NİCEL FİNANS MODELLERİNDE SIÇRAMA-DİFÜZYON VE PURE SIÇRAMA SÜREÇLERİ: LÉVY TABANLI YAKLAŞIMLAR

Akbar  BARATI CHIYANEH; Hamit  MİRTAGİOĞLU; Yıldırım  DEMİR

doi:10.63127/tuaz.by.220

JUMP-DIFFUSION AND PURE JUMP PROCESSES IN QUANTITATIVE FINANCE MODELS: LÉVY-BASED APPROACHES

Authors

Assist. Prof. Akbar Baratı Chıyaneh

University of Tabriz

https://orcid.org/0000-0003-4401-5477

Prof. Hamit Mirtagioğlu

Bitlis Eren University

https://orcid.org/0000-0003-2952-9584

Assoc. Prof. Yıldırım Demir

Van Yüzüncü Yıl University

https://orcid.org/0000-0002-6350-8122

DOI: https://doi.org/10.63127/tuaz.by.220.c164

Synopsis

Traditionally, continuous models based on Brownian motion and the assumption of normal distribution (such as Black-Scholes) have been used to model financial asset prices. However, recent empirical studies demonstrate that financial return distributions are skewed, exhibit heavy tails and volatility clustering, and that price paths are not continuous but rather contain sudden jumps. This study highlights the inadequacy of classical diffusion models, particularly in explaining short-term price movements and market microstructure, through comparisons using SLM stock and S&P 500 index data. The study focuses on Lévy-based approaches, which better represent deviations from the normal distribution and discontinuities in market dynamics. In this context, jump-diffusion and pure jump processes, which have the capacity to explain the volatility smile in option pricing and produce more realistic results in risk management, are examined. The theoretical foundations of these models and their advantages in financial modeling are discussed in detail.

Author Biographies

Assist. Prof. Akbar Baratı Chıyaneh, University of Tabriz

Baratı Chıyaneh, Akbar
Assist. Prof. Akbar Baratı Chıyaneh serves as a faculty member at the Department of Applied Mathematics, Faculty of Mathematical, Statistical and Computer Sciences, University of Tabriz, Tabriz, Iran. Baratı Chıyaneh completed undergraduate education at Payame Noor University in the department of Mathematics in 2002, master's education at Tabriz Payame Noor University; Bitlis Eren University in the department of Optimization; Applied Statistics in 2006; 2024, and Ph.D. degree from Van Yüzüncü Yıl University in the field of Applied Mathematics in 2017. Primary research interests include numerical analysis, perturbation methods, stochastic differential equations, artificial neural networks and machine learning, optimization. Baratı Chıyaneh has national and international articles published.
E-mail: baratiakbar@tabrizu.ac.ir, baratiakbar@yahoo.com | ORCID: https://orcid.org/0000-0003-4401-5477

Prof. Hamit Mirtagioğlu, Bitlis Eren University

Mirtagioğlu, Hamit
Prof. Hamit Mirtagioğlu serves as a head of statistics department, head of applied statistics department at the Department of Statistics, Faculty of Arts and Sciences, Bitlis Eren University, Bitlis, Türkiye. Mirtagioğlu completed undergraduate education at Gazi University in the department of Statistics in 1987, and Ph.D. degree from Ankara University in the field of Animal Science Dept., Biometry and Genetics in 2001. Primary research interests include applied statistics. Mirtagioğlu has national and international articles and book chapters published in Turkish and English.
E-mail: hmirtagioglu@beu.edu.tr, hamitsa86@gmail.com | ORCID: https://orcid.org/0000-0003-2952-9584

Assoc. Prof. Yıldırım Demir, Van Yüzüncü Yıl University

Demir, Yıldırım
Assoc. Prof. Yıldırım Demir serves as a faculty member at the Department of Econometrics, Faculty of Economics and Administrative Sciences, Van Yüzüncü Yıl University, Van, Türkiye. Demir completed undergraduate education at Marmara University in the department of Electrical Education in 2001, master's education at Van Yüzüncü Yıl University in the department of Animal Science Dept., Biometry and Genetics in 2008, and Ph.D. degree from AtaTürk University in the field of Animal Science Dept., Biometry and Genetics in 2016. Primary research interests include applied statistics, quantitative decision methods. Demir has national and international articles and book chapters published in Turkish and English.
E-mail: ydemir@yyu.edu.tr, ydemir.yyu@gmail.com | ORCID: https://orcid.org/0000-0002-6350-8122