4 ms·

"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 metho

"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 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.

scott00 3y ago
Is that method extensible to discrete dividends?
- fakesson 3y ago
  I googled and found slides there Leif extends the method to discrete dividends: https://www.math.cmu.edu/CCF/CCFevents/shreve/abstracts/L.Andersen.pdf 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.
  - quanto 3y 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 3y 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-%20Jesper%20Andreasen%20american%20cqf%202021.pdf https://www.cqfinstitute.org/sites/default/files/4%20-%20Jes...
    - Agingcoder 3y ago
      I go through academic literature on a regular basis, hoping that some kind of really major improvement might magically appear. Usually the ideas are great, but they don’t survive real life equities markets ( from dividends to non convex payoffs, local vol etc )

scott00 3y ago

Is that method extensible to discrete dividends?

fakesson 3y ago
I googled and found slides there Leif extends the method to discrete dividends: https://www.math.cmu.edu/CCF/CCFevents/shreve/abstracts/L.Andersen.pdf 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.
- quanto 3y 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 3y 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-%20Jesper%20Andreasen%20american%20cqf%202021.pdf https://www.cqfinstitute.org/sites/default/files/4%20-%20Jes...
  - Agingcoder 3y ago
    I go through academic literature on a regular basis, hoping that some kind of really major improvement might magically appear. Usually the ideas are great, but they don’t survive real life equities markets ( from dividends to non convex payoffs, local vol etc )