In this article we review the LSMC approach with particular emphasis on regression polynomial selection, conducted on a specific financial product consisting of a bond, a stock and a put option. We will see that by using LSMC, we can accurately capture most properties of the future distribution of portfolio values, at a substantial gain in runtime compared to if we perform a full nested simulation. Furthermore, we will see that our algorithm for generating optimal regression functions efficiently produces polynomials that are resistant to overfitting and exhibit low complexity, while maintaining high accuracy.