Instabilities of Super-Time-Stepping Methods on the Heston Stochastic Volatility Model

ArXiv ID: 2309.00540 “View on arXiv”

Authors: Unknown

Abstract

This note explores in more details instabilities of explicit super-time-stepping schemes, such as the Runge-Kutta-Chebyshev or Runge-Kutta-Legendre schemes, noticed in the litterature, when applied to the Heston stochastic volatility model. The stability remarks are relevant beyond the scope of super-time-stepping schemes.

Keywords: super-time-stepping schemes, Heston stochastic volatility model, Runge-Kutta-Chebyshev, numerical stability, stochastic differential equations, Equity (Derivatives Pricing)

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 6.0/10
• Quadrant: Holy Grail
• Why: The paper involves advanced numerical analysis and PDE discretization theory with complex eigenvalue analysis, reflecting high mathematical complexity. It provides concrete implementation details like grid transformations and boundary discretizations, and compares numerical results with reference schemes, indicating strong empirical grounding.

  flowchart TD
    A["Research Goal<br>Analyze stability of explicit<br>super-time-stepping methods<br>on Heston model"] --> B["Key Methodology<br>Apply Runge-Kutta-Chebyshev &<br>Runge-Kutta-Legendre schemes<br>to Stochastic Volatility PDE"]
    B --> C["Data / Inputs<br>Instability findings from<br>existing literature<br>on SDE discretization"]
    C --> D["Computational Process<br>Simulate schemes on<br>Heston model parameters<br>test stability boundaries"]
    D --> E["Key Findings / Outcomes<br>Instabilities exist beyond<br>super-time-stepping methods<br>relevant for Equity Derivatives"]