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Practical Checks and Improvements for Least Squares Monte Carlo Pricing

Article Quant Q&A · Author: Probilitator
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Summary

The document collects implementation advice for Longstaff–Schwartz least squares Monte Carlo (LSM), a method used to price Bermudan and other early-exercise derivatives. It emphasizes that basis-function choice affects results, regression can be numerically unstable, and enhancements such as policy iteration or multiple regression may improve the approach. It also recommends building the exercise strategy in one simulation pass and estimating its value in a separate pass, then comparing the estimates as a diagnostic.

For validation, the answer advises implementing an upper bound and testing difficult, long-dated, high-dimensional cases. It warns that implementation bugs often produce downward bias and recommends careful testing, including a simple spreadsheet prototype. A second response points to leave-one-out cross-validation as a way to address look-ahead bias. These are practical suggestions rather than a complete implementation guide or quantified comparison: the document gives no benchmark results, and choices of basis, enhancement, and validation method still require case-specific assessment.

Key ideas

  • The choice of regression basis can materially affect LSM pricing results.
  • Separate strategy construction from valuation and compare the resulting estimates as a diagnostic.
  • Use upper bounds and challenging long-dated, high-dimensional cases to assess pricing quality.
  • Regression instability and downward-biased implementation errors warrant careful validation.
  • Leave-one-out cross-validation is suggested as a way to reduce look-ahead bias.

Tags

Derivatives pricingOptionsStatisticsBacktesting
Full text
# Practical implementation of Least Squares Monte Carlo (tweaks and pittfalls)


# Practical implementation of Least Squares Monte Carlo (tweaks and pittfalls)












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

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

- 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) ?

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

## Answer by Mark Joshi (score 12, accepted)

https://quant.stackexchange.com/a/15434

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

## Answer by jaehyukchoi49 (score 1)

https://quant.stackexchange.com/a/42305

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

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.