Worst-Case Scenarios For American Options

One approach to cope with uncertain diffusion parameters when pricing options portfolios is to identify the parameters$\hat p$in a subset$\mathbb C$of the parameter space which form the worst-case for a particular portfolio. For the sell-side, this leads to a nonlinear algorithm that maximizes the expected liability under the risk-neutral measure.$\hat p$depends on the portfolio under consideration. Moreover, the algorithm must take into account that the exposure to$\mathbb C$-risk changes when non-vanilla components such as barrier or American options knock out or are exercised early. In this paper, we describe techniques to price portfolios with American options under worst-case scenarios based on uncertain volatility models. We also present heuristics which reduce the computational complexity that arises from the necessity to consider many early exercise combinations at a time. These heuristics reduce the compute time by almost one half.