Monte Carlo simulation for Barndorff-Nielsen and Shephard model under change of measure

ArXiv ID: 2306.05750 “View on arXiv”

Authors: Unknown

Abstract

The Barndorff-Nielsen and Shephard model is a representative jump-type stochastic volatility model. Still, no method exists to compute option prices numerically for the non-martingale case with infinite active jumps. We develop two simulation methods for such a case under change of measure and conduct some numerical experiments.

Keywords: Barndorff-Nielsen and Shephard Model, Stochastic Volatility, Jump Diffusion, Option Pricing, Monte Carlo Simulation, Options

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 5.0/10
• Quadrant: Holy Grail
• Why: The paper is mathematically dense, focusing on advanced stochastic calculus and measure theory to develop novel simulation methods for a complex financial model. While it includes numerical experiments and algorithmic details, the empirical component is more theoretical validation than heavy backtesting with real-world data.

  flowchart TD
    A["Research Goal: Develop Monte Carlo methods for<br>Barndorff-Nielsen and Shephard model<br>under change of measure with infinite active jumps"] --> B["Methodology: Develop Two Simulation Approaches"]
    
    B --> C["Input: Model Parameters<br>Volatility Jump Lévy Measure &<br>Infinitely Active Jumps"]
    
    C --> D["Computational Process: Monte Carlo Simulation"]
    D --> E{"Simulation Substeps"}
    E --> E1["Discretize Time &<br>Generate Jump Times"]
    E --> E2["Simulate Volatility Dynamics<br>under Change of Measure"]
    E --> E3["Simulate Asset Price Paths<br>with Infinite Jumps"]
    E --> E4["Calculate Option Payoffs<br>& Discount Values"]
    
    E --> F["Computational Process: Average Results<br>across Many Simulations"]
    
    F --> G["Outcomes: Numerical Option Prices<br>for Non-Martingale Case<br>Validated via Numerical Experiments"]