Greeks for barriers on a tree

pj · Post by pj » Wed Jan 16, 2008 3:53 pm

Are they stable? (I have impression not)

How could they estimated better?

Richardson extrapolation?

Graeme · Post by **Graeme** » Wed Jan 16, 2008 4:03 pm

As I recall not even greeks on a vanilla tree are very pleasant.

pj · Post by pj » Wed Jan 16, 2008 4:16 pm

> 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?

mj · Post by mj » Wed Jan 16, 2008 11:38 pm

how about using the likelihood ratio method?

pj · Post by pj » Thu Jan 17, 2008 9:08 am

> how about using the likelihood ratio method?

That's too cryptic to me. Please expand Worship

functor · Post by **functor** » Fri Jan 18, 2008 9:28 pm

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.

mj · Post by mj » Sat Jan 19, 2008 4:08 am

i thought i discussed the LR method in concepts...

It's normally applied to Monte Carlo but the same idea works for trees.