Abstract

This paper introduces parallel computation for spread options using two-dimensional Fourier transform. Spread options are multi-asset options whose payoffs depend on the difference of two underlying financial securities. Pricing these securities, however, cannot be done using closed-form methods; as such, we propose an algorithm which employs the fast Fourier Transform (FFT) method to numerically solve spread option prices in a reasonable amount of short time while preserving the pricing accuracy. Our results indicate a significant increase in computational performance when the algorithm is performed on multiple CPU cores and GPU. Moreover, the literature on spread option pricing using FFT methods documents that the pricing accuracy increases with FFT grid size while the computational speed has opposite effect. By using the multi-core/GPU implementation, the trade-off between pricing accuracy and speed is taken into account effectively.

Highlights

  • Spread options have widespread uses across many industries, remarkably in the seasonal commodity market futures

  • To ascertain the impact of the different environments as well as the different methods of execution on the computational efficiency of the algorithm, we record the times of execution for different values of fast Fourier Transform (FFT) grid size N, which is the number of grid points of discretization of the characteristic function along the two asset dimensions, for both the classical single-core implementation and the multi-core/GPU implementation

  • We built on the literature on fast and accurate pricing of spread options based on two-dimensional FFT method using parallel computation

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Summary

Introduction

Spread options have widespread uses across many industries, remarkably in the seasonal commodity market futures. We adapt the parallel computing Toolbox in MATLAB to take advantage of the multi-core capabilities of GPU processing, to substantially improve the performance and computational efficiency of the algorithm for spread options. To ascertain the impact of the different environments as well as the different methods of execution on the computational efficiency of the algorithm, we record the times of execution for different values of FFT grid size N, which is the number of grid points of discretization of the characteristic function along the two asset dimensions, for both the classical single-core implementation and the multi-core/GPU implementation This approach completely eliminates the trade off between computational accuracy and speed, that is, we price spread option accurately and in a fastest possible way

Spread option valuation
Model characteristic function
Two-dimensional geometric Brownian motion (GBM)
Two-dimensional normal inverse Gaussian (NIG) Levy process
Implementation outlook
Findings
Conclusion

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