for barriers on a tree
Posted: Sat Jan 19, 2008 4:08 am
by mj
i thought i discussed the LR method in concepts...
It's normally applied to Monte Carlo but the same idea works for trees.