Journal of the Korean Society for Industrial and Applied Mathematics

Korean Society for Industrial and Applied Mathematics (한국산업응용수학회)
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AN EFFICIENT HYBRID NUMERICAL METHOD FOR THE TWO-ASSET BLACK-SCHOLES PDE

  • DELPASAND, R. (DEPARTMENT OF APPLIED MATHEMATICS AND MAHANI, MATHEMATICAL RESEARCH CENTER FACULTY OF MATHEMATICS AND COMPUTER SHAHID BAHONAR UNIVERSITY OF KERMAN) ;
  • HOSSEINI, M.M. (DEPARTMENT OF APPLIED MATHEMATICS AND MAHANI, MATHEMATICAL RESEARCH CENTER FACULTY OF MATHEMATICS AND COMPUTER SHAHID BAHONAR UNIVERSITY OF KERMAN)
  • Received : 2021.03.31
  • Accepted : 2021.06.28
  • Published : 2021.09.25
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Abstract

In this paper, an efficient hybrid numerical method for solving two-asset option pricing problem is presented based on the Crank-Nicolson and the radial basis function methods. For this purpose, the two-asset Black-Scholes partial differential equation is considered. Also, the convergence of the proposed method are proved and implementation of the proposed hybrid method is specifically studied on Exchange and Call on maximum Rainbow options. In addition, this method is compared to the explicit finite difference method as the benchmark and the results show that the proposed method can achieve a noticeably higher accuracy than the benchmark method at a similar computational time. Furthermore, the stability of the proposed hybrid method is numerically proved by considering the effect of the time step size to the computational accuracy in solving these problems.

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References

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