Simulation schemes for the Heston model with Poisson conditioning

Paper: arXiv 2301.02800

Authors: Jaehyuk Choi, Yue Kuen Kwok

Abstract

Exact simulation schemes under the Heston stochastic volatility model (e.g., Broadie-Kaya and Glasserman-Kim) suffer from computationally expensive modified Bessel function evaluations. We propose a new exact simulation scheme without the modified Bessel function, based on the observation that the conditional integrated variance can be simplified when conditioned by the Poisson variate used for simulating the terminal variance. Our approach also enhances the low-bias and time discretization schemes, which are suitable for pricing derivatives with frequent monitoring. Extensive numerical tests reveal the good performance of the new simulation schemes in terms of accuracy, efficiency, and reliability when compared with existing methods.

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper provides a mathematically sophisticated approach to exact simulation for the Heston model by conditioning on Poisson variates to avoid expensive Bessel function evaluations. It demonstrates solid numerical rigor through comprehensive efficiency and accuracy benchmarking against established Monte Carlo techniques.

Research Flowchart

  flowchart TD
    A["Research Goal: Eliminate expensive Bessel functions in Heston exact simulation"] --> B["Inputs: Heston SV Model Parameters & Poisson Conditioning Variate"]
    B --> C["Derive Simplified Conditional Integrated Variance Formula"]
    C --> D["Develop New Exact & Low-Bias Time Discretization Schemes"]
    D --> E["Run Numerical Tests vs. Broadie-Kaya & Glasserman-Kim"]
    E --> F["Outcomes: Enhanced Accuracy, Efficiency & Reliability for Derivative Pricing"]