Quasi-Monte Carlo methods for calculating derivatives sensitivities on the GPU

TL;DR

This paper introduces a GPU-accelerated Quasi-Monte Carlo method with a smoothing technique for efficiently calculating higher-order option Greeks, demonstrating significant variance reduction and speedups over CPU methods.

Contribution

It presents a novel combination of QMC-CPW with GPU simulation to improve accuracy and speed in computing complex derivatives sensitivities for exotic options.

Findings

Variance reduction factors up to 10^18

GPU speedups over 200x compared to CPU implementations

Effective smoothing of payoff functions for higher-order Greeks

Abstract

The calculation of option Greeks is vital for risk management. Traditional pathwise and finite-difference methods work poorly for higher-order Greeks and options with discontinuous payoff functions. The Quasi-Monte Carlo-based conditional pathwise method (QMC-CPW) for options Greeks allows the payoff function of options to be effectively smoothed, allowing for increased efficiency when calculating sensitivities. Also demonstrated in literature is the increased computational speed gained by applying GPUs to highly parallelisable finance problems such as calculating Greeks. We pair QMC-CPW with simulation on the GPU using the CUDA platform. We estimate the delta, vega and gamma Greeks of three exotic options: arithmetic Asian, binary Asian, and lookback. Not only are the benefits of QMC-CPW shown through variance reduction factors of up to $1.0 \times 10^{18}$, but the increased computational speed through usage of the GPU is shown as we achieve speedups over sequential CPU implementations of more than $200$x for our most accurate method.