High-Performance Simulation of Advanced Stochastic Volatility Models for Financial Applications

Abstract

This paper introduces a novel two-factor stochastic volatility model designed to capture the empirical features of asset price dynamics, such as skewness, kurtosis, and volatility smiles, which are often inadequately described by classical models like Black-Scholes and Heston. The proposed model is governed by two correlated mean-reverting processes and employs a convex combination of volatilities to enhance flexibility in the risk-neutral density (RND).

The pricing equation is discretized using a finite difference scheme in space and an implicit backward Euler method in time, resulting in large-scale sparse linear systems. To solve these efficiently, we implement parallel Schwarz domain decomposition methods using both synchronous and asynchronous relaxation strategies with MPI.

Numerical experiments on the HPC@LR platform demonstrate the model’s ability to match real market option prices with high accuracy and show that asynchronous parallelism provides significant performance gains in terms of speed-up and efficiency, particularly in large-scale simulations. The results confirm the model’s robustness and suitability for real-time and high-dimensional option pricing tasks.