A nested MLMC framework for efficient simulations on FPGAs

ArXiv ID: 2502.07123 “View on arXiv”

Authors: Unknown

Abstract

Multilevel Monte Carlo (MLMC) reduces the total computational cost of financial option pricing by combining SDE approximations with multiple resolutions. This paper explores a further avenue for reducing cost and improving power efficiency through the use of low precision calculations on configurable hardware devices such as Field-Programmable Gate Arrays (FPGAs). We propose a new framework that exploits approximate random variables and fixed-point operations with optimised precision to generate most SDE paths with a lower cost and reduce the overall cost of the MLMC framework. We first discuss several methods for the cheap generation of approximate random Normal increments. To set the bit-width of variables in the path generation we then propose a rounding error model and optimise the precision of all variables on each MLMC level. With these key improvements, our proposed framework offers higher computational savings than the existing mixed-precision MLMC frameworks.

Keywords: Monte Carlo methods, option pricing, low precision calculation, FPGA, fixed-point arithmetic, derivatives

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 4.0/10
• Quadrant: Lab Rats
• Why: The paper presents a sophisticated theoretical framework with advanced stochastic analysis, error modeling, and precision optimization for FPGA implementation, indicating high mathematical complexity. However, it relies on Matlab simulations with assumptions rather than live backtesting or high-frequency data, placing it closer to laboratory research than street-ready trading systems.

  flowchart TD
    A["Research Goal: Enhance MLMC efficiency & power<br>using low precision on FPGAs"] --> B{"Key Methodology"}
    
    subgraph B ["Key Methodology"]
        B1["Approx. Random Generation<br>for SDE Increments"]
        B2["Rounding Error Model<br>for Bit-width Optimization"]
    end
    
    B --> C["MLMC Framework<br>Execution on FPGA"]
    
    C --> D{"Computational Processes"}
    subgraph D [" "]
        D1["Fixed-point Arithmetic<br>Optimized Precision"]
        D2["Multi-level Path Generation<br>Low/High Resolutions"]
    end
    
    D --> E
    
    subgraph E ["Data & Inputs"]
        E1["Financial Option Data"]
        E2["Fixed-point Configs<br>Bit-widths"]
    end
    
    E --> F["Key Findings: Higher computational savings<br>and improved power efficiency"]