Comparing Monte Carlo Methods for American Option Pricing

Summary

The document compares Longstaff–Schwartz least-squares Monte Carlo with a forward Monte Carlo approach for pricing an American call. It explains that each method relies on an estimated exercise policy, so each reported price is a lower bound on the option’s true value. Choosing whichever method returns the higher estimate can serve as a simple comparison, but it does not reveal the size of the pricing error.

For a fairer comparison, the answer recommends using the same simulated underlying paths and keeping the variance of each estimate reasonably low. A dual method can supply an upper bound, creating a range for the true price rather than treating either lower estimate as exact. That range still depends on whether the simulated stock process and volatility model are appropriate. The document offers methodological guidance, but no numerical experiment, convergence evidence, or universal rule for deciding which estimator performs better.

Key ideas

• Both approaches estimate an exercise policy, so their prices are lower bounds.
• Using the same simulated underlying paths makes the method comparison more consistent.
• Lower variance improves the usefulness of each Monte Carlo price estimate.
• A dual method can provide an upper bound and bracket the true option value.
• The bounds are only meaningful when the underlying simulation model is suitable.

Tags

# Shall I use the Longstaff and Schwartz method or the forward Monte Carlo method to price an American call?


# Shall I use the Longstaff and Schwartz method or the forward Monte Carlo method to price an American call?












I am comparing two methods: Least squares by Longstaff and Schwartz and A Forward Monte Carlo method. I am not sure what price I should consider as the "true value" to compare these two approaches. Any suggestions are greatly appreciated. The option is an American call.

## Answer by vara (score 1, accepted)

https://quant.stackexchange.com/a/33933

Given the optimal exercise boundary is only an estimate, both the methods underestimate the "true value" of the option.

A simple comparison would be whichever method produced higher price for the option is better.

For this comparison to make sense, you could

- re-use underlying stock simulation across both the methods.

- make sure variance of price produced is reasonably low for both.

The "better" value of the two is still a lower bound and doesn't really throw information on how big the error is.

You could implement dual method to produce upper bound and thus a range for the true option price.

Again, this range is meaningful only if the underlying stock simulation ( vol model ) is meaningful.

Remember 'garbage in garbage out'

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