The Black-Scholes (BS) model gives the value of a European option when the underlying follows a lognormal distribution with constant volatility. American options, however, require more elaborate procedures, typically coming from what amounts to an approximate solution to a “backward” partial differential equation. Time varying volatility is fairly easily accommodated for European options, so long as it is non-stochastic, but for American options things become more complicated. More complex derivatives, involving compound optionality, for example, can be solved for the simplest cases, but quickly get beyond easy application of current techniques, as complexity grows. In any case, the existing solutions are such that each option requires its own full valuation routine. In this rather remarkable article, Buraschi and Dumas develop a new technique, based on solving a forward equation, that greatly simplifies the entire process. The result is a valuation algorithm that easily handles time varying (non-stochastic) volatility, compound optionality and American exercise. Unlike the “backward” technique, their approach produces an entire valuation surface defined in terms of strike and time to maturity, given current date and stock price. This allows valuation of multiple options on the same underlying with essentially no more computation than pricing a single one.