EVALUATION OF FINANCIAL OPTIONS UNDER STOCHASTIC VOLATILITY WITH NUMERICAL EXPERIMENTS

Abstract

In this work, we priced European options by proposing a mathematical model to address price fluctuations not explained by the Black-Scholes model, particularly the volatility smile effect. It discusses temporal and spatial discretization, proving that the discretization matrix is an M -matrix, ensuring numerical solution convergence, and analyzing the convergence of synchronous and asynchronous algorithms. Parallel numerical methods, such as the Schwarz alternating method, are implemented to solve large-scale algebraic systems. The study concludes with numerical experiments.