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A Red-Black Successive Over-Relaxation Method for Arithmetic Asian Option Pricing
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DOI：10.17576/jsm-2026-5504-13.png)
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Abstract
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The valuation of arithmetic Asian options is a challenging problem in financial mathematics due to the absence of a closed-form solution. In this study, the Red-Black Successive Over-Relaxation (RBSOR) method is developed for the numerical solution of arithmetic Asian option pricing. The pricing model, governed by the Black-Scholes partial differential equation (PDE), is discretized using the Crank-Nicolson finite difference scheme, resulting in a system of linear equations. The RBSOR iterative method is then applied to efficiently solve the resulting linear system. Several numerical experiments are conducted, and the results are compared with those obtained using Gauss-Seidel (GS), Successive Over-Relaxation (SOR), and Red-Black Gauss-Seidel (RBGS) iterative methods. Computational performance is evaluated in terms of number of iterations, computational time, and root mean squared error (RMSE). RMSE is used to evaluate the accuracy of each iterative method by comparing the numerical results with the analytical solution. The findings demonstrate that the RBSOR method achieves comparable accuracy while significantly reducing iteration counts and computational time, indicating its computational efficiency for numerical option pricing.
Keywords:
Arithmetic Asian option pricing
Black-Scholes PDE
Crank-Nicolson scheme
Red-Black SOR method
resource efficiency
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