jaem TWMS Journal of Applied and Engineering Mathematics 2146-1147 2587-1013 Işık University Press Financial Mathematics Finansal Matematik MEASURING JUMP SIZES IN ASSET PRICES WITH AN INDIRECT APPROACH https://orcid.org/0009-0008-8571-9773 Paziresh Mehran University of Tabriz https://orcid.org/0000-0001-9780-6470 Ivaz K. University of Tabriz 04 07 2026 16 4 457 471 03 08 2025 08 15 2025 Copyright © 2010, TWMS Journal of Applied and Engineering Mathematics 2010 TWMS Journal of Applied and Engineering Mathematics

The aim of this article is to estimate the magnitude of asset price jump sizes using an inverse method applied to historical financial data. Specifically, we adapt a particular form of the Merton jump-diffusion model for this estimation. The model is then discretized using the characteristics of the Poisson process along with the Euler-Maruyama numerical method. Using historical financial data from various assets including global gold ounce prices, Alphabet (Google) stock, and crude oil collected over 2, 6, and 5-year periods, we estimate the price jump size for a short one-week time frame for these assets. This estimation is carried out by minimizing the price jump size inversely, using the discretized function obtained from the Euler-Maruyama numerical method, implemented through simulation in Python software. Finally, the effectiveness of the inverse method in estimating asset price jump sizes is evaluated by comparing the estimated values with the actual observed price jump sizes in the historical data of each asset, taking into account the calculated error.

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