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Abstract
A stress test is an important tool for assessing risk in a portfolio. In this article, the authors consider a stress test implemented by an evaluation under stressed model parameters. The authors will compare Monte Carlo with partial differential equation (PDE) valuation and propose a new, robust variant: Monte Carlo simulation with boundary conditions. The way a Monte Carlo valuation algorithm can fool you can be observed for even the simplest model and the simplest product: valuation of a call option under a Black-Scholes model. With respect to stress testing, the authors found that the super/sub-hedge boundary condition is a very promising choice. It gives a stable upper/lower bound for the true value with low Monte Carlo error. The bound can be made as sharp as the original Monte Carlo simulation when the model in its non-stressed region. If the boundary value process is good, then the method gives even better results than a corresponding PDE algorithm.