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The Longstaff-Schwartz LSM approach is nowadays ubiquitous(at least in the academic literature) in pricing path dependant derivatives. Up to now I have mostly worked with lattice methods. My experience in impelemting those has shown that there are often ways to tweak them and also lot of pittfalls along the way.

To those of you who have some experience in working with LSM:

  1. Aside from the usual Monte-Carlo-Optimization techniques (e.g. variance reduction, importance sampling etc.) are there any optimizations that are particular to the LSM approach ? (Perhaps some paper on the choice of the interpolating polynomial) ?

  2. What are possible pittfalls when implementing and working with the model ? When can LSM go really wrong/ in which cases does it fail to price correctly ?

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  • $\begingroup$ Upvoted, though I'm not sure "ubiquitous" is really true. What desks is it ubiquitous for? Or are you thinking more of academic literature? $\endgroup$
    – Brian B
    Commented Mar 4, 2014 at 16:54
  • $\begingroup$ well in academic literature for sure. Also I am not aware of any other methods but lattice (and these don't work in n-dimensions) - I am not working in the front office so I wouldn't know about which desks use what - I will edit the question. $\endgroup$
    – Probilitator
    Commented Mar 4, 2014 at 16:59

2 Answers 2

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LSM is very fiddly.

The most important things in my view are

1) don't believe anyone who says that the choice of basis functions doesn't matter.

2) implement an upper bounder, eg Andersen--Broadie (2003) or Joshi-Tang (2014) so you can tell if your prices are good

3) do two passes, one to build the strategy, one to price, if they give very different prices you have a problem

4) use an enhancement, eg LSA, policy iteration, multiple regression

5) discount to the current time frame when doing IRD not the initial time,

6) bugs tend to lead to downwards bias not huge errors so very careful testing is important

7) do it in a spreadsheet first

8) the numerical regressions tend to be unstable so guard against this

9) test on long-dated high dimensional examples. These are the hardest.

10) price cancellables not callables

Some papers

Practical Policy Iteration: Generic Methods for Obtaining Rapid and Tight Bounds for Bermudan Exotic Derivatives Using Monte Carlo Simulation Beveridge Joshi Tang

Kooderive: Multi-Core Graphics Cards, the Libor Market Model, Least-Squares Monte Carlo and the Pricing of Cancellable Swaps, Joshi

Effective Sub-Simulation-Free Upper Bounds for the Monte Carlo Pricing of Callable Derivatives and Various Improvements to Existing Methodologies Joshi Tang

see also Chapter 13 of More Mathematical Finance

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  • $\begingroup$ thank you :) You answer contains some quite reasonable suggestions $\endgroup$
    – Probilitator
    Commented Dec 17, 2014 at 10:03
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My recent paper (Arxiv | SSRN) discusses how look-ahead bias can be efficiently removed with LOOCV, a cross-validation method in machine learning. Also see https://quant.stackexchange.com/a/42303/26559

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