Handling Path Dependence and Prior Decisions in Least-Squares Monte Carlo

Summary

The document addresses whether least-squares Monte Carlo can price options whose payoffs depend on past exercise decisions. Its answer is that path dependence alone does not rule out the method: relevant path information can be included as auxiliary variables among the regression inputs. This allows the regression to condition estimated continuation values on the information that affects future payoffs.

When the payoff also depends on earlier decisions, the approach may require separate regressions for different possible decision histories, or encoding those decisions as variables in the regression. The discussion gives a general modeling principle rather than a named class of options or examples of specific listed products. It does not provide implementation details, convergence analysis, or evidence that any particular choice of regression variables will work well; the usefulness of the method depends on representing the relevant state adequately.

Key ideas

• Path-dependent payoffs can be handled by including relevant accumulated path information in the regression state.
• Past exercise decisions may be represented as regression variables.
• Separate regressions can be used for distinct possible decision histories.
• The answer gives a general modeling method, without naming particular traded products or assessing numerical accuracy.

Tags

# Example of options that cannot be priced with least-square Monte Carlo


# Example of options that cannot be priced with least-square Monte Carlo












Can you give some example of options that cannot be priced with least-square Monte Carlo?

Intuitively, this is any option for which a payoff depends on a previous exercise decision. It's relatively easy to cook-up some example by hand.

Is there a name for such class of option?

Can you give the name of such options that are sold in financial market?

## Answer by Mark Joshi (score 1, accepted)

https://quant.stackexchange.com/a/23071

you just add in any auxiliary variables accumulated along the path that determine the pay-off to the regression variables. So path-dependence is not a problem.

If you have previous decisions, you may need to do different regressions based on their possible values or make them into a continuous variables that can be used for regression.

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