Modelling exchange rate volatility under jump process and application analysis

Guifang Liu; Yuhang Zheng; Fan Hu; Zhidi Du; Guifang Liu; Yuhang Zheng; Fan Hu; Zhidi Du

doi:10.3934/math.2023432

AIMS Mathematics

2023, Volume 8, Issue 4: 8610-8632. doi: 10.3934/math.2023432

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Modelling exchange rate volatility under jump process and application analysis

School of Finance, Guangdong University of Finance & Economics, Guangzhou 510320, China

Received: 28 November 2022 Revised: 08 January 2023 Accepted: 13 January 2023 Published: 06 February 2023
MSC : 62P20, 62P25, 91B05

Exchange rate is an important part of financial markets. Our analysis finds that the fluctuations of exchange rates have several obvious features, such as spikes, thick tails, fluctuation aggregations and asymmetry. Based on this, we build novel GARCH class model by introducing a jumping process to describe the dynamics of their fluctuations. Our empirical results show that the models with jump factors can better characterize the agglomeration and thick tail characteristics of these return fluctuations than the models without jump factors. In particular, the model with double exponential jumps can fully handle and capture the fluctuation characteristics of the returns. Our findings will be useful for individuals and governments to predict exchange rate fluctuations, provide reference for the effective management of exchange rate risk in China, and further improve the financial risk management mechanism.
- exchange rate,
- jump process,
- fluctuations,
- GARCH class models
Citation: Guifang Liu, Yuhang Zheng, Fan Hu, Zhidi Du. Modelling exchange rate volatility under jump process and application analysis[J]. AIMS Mathematics, 2023, 8(4): 8610-8632. doi: 10.3934/math.2023432

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Abstract

Exchange rate is an important part of financial markets. Our analysis finds that the fluctuations of exchange rates have several obvious features, such as spikes, thick tails, fluctuation aggregations and asymmetry. Based on this, we build novel GARCH class model by introducing a jumping process to describe the dynamics of their fluctuations. Our empirical results show that the models with jump factors can better characterize the agglomeration and thick tail characteristics of these return fluctuations than the models without jump factors. In particular, the model with double exponential jumps can fully handle and capture the fluctuation characteristics of the returns. Our findings will be useful for individuals and governments to predict exchange rate fluctuations, provide reference for the effective management of exchange rate risk in China, and further improve the financial risk management mechanism.

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