Least-Squares Monte Carlo for American Options: Bias and Validation
Summary
The document examines a reported overvaluation from least-squares Monte Carlo (LSM) applied to American calls on a non-dividend-paying stock, whose value should match that of the corresponding European call. The response explains that the Longstaff–Schwartz method estimates continuation values through regression and, when implemented appropriately, yields a lower bound on the true option value. A noisy continuation estimate can affect exercise decisions, but does not justify assuming that early exercise should raise the estimate above the European value.
A central implementation concern is using the same simulated paths both to fit the exercise rule and to value the option; separate path sets help avoid this bias. The answer also notes that accuracy depends on choices such as the regression sample, basis functions, path count, and model assumptions. Since the question supplies no implementation details, the stated overvaluation cannot be diagnosed precisely, and the discussion gives no numerical validation beyond the questioner's report.
Key ideas
- For a non-dividend-paying stock, an American call has the same value as its European counterpart.
- LSM estimates continuation values by regression and can produce a lower bound on the true option value.
- Using separate path sets for fitting the exercise policy and valuing the option can reduce bias.
- LSM accuracy depends on simulation design, regression basis, and which paths enter the regression.
- The document lacks enough implementation details to identify the source of the reported overvaluation.
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# Least Square Monte Carlo - american Call Option # Least Square Monte Carlo - american Call Option An American Call Option on an non dividend paying stock has the same value as a european one. I tired to compare the results given by the LSM with the results given by the B&S formular. It seems like LSM is really bad for valuing american call options. It always overestimate the value by 5-20%. But why is the algorithm so bad for call options and so good for put options ? Are there some studies concerning this problem ? ## Answer by Quantuple (score 8) https://quant.stackexchange.com/a/30211 If implemented properly, least-squares Monte Carlo as originally suggested by Longstaff-Schwartz should allow you to identify sub-optimal exercise dates and a lower bound of the true option price. There are many articles out there discussing this non trivial topic. @MarkJoshi can probably shed some more light, see this nice paper. You claim that your LSM procedure overestimates the true option price: I guess that you did not use 2 independent set of paths i.e. one for calibrating the exercise boundary through regressions and a separate one for determining the exercise dates. Regarding the precision of $5\%-20\%$, IMHO you must have a problem with your implementation. However, it is difficult to say anything more concerning your precision issue since you don't provide all the details: How many paths do you simulate and under what working modelling assumption, did you only use ITM paths during the regression pass, what type of basis functions did you choose and how many of them etc. ## Answer by student (score 0) https://quant.stackexchange.com/a/30235 Maybe I have something wrong with my calculation. But this is not my whole point. When calculating the value of an American put I totally understand why the LSM algorithms underestimates the value. Mainly because I only have an estimated conditional expectation function. But with Call option I don’t understand why the algorithms also have to underestimate the value. For me it makes total sense that the LSM approach overestimates the value. Again I only have an estimate of the conditional expectation function. So there can happen two things. Either the LSM algorithms determines that early exercise is favourable. Then the value has to be higher than the European value (overestimation). Or the LSM algorithm determines that early exercise is disadvantageous. Then the value must be exactly the same.
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