This talk is about the valuation of American options by Monte Carlo simulation in the presence of stochastic volatility and interest rates. For practitioners, it is important to have available efficient -- i.e. accurate and fast -- valuation algorithms in such a context.
Recently, Medvedev and Scaillet (2009) introduced new value approximation techniques whose technical implementation takes less than one second per American option valuation. They state that the valuation by Monte Carlo simulation with Matlab takes "dozens of minutes" in comparison.
Our Python/Numpy implementation of an improved Monte Carlo algorithm takes only 1.5 seconds (on a typical notebook) for an accurateness that is consistent with market requirements. Our results underline that the Python/Numpy combination is appropriate for computationally demanding finance applications.