Pricing American options with Least Squares Monte Carlo

In this recipe, we learn how to valuate American options. The key difference between European and American options is that the latter can be exercised at any time before and including the maturity date—basically, whenever the underlying asset’s price moves favorably for the option holder.

This behavior introduces additional complexity to the valuation and there is no closed-form solution to this problem. When using Monte Carlo simulations, we cannot only look at the terminal value on each sample path, as the option’s exercise can happen anywhere along the path. That is why we need to employ a more sophisticated approach called Least Squares Monte Carlo (LSMC), which was introduced by Longstaff and Schwartz (2001).

First of all, the time axis spanning [0, T] is discretized into a finite number of equally spaced intervals and the early exercise can happen only at those particular time steps. Effectively...