Numerical Methods in UnRısk

This technical paper explores the numerical methodologies employed in the UnRısk framework, focusing on adaptive integration and streamline diffusion. The document initially introduces the adaptive integration techniques applied in option pricing under the Black-Scholes framework, emphasizing the use of high-order integration schemes and adaptive gridding for precise and stable computations.

Furthermore, the paper addresses the challenge of accurately valuating financial derivatives, highlighting the robustness and efficiency of these methods in computing option values and their Greeks. The latter part of the paper delves into streamline diffusion as a stabilization technique within finite element analysis for solving partial differential equations associated with two-factor interest rate models, specifically discussing the generalized Hull & White two-factor model. The integration of Crank-Nicolson time discretization and space discretization through finite elements is explained to ensure the convergence and stability of the numerical solutions.

The paper concludes by discussing the implementation nuances in terms of time and space gridding to optimize computational resources and maintain result accuracy.