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Specification Tests for Jump‐Diffusion Models Based on the Characteristic Function

Gerrit Lodewicus Grobler et al.

International Statistical Review2026https://doi.org/10.1111/insr.70022article
AJG 3ABDC A
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0.50

Abstract

Summary Goodness‐of‐fit tests are suggested for several popular jump‐diffusion processes. The suggested test statistics utilise the marginal characteristic function of the model and its L2‐type discrepancy from an empirical counterpart. Model parameters are estimated either by minimising the aforementioned L2‐type discrepancy or by maximum likelihood. A hybrid estimation method that uses moment estimation is also proposed as a standalone method, or to calculate initial points. A fairly extensive Monte Carlo study is conducted in which the performance of a bootstrap version of the new tests is measured against classical specification procedures involving the empirical distribution function. The study concludes with empirical applications on a number of financial assets, as well as an analysis on the impact of misspecification on option pricing.

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https://doi.org/https://doi.org/10.1111/insr.70022

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@article{gerrit2026,
  title        = {{Specification Tests for Jump‐Diffusion Models Based on the Characteristic Function}},
  author       = {Gerrit Lodewicus Grobler et al.},
  journal      = {International Statistical Review},
  year         = {2026},
  doi          = {https://doi.org/https://doi.org/10.1111/insr.70022},
}

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Specification Tests for Jump‐Diffusion Models Based on the Characteristic Function

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