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Asset pricing for an affine jump‐diffusion model using an FD method of lines on nonuniform meshes
Author(s) -
Soleymani Fazlollah,
Akgül Ali
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5363
Subject(s) - mathematics , jump diffusion , discretization , method of lines , polygon mesh , partial differential equation , jump , quadratic growth , affine transformation , degenerate energy levels , numerical analysis , valuation of options , mathematical analysis , differential equation , ordinary differential equation , geometry , physics , quantum mechanics , econometrics , differential algebraic equation
We present a novel numerical scheme for the valuation of options under a well‐known jump‐diffusion model. European option pricing for such a case satisfies a 1 + 2 partial integro‐differential equation (PIDE) including a double integral term, which is nonlocal. The proposed approach relies on nonuniform meshes with a focus on the discontinuous and degenerate areas of the model and applying quadratically convergent finite difference (FD) discretizations via the method of lines (MOL). A condition for observing the time stability of the fully discretized problem is given. Also, we report results of numerical experiments.