Fast and Accurate Computation of the Regime-Switching Jump-Diffusion Option Prices Using Laplace Transform and Compact Difference with Convergence Guarantee

Yong Chen ()
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Yong Chen: Xihua University

Computational Economics, 2024, vol. 64, issue 1, No 3, 57-80

Abstract: Abstract The accuracy and efficiency for computing option prices play very important in the financial risk management and hedging for the investors. In this paper, we for the first time develop a fast and accurate numerical method that combines Laplace transform for time variable and compact difference for spatial discretization, for computing option prices governed by the partial integro-differential equation system under the regime-switching jump-diffusion models. We then invert the Laplace transform through the numerical contour integral to recover the option prices. Furthermore, we prove that the method is convergent in the discrete $$L^2$$ L 2 and $$L^\infty $$ L ∞ norms with fourth-order in space and exponential-order with respect to the quadrature nodes for the numerical Laplace inversion. Finally, several numerical examples are reported to illustrate the convergence theory and show the advantages of the method over the benchmarks in regards to the accuracy and efficiency.

Keywords: Option pricing; Jump-diffusion models; Partial integro-differential equations; Laplace transform; Compact difference methods; Convergence rates (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10614-023-10426-y

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