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.
Keywords: Partial integro-differential equations, implicit–explicit midpoint formula, options pricing, jump-diffusion model, finite difference method, stability, error estimates
@article{M2AN_2021__55_3_913_0,
author = {Wang, Wansheng and Mao, Mengli and Wang, Zheng},
title = {An efficient variable step-size method for options pricing under jump-diffusion models with nonsmooth payoff function},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {913--938},
year = {2021},
publisher = {EDP-Sciences},
volume = {55},
number = {3},
doi = {10.1051/m2an/2021012},
mrnumber = {4253168},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an/2021012/}
}
TY - JOUR AU - Wang, Wansheng AU - Mao, Mengli AU - Wang, Zheng TI - An efficient variable step-size method for options pricing under jump-diffusion models with nonsmooth payoff function JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2021 SP - 913 EP - 938 VL - 55 IS - 3 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/m2an/2021012/ DO - 10.1051/m2an/2021012 LA - en ID - M2AN_2021__55_3_913_0 ER -
%0 Journal Article %A Wang, Wansheng %A Mao, Mengli %A Wang, Zheng %T An efficient variable step-size method for options pricing under jump-diffusion models with nonsmooth payoff function %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2021 %P 913-938 %V 55 %N 3 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/m2an/2021012/ %R 10.1051/m2an/2021012 %G en %F M2AN_2021__55_3_913_0
Wang, Wansheng; Mao, Mengli; Wang, Zheng. An efficient variable step-size method for options pricing under jump-diffusion models with nonsmooth payoff function. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 55 (2021) no. 3, pp. 913-938. doi: 10.1051/m2an/2021012
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