Longstaff-Schwartz Method for Pricing American Options

[yfnaji]

Pull request contributes to this issue regarding pricers for American options.

The Longstaff-Schwartz method is a Monte Carlo technique that uses least squares regression on in-the-money paths at each backwards time step to estimate the continuation value (the option’s value if it is not exercised).

In this implementation, I chose Legendre polynomials up to order 4 (i.e., orders 0 to 4) as the basis functions for the regression step. However, other basis functions, such as Hermite or Chebyshev, can also be used.

The unit tests were designed to pass within a tolerance threshold due to the variance in this method’s outcomes.

Note that at some point, as with the finite difference pricers, we will likely eventually implement these pricers on types/objects (as opposed to keeping struct pricers).

The Longstaff-Schwartz algorithm

I have outlined the algorithm in this PDF.