The $ logTG $-$ SV $ model: A threshold-based volatility framework with logarithmic shocks for exchange rate dynamics

R. Alraddadi; R. Alraddadi

doi:10.3934/math.2025870

AIMS Mathematics

2025, Volume 10, Issue 8: 19495-19511. doi: 10.3934/math.2025870

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Research article

The $ logTG $-$ SV $ model: A threshold-based volatility framework with logarithmic shocks for exchange rate dynamics

R. Alraddadi ^,

Department of Mathematics and Statistics, College of Science in Yanbu, Taibah University, Madinah 46423, Saudi Arabia

Received: 27 June 2025 Revised: 05 August 2025 Accepted: 12 August 2025 Published: 26 August 2025
MSC : 62M05, 62M10

This paper introduces a novel logarithmic threshold stochastic volatility $ GARCH $ model as an advanced extension of traditional $ GARCH $ frameworks. The model combines a logarithmic transformation of volatility shocks with a dynamic threshold, allowing it to better capture asymmetric behavior and sudden regime shifts commonly observed in financial markets. We provide clear theoretical conditions for strict and second-order stationarity, and for the existence of higher-order moments, which fills an important gap in the literature on stochastic volatility models. Monte Carlo simulations demonstrate the model's efficiency in estimating parameters, yielding accurate results with minimal bias for a sample size of 5,000. When applied to Algerian Dinar/Euro exchange rate data from 2000 to 2011, the model successfully captures volatility clustering and leverage effects, revealing a 30% increase in volatility in response to negative shocks relative to positive ones. It also improves predictive accuracy by 15% over standard models, underscoring its strength in capturing volatility in emerging markets with complex and nonlinear patterns.
- stochastic volatility model,
- $ \log \; GARCH $ model,
- stationarity,
- QMLE,
- threshold effect
Citation: R. Alraddadi. The $ logTG $-$ SV $ model: A threshold-based volatility framework with logarithmic shocks for exchange rate dynamics[J]. AIMS Mathematics, 2025, 10(8): 19495-19511. doi: 10.3934/math.2025870

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Abstract

This paper introduces a novel logarithmic threshold stochastic volatility $ GARCH $ model as an advanced extension of traditional $ GARCH $ frameworks. The model combines a logarithmic transformation of volatility shocks with a dynamic threshold, allowing it to better capture asymmetric behavior and sudden regime shifts commonly observed in financial markets. We provide clear theoretical conditions for strict and second-order stationarity, and for the existence of higher-order moments, which fills an important gap in the literature on stochastic volatility models. Monte Carlo simulations demonstrate the model's efficiency in estimating parameters, yielding accurate results with minimal bias for a sample size of 5,000. When applied to Algerian Dinar/Euro exchange rate data from 2000 to 2011, the model successfully captures volatility clustering and leverage effects, revealing a 30% increase in volatility in response to negative shocks relative to positive ones. It also improves predictive accuracy by 15% over standard models, underscoring its strength in capturing volatility in emerging markets with complex and nonlinear patterns.

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