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Longstaff–Schwartz Accuracy Limits in American Option Pricing

Article Quant Q&A · Author: efwofo
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Summary

The document asks how long a standard implementation of the Longstaff–Schwartz Monte Carlo method would need to price an American put under Black–Scholes to more than ten digits of accuracy. It gives one practitioner’s response: their C++ implementation did not reach that precision, which they attribute to imperfections in machine-generated uniform random samples.

This is an anecdotal observation rather than a timing estimate or a demonstrated accuracy bound. The document supplies no benchmark, implementation details, error analysis, or comparison with variance reduction and alternative numerical methods. It therefore highlights sampling and numerical precision as concerns, but does not establish that ten-digit accuracy is impossible or say how many seconds the calculation would take.

Key ideas

  • The document frames American put valuation under Black–Scholes as a Longstaff–Schwartz Monte Carlo accuracy question.
  • One practitioner reports that their implementation did not attain more than ten digits of precision.
  • The response attributes the limitation to imperfections in machine-generated random samples.
  • The document provides no timing benchmark or evidence that the reported limitation applies generally.

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Full text
# How many seconds of Longstaff Schwartz would it take to get machine accuracy?


# How many seconds of Longstaff Schwartz would it take to get machine accuracy?












Roughly speaking, using a standard programming language, a standard computer, and a standard implementation, how many seconds would it take to price an American put option to 10+ digits of accuracy in Black Scholes model?

## Answer by Valometrics.com (score 1)

https://quant.stackexchange.com/a/51375

I've already built an LS american options pricer using C++ and I can tell that you will never have a precision of 10+ digits. It's due to the non-perfect randomness of uniform samples generated by the machine.

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