查看文章

We introduce a novel numerical framework for pricing American options in high dimensions. Our scheme manages to alleviate the problem of dimension scaling through the use of adaptive sparse grids. We approximate the value function with a low number of points and recursively apply fast approximations of the expectation operator from an exercise period to the previous period. Given that available option databases gather several thousands of prices, there is a clear need for fast approaches in empirical work. Our method processes an entire cross section of options in a single execution and offers an immediate solution to the estimation of hedging coefficients through finite differences. It thereby brings valuable advantages over Monte Carlo simulations, which are usually considered to be the tool of choice in high dimensions, and satisfies the need for fast computation in empirical work with current …