Exact simulation scheme for the Ornstein-Uhlenbeck driven stochastic volatility model with the Karhunen-Loève expansions

ArXiv ID: 2402.09243 “View on arXiv”

Authors: Unknown

Abstract

This study proposes a new exact simulation scheme of the Ornstein-Uhlenbeck driven stochastic volatility model. With the Karhunen-Loève expansions, the stochastic volatility path following the Ornstein-Uhlenbeck process is expressed as a sine series, and the time integrals of volatility and variance are analytically derived as the sums of independent normal random variates. The new method is several hundred times faster than Li and Wu [“Eur. J. Oper. Res., 2019, 275(2), 768-779”] that relies on computationally expensive numerical transform inversion. The simulation algorithm is further improved with the conditional Monte-Carlo method and the martingale-preserving control variate on the spot price.

Keywords: Stochastic Volatility, Ornstein-Uhlenbeck Process, Karhunen-Loève Expansion, Exact Simulation, Conditional Monte Carlo, Equity Derivatives / Volatility

Complexity vs Empirical Score

• Math Complexity: 9.5/10
• Empirical Rigor: 2.0/10
• Quadrant: Lab Rats
• Why: The paper introduces advanced stochastic calculus concepts like Karhunen-Loève expansions for infinite series representations of OU processes, requiring dense functional analysis and exact distributional derivations. While it includes theoretical performance claims and error bounds, it lacks backtested implementation details, actual code, or real-world data analysis, focusing instead on theoretical algorithmic improvements.

  flowchart TD
    A["Research Goal: Efficient Exact Simulation<br>of Ornstein-Uhlenbeck Stochastic Volatility"] --> B["Method: Karhunen-Loève Expansion"]
    
    B --> C["Process Path Generation<br>Sine Series Representation"]
    
    C --> D["Analytical Computation<br>Time Integrals of Volatility & Variance"]
    
    D --> E{"Optimization Step"}
    
    E --> F["Conditional Monte Carlo"]
    E --> G["Martingale-Preserving Control Variate"]
    
    F --> H
    G --> H["Final Algorithm<br>Significant Speed Improvement"]
    
    H --> I["Key Outcomes<br>- Exact Simulation<br>- 100x Faster than Li & Wu 2019<br>- Applicable to Equity Derivatives"]