I am implementing LSMC to price American options based on a custom model. I now need to make a choice of basis functions, so I am looking for the theoretical justification for using Laguerre polynomials in the Longstaff Schwartz paper.
The section "8.3 Choice of basis functions" in the Longstaff Schwartz paper seems to provide (in words-- not math-) some justification for this choice that might be understandable to a statistician, but sufficiently explain to me the preference for Laguerre polynomials:
Finally, the choice of basis functions also has implications for the statistical significance of individual basis functions in the regression. In particular, some choices of basis functions are highly correlated with each other, resulting in estimation difficulties for individual regression coefficients akin to the multicolinearity problem in econometrics.
In the paper "The Valuation of Real Options with the Least Squares Monte Carlo Simulation Method", a justification for Laguerre polynomials is given that these produce better numerical results:
In our analysis, we have compared eleven polynomial families, used as basis functions to estimate the continuation value, and we have analysed the convergence of the method increasing the number of basis functions. The numerical results suggest that the weighted Laguerre polynomials provide more accurate results, particularly for the case of compound and mutually exclusive options.
Is there a better mathematical explanation for why Laguerre polynomials are a good choice of basis functions?