We introduce two new methods to calculate bounds for zero-sum game options using Monte Carlo simulation. These extend and generalise the duality results of Haugh–Kogan/Rogers and Jamshidian to the case where both parties of a contract have Bermudan optionality. It is shown that the Andersen–Broadie method can still be used as a generic way to obtain bounds… (More)
In this article we propose a novel approach to reduce the computational complexity of the dual method for pricing American options. We consider a sequence of martingales that converges to a given target martingale and decompose the original dual representation into a sum of representations that correspond to different levels of approximation to the target… (More)
We first develop an efficient algorithm to compute Deltas of interest rate derivatives for a number of standard market models. The computational complexity of the algorithms is shown to be proportional to the number of rates times the number of factors per step. We then show how to extend the method to efficiently compute Vegas in those market models.