Derivatives Sensitivities Computation under Heston Model on GPU

ArXiv ID: 2309.10477 “View on arXiv”

Authors: Unknown

Abstract

This report investigates the computation of option Greeks for European and Asian options under the Heston stochastic volatility model on GPU. We first implemented the exact simulation method proposed by Broadie and Kaya and used it as a baseline for precision and speed. We then proposed a novel method for computing Greeks using the Milstein discretisation method on GPU. Our results show that the proposed method provides a speed-up up to 200x compared to the exact simulation implementation and that it can be used for both European and Asian options. However, the accuracy of the GPU method for estimating Rho is inferior to the CPU method. Overall, our study demonstrates the potential of GPU for computing derivatives sensitivies with numerical methods.

Keywords: option Greeks, Heston model, GPU computing, stochastic volatility, Milstein discretisation, Derivatives (Options)

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 6.0/10
• Quadrant: Holy Grail
• Why: The paper is heavy on advanced mathematics, featuring detailed SDE formulations, Monte Carlo simulation algorithms (Broadie and Kaya), and specific discretization methods (Milstein), requiring significant theoretical understanding. Empirically, it involves concrete GPU implementation, performance benchmarking (200x speed-up), and accuracy comparisons against CPU baselines for derivatives sensitivities, making it directly applicable to quantitative finance engineering.

  flowchart TD
    A["Research Goal: Compute Heston Model Greeks for European & Asian Options on GPU"] --> B["Data & Inputs"]
    B --> C["Methodology: Baseline CPU & Proposed GPU"]
    subgraph C ["Methodology"]
        C1["Baseline: Broadie-Kaya<br>Exact Simulation CPU"]
        C2["Proposed: Milstein Discretisation<br>on GPU"]
    end
    C --> D["Computational Process: Parallel Simulation & Greeks Calculation"]
    D --> E["Key Findings & Outcomes"]
    subgraph E ["Outcomes"]
        E1["200x Speed-up vs Baseline"]
        E2["Valid for European & Asian Options"]
        E3["Limitation: Rho Accuracy < CPU"]
    end

%% Data/Inputs Node Details
    B1["Market Data: Spot, Strike, T, r, q"] --> B
    B2["Heston Parameters: kappa, theta, sigma, rho"] --> B
    B3["Simulation Parameters: Maturity, Paths, Steps"] --> B