Almost-Exact Simulation Scheme for Heston-type Models: Bermudan and American Option Pricing

ArXiv ID: 2601.00815 “View on arXiv”

Authors: Mara Kalicanin Dimitrov, Marko Dimitrov, Anatoliy Malyarenko, Ying Ni

Abstract

Recently, an Almost-Exact Simulation (AES) scheme was introduced for the Heston stochastic volatility model and tested for European option pricing. This paper extends this scheme for pricing Bermudan and American options under both Heston and double Heston models. The AES improves Monte Carlo simulation efficiency by using the non-central chi-square distribution for the variance process. We derive the AES scheme for the double Heston model and compare the performance of the AES schemes under both models with the Euler scheme. Our numerical experiments validate the effectiveness of the AES scheme in providing accurate option prices with reduced computational time, highlighting its robustness for both models. In particular, the AES achieves higher accuracy and computational efficiency when the number of simulation steps matches the exercise dates for Bermudan options.

Keywords: Heston Model, Monte Carlo Simulation, American Options, Bermudan Options, Numerical Methods, Equity Derivatives

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail
• Why: The paper involves advanced stochastic calculus and PDE analysis, justifying a high math score, while its focus on simulation implementation with numerical experiments for computational efficiency provides substantial empirical rigor.

  flowchart TD
    A["Research Goal: Extend AES scheme for Bermudan/American option pricing under Heston & Double Heston models"] --> B["Methodology: Derive AES scheme for Double Heston & simulate with Monte Carlo"]
    B --> C["Inputs: Model Parameters, Option Exercise Dates, Step Sizes"]
    C --> D["Computational Process: Simulate Variance & Asset Paths using Non-central Chi-square Distribution"]
    D --> E["Estimate Option Prices via Least Squares Monte Carlo"]
    E --> F["Key Findings: AES provides accurate prices & faster computation vs. Euler scheme"]