MEASURING JUMP SIZES IN ASSET PRICES WITH AN INDIRECT APPROACH

Mehran Paziresh; K. Ivaz

MEASURING JUMP SIZES IN ASSET PRICES WITH AN INDIRECT APPROACH

Abstract

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.

Keywords

Thanks

The authors would like to extend their gratitude to anonymous referees for their valuable comments and suggestions.

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Details

Primary Language

English

Subjects

Financial Mathematics

Journal Section

Research Article

Authors

Mehran Paziresh This is me
0009-0008-8571-9773
Iran

K. Ivaz ^*
0000-0001-9780-6470
Iran

Publication Date

April 7, 2026

Submission Date

March 8, 2025

Acceptance Date

August 15, 2025

Published in Issue

Year 2026 Volume: 16 Number: 4

IZ

https://izlik.org/JA36GC97CM

Cite

RIS / Bibtex

APA

Paziresh, M., & Ivaz, K. (2026). MEASURING JUMP SIZES IN ASSET PRICES WITH AN INDIRECT APPROACH. TWMS Journal of Applied and Engineering Mathematics, 16(4), 457-471. https://izlik.org/JA36GC97CM

AMA

1.Paziresh M, Ivaz K. MEASURING JUMP SIZES IN ASSET PRICES WITH AN INDIRECT APPROACH. JAEM. 2026;16(4):457-471. https://izlik.org/JA36GC97CM

Chicago

Paziresh, Mehran, and K. Ivaz. 2026. “MEASURING JUMP SIZES IN ASSET PRICES WITH AN INDIRECT APPROACH”. TWMS Journal of Applied and Engineering Mathematics 16 (4): 457-71. https://izlik.org/JA36GC97CM.

EndNote

Paziresh M, Ivaz K (April 1, 2026) MEASURING JUMP SIZES IN ASSET PRICES WITH AN INDIRECT APPROACH. TWMS Journal of Applied and Engineering Mathematics 16 4 457–471.

IEEE

[1]M. Paziresh and K. Ivaz, “MEASURING JUMP SIZES IN ASSET PRICES WITH AN INDIRECT APPROACH”, JAEM, vol. 16, no. 4, pp. 457–471, Apr. 2026, [Online]. Available: https://izlik.org/JA36GC97CM

ISNAD

Paziresh, Mehran - Ivaz, K. “MEASURING JUMP SIZES IN ASSET PRICES WITH AN INDIRECT APPROACH”. TWMS Journal of Applied and Engineering Mathematics 16/4 (April 1, 2026): 457-471. https://izlik.org/JA36GC97CM.

JAMA

1.Paziresh M, Ivaz K. MEASURING JUMP SIZES IN ASSET PRICES WITH AN INDIRECT APPROACH. JAEM. 2026;16:457–471.

MLA

Paziresh, Mehran, and K. Ivaz. “MEASURING JUMP SIZES IN ASSET PRICES WITH AN INDIRECT APPROACH”. TWMS Journal of Applied and Engineering Mathematics, vol. 16, no. 4, Apr. 2026, pp. 457-71, https://izlik.org/JA36GC97CM.

Vancouver

1.Mehran Paziresh, K. Ivaz. MEASURING JUMP SIZES IN ASSET PRICES WITH AN INDIRECT APPROACH. JAEM [Internet]. 2026 Apr. 1;16(4):457-71. Available from: https://izlik.org/JA36GC97CM