We introduce a new methodology for computing Hessians from algorithms for function evaluation, using backwards methods. We show that the complexity of the Hessian calculation is a linear function of the number of state variables times the complexity of the original algorithm. We apply our...

When pricing Bermudan derivatives by regression-based methods, foresight bias will appear in lower bounds when using a single simulation to estimate the exercise strategy and to compute lower bounds. In this paper, we propose a new method to remove this kind of bias without introducing an...

We derive the first known multiplicative dual for Bermudan type options that can be exercised more than once. Our multiplicative dual possesses the almost sure property, thus making it a viable alternative to the additive one. A method to compute the multiplicative upper bound is presented and...