Journal
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE
Volume 55, Issue 3, Pages 913-938Publisher
EDP SCIENCES S A
DOI: 10.1051/m2an/2021012
Keywords
Partial integro-differential equations; implicit– explicit midpoint formula; options pricing; jump-diffusion model; finite difference method; stability; error estimates
Categories
Funding
- National Natural Science Foundation of China [11771060]
- Shanghai Science and Technology Planning Projects [20JC1414200]
- Natural Science Foundation of Shanghai [20ZR1441200]
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The study introduces a numerical method for solving parabolic partial integro-differential equations with nonsmooth payoff functions, which shows good performance in jump-diffusion option pricing models.
We develop an implicit-explicit midpoint formula with variable spatial step-sizes and variable time step to solve parabolic partial integro-differential equations with nonsmooth payoff function, which describe the jump-diffusion option pricing model in finance. With spatial differential operators being treated by using finite difference methods and the jump integral being computed by using the composite trapezoidal rule on a non-uniform space grid, the proposed method leads to linear systems with tridiagonal coefficient matrices, which can be solved efficiently. Under realistic regularity assumptions on the data, the consistency error and the global error bounds for the proposed method are obtained. The stability of this numerical method is also proved by using the Von Neumann analysis. Numerical results illustrate the effectiveness of the proposed method for European options under jump-diffusion models.
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