fakesson (u/fakesson)

fakesson commented on Pricing Americans with finite-difference tastyhedge.com/blog/finit... · Posted by u/gituliar

quanto · 2 years ago

Your intuition is quite correct. These methods (Leif et al) do not extend well to different boundary or intermediate conditions that are quite necessary in real life scenarios. AFAIK, there are a few teams on the Street that do fairly advanced numerical analysis, but most resort to Monte Carlo or some statistically-informed perturbation theory.

(I wish I could talk more, but yeah, legal obligations)

fakesson · 2 years ago

Monte Carlo might be ok to OTC derivatives, however for automatic market making of exchange traded option, which are mostly American, it would be too slow.

After a bit more googling, I found these more recent slides by Jesper Andersen, where he believes that the Leif et al method could be extended for local vol (see page 25): https://www.cqfinstitute.org/sites/default/files/4%20-%20Jes...

fakesson commented on Pricing Americans with finite-difference tastyhedge.com/blog/finit... · Posted by u/gituliar

scott00 · 2 years ago

Is that method extensible to discrete dividends?

fakesson · 2 years ago

I googled and found slides there Leif extends the method to discrete dividends: https://www.math.cmu.edu/CCF/CCFevents/shreve/abstracts/L.An...

( I'm a fixed income quant, so I didn't look for it until now.) For a more advance model than Black-Scholes, e.g. local vol I don't expect it can be extended, and one would then need use some PDE based method.

fakesson commented on Pricing Americans with finite-difference tastyhedge.com/blog/finit... · Posted by u/gituliar

quanto · 2 years ago

what's a faster method than a Crank Nicolson implementation discussed in the post?

fakesson · 2 years ago

"High Performance American Option Pricing" by Leif Andersen et al is many orders of magnitude faster than any finite difference method or other PDE / tree method. https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2547027

Given the exercise boundary, the American Option Price can be written exactly as a one-dimensional integral. That is the key insight to this superior method.