Some quick algorithms for quantitative finance.

Summary In this thesis, we focus on critical nodes of counterparty risk computation, the rapid valuation of derivatives and their sensitivities. We propose several mathematical and computational methods to address this problem. We contribute to four different areas: an extension of the Vibrato method and the application of multilevel Monte Carlo methods for the computation of high order Greeks n>1 with an automatic differentiation technique. The third contribution concerns the valuation of American products, here we use a parareal scheme for the acceleration of the valuation process and we also make an application for the solution of a backward stochastic differential equation. The fourth contribution is the design of a high-performance computing engine with parallel architecture.