"Fractional Derivative and Financial Instruments: Waiting Time Distribu" by Bambang Hendriya Guswanto, Muhammad Rizki Pratama et al.

Progress in Fractional Differentiation & Applications

Article Title

Fractional Derivative and Financial Instruments: Waiting Time Distributions for the Exchange Rate Movement of US Dollar to Japanese Yen

Authors

Bambang Hendriya Guswanto, Department of Mathematics, Jenderal Soedirman University, Purwokerto, IndonesiaFollow
Muhammad Rizki Pratama, Department of Mathematics, Jenderal Soedirman University, Purwokerto, IndonesiaFollow
Agung Prabowo, Department of Mathematics, Jenderal Soedirman University, Purwokerto, IndonesiaFollow
Jajang Jajang, Department of Mathematics, Jenderal Soedirman University, Purwokerto, IndonesiaFollow
Idha Sihwaningrum, Department of Mathematics, Jenderal Soedirman University, Purwokerto, IndonesiaFollow

Author Country (or Countries)

Indonesia

Abstract

In this article, a mathematical model for exchange rate movements is derived by applying random walks theory and involving Caputo fractional derivative operator. The waiting time distributions for the exchange rate movement of US Dollar to Japanese Yen, which are intimately related to the mathematical model, during February 2019 are also studied. Three types of waiting time distributions, i.e., exponential, stretched exponential, and Mittag-Leffler distributions are compared. The result shows that Mittag-Leffler Distribution is the best distribution to approximate the empirical distribution of the exchange rate data during February 2019 except the data of February 18, 2019 which is approximated better by stretched exponential distribution.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/pfda/090212

Recommended Citation

Hendriya Guswanto, Bambang; Rizki Pratama, Muhammad; Prabowo, Agung; Jajang, Jajang; and Sihwaningrum, Idha (2023) "Fractional Derivative and Financial Instruments: Waiting Time Distributions for the Exchange Rate Movement of US Dollar to Japanese Yen," Progress in Fractional Differentiation & Applications: Vol. 9: Iss. 2, Article 12.
DOI: http://dx.doi.org/10.18576/pfda/090212
Available at: https://digitalcommons.aaru.edu.jo/pfda/vol9/iss2/12

Download

COinS