Numerical methods for valuation and hedging of exotic multi-underlying options: market models and models with uncertain volatility.

Summary The valuation of high-dimensional expected exercise products requires discretization techniques for Monte Carlo methods. The objective of this thesis is to solve this type of problem in the context of market models and models with uncertain volatility. In the first case we seek to solve an optimal stopping time problem, in the second we seek to solve a stochastic optimal control problem. The associated backward equations involve conditional expectations that we seek to estimate numerically. The accuracy of the estimates of prices and hedge ratios is crucial for the management of structured product portfolios. Thus we also study in this thesis the variance reduction methods applied to Monte Carlo techniques.