ABSTRACT
We have introduced the uncertain volatility model in Section 5.2 in the onedimensional setting. This model has long attracted the attention of practitioners as it provides a worst-case pricing scenario for the sell-side. As seen in Section 5.2, the valuation of financial derivatives based on this model requires solving a nonlinear PDE. One can rely on finite difference schemes only when the number of variables (that is, underlyings and path-dependent variables) is small-in practice no more than three. In all other cases, the numerical valuation seems out of reach. In this chapter, we suggest two new, accurate, easy-implementable Monte Carlo methods which hardly suffer from the curse of dimensionality. The first method requires a parameterization of the optimal covariance matrix and consists in a series of backward low-dimensional optimizations. The second method relies heavily on second order backward stochastic differential equations. Parts of this research have been published in [120].
