Derivatives Sensitivities Computation under Heston Model on GPU

TL;DR

This paper explores GPU-based computation of option Greeks under the Heston model, introducing a novel Milstein discretisation method that significantly accelerates calculations for European and Asian options.

Contribution

A new GPU-accelerated method using Milstein discretisation for computing Greeks under the Heston model, achieving up to 200x speed-up over exact simulation.

Findings

Speed-up of up to 200x compared to exact simulation

Effective for European and Asian options

Lower accuracy for Rho estimation on GPU

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.