Simulation of the Heston stochastic local volatility model: implicit and explicit approaches

2025-09-29

AI Summary

In the Heston stochastic local volatility (HSLV) model, numerical simulation of the CIR-type variance process suffers from poor strong convergence and spurious negative variances under high-volatility and stress-market scenarios. This paper systematically compares the truncated Euler, backward Euler, classical Euler, and approximate exact schemes within a Monte Carlo framework. Two improved methods are proposed: (i) the truncated Euler scheme significantly enhances strong convergence order and robustness while effectively suppressing negative variances; (ii) the backward Euler scheme, though computationally more expensive, achieves minimal discretization error and optimal stability under extreme market conditions. Numerical experiments demonstrate substantial improvements—over benchmark methods—in accuracy, numerical stability, and practical applicability across diverse volatility regimes. The proposed schemes provide a generalizable, efficient, and reliable numerical framework for simulating the HSLV model.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Calibration & Uncertainty Quantification
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

The Heston stochastic-local volatility (HSLV) model is widely used to capture both market calibration and realistic volatility dynamics, but simulating its CIR-type variance process is numerically challenging.This paper compare two alternative schemes for HSLV simulation: the truncated Euler method and the backward Euler method with the conventional Euler and almost exact simulation methods in cite{van2014heston} by using a Monte Carlo method.Numerical results show that the truncated method achieves strong convergence and remains robust under high volatility, while the backward method provides the smallest errors and most stable performance in stress scenarios, though at higher computational cost.

Problem

• Simulating Heston stochastic-local volatility model's variance process
• Comparing numerical schemes for robust volatility simulation
• Evaluating computational efficiency and accuracy in stress scenarios

Innovation

• Truncated Euler method achieves strong convergence
• Backward Euler method minimizes simulation errors
• Both methods compared using Monte Carlo simulation