I am trying to implement a LSMC to value an american-style real option with an underlying project value that is exposed to several risk factors.
In the paper of Longstaff & Schwartz, they use the first three Laguerre polynomials to execute their regressions. Unfortunately, they don't provide any explanation about what these functions are and how they are used.
My question is, can we always use these same functions irrespective of the dynamics of the underlying/model setup? How do we choose these basis functions and what do they actually mean?
Obviously I am new to this, so besides the technical stuff, I would very much appreciate some intuitive explanation.
Thank you for your support!