Efficient simulation of prices for European call options under Heston stochastic-local volatility model: a comparison of methods

ArXiv ID: 2509.24449 “View on arXiv”

Authors: Meng cai, Tianze Li

Abstract

The Heston stochastic-local volatility model, consisting of a asset price process and a Cox–Ingersoll–Ross-type variance process, offers a wide range of applications in the financial industry. The pursuit for efficient model evaluation has been assiduously ongoing and central to which is the numerical simulation of CIR process. Different from the weakly convergent noncentral chi-squared approximation used in 25, this paper considers two strongly convergent and positivity-preserving methods for CIR process under Lamperti transformation, namely, the truncated Euler method and the backward Euler method. It should be noted that these two methods are completely different. The explicit truncated Euler method is computationally effective and remains robust under high volatility, while the implicit backward Euler method provides high computational accuracy and stable performance. Numerical experiments on European call options are presented to show the superiority of different methods.

Keywords: Cox-Ingersoll-Ross (CIR) process, Lamperti transformation, truncated Euler method, backward Euler method, stochastic-local volatility model, Equity Derivatives

Complexity vs Empirical Score

• Math Complexity: 9.2/10
• Empirical Rigor: 4.1/10
• Quadrant: Lab Rats
• Why: The paper heavily employs advanced stochastic calculus, SDE theory, and numerical analysis with strong convergence proofs and Lamperti transformations, indicating very high mathematical density. However, it focuses on theoretical comparisons of numerical methods with limited empirical data, lacking backtests or implementation-heavy details.

  flowchart TD
    A["Research Goal<br/>Efficient Simulation of<br/>Heston SLV Model for<br/>European Call Options"] --> B["Identified Methods<br/>for CIR Process under Lamperti Transform"]
    B --> C{"Numerical Simulation<br/>for European Call Options"}
    C --> D["Truncated Euler Method<br/>Explicit, Fast, Robust"]
    C --> E["Backward Euler Method<br/>Implicit, Highly Accurate, Stable"]
    D --> F["Performance Evaluation<br/>vs. Reference & Noncentral Chi-sq"]
    E --> F
    F --> G["Key Findings"]
    G --> H["Truncated Euler: Superior Efficiency<br/>under High Volatility Regimes"]
    G --> I["Backward Euler: Superior Accuracy<br/>for Stability-sensitive Scenarios"]