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<p>Exchange rate data is highly volatile, influenced by historical financial and economic conditions. In this work, we introduced a novel mixture of Laplace and skew-Laplace distributions, applicable to modeling GBP/USD exchange rates. This generalized mixture encompasses both standard Laplace and skew Laplace distributions as special cases, offering a flexible framework to capture financial data’s asymmetry and heavy tails. We explored key statistical properties of this distribution and conducted simulations to assess parameter effectiveness. Using real-world data, our findings demonstrate that this new distribution outperforms some existing models in terms of log-likelihood, AIC, and BIC. We performed a comprehensive financial risk evaluation using various metrics, including Peaks Over Random Threshold Value-at-Risk (PORT-VaR), Value-at-Risk (VaR), Tail Value-at-Risk (TVaR), and the Mean of Order PP (MOP). Notably, PORT-VaR enhances risk assessments by allowing randomness in threshold selection, while VaR and TVaR measure potential losses at defined confidence levels, with TVaR providing insights into severe tail risks. The MOP approach helps balance financial objectives when optimizing portfolios amid uncertainty.</p>

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A novel mixture of Laplace and Skew-Laplace distributions: properties, applications and risk analysis for the GBP/USD exchange rates with mean of order P assessment

  • 期刊论文

  • 发表日期：

    2026年3月16日

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  • Jondeep Das,
  • Partha Jyoti Hazarika,
  • Anupama Nandi,
  • Morad Alizadeh,
  • Javier E. Contreras-Reyes,
  • Haitham M. Yousof

摘要

Exchange rate data is highly volatile, influenced by historical financial and economic conditions. In this work, we introduced a novel mixture of Laplace and skew-Laplace distributions, applicable to modeling GBP/USD exchange rates. This generalized mixture encompasses both standard Laplace and skew Laplace distributions as special cases, offering a flexible framework to capture financial data’s asymmetry and heavy tails. We explored key statistical properties of this distribution and conducted simulations to assess parameter effectiveness. Using real-world data, our findings demonstrate that this new distribution outperforms some existing models in terms of log-likelihood, AIC, and BIC. We performed a comprehensive financial risk evaluation using various metrics, including Peaks Over Random Threshold Value-at-Risk (PORT-VaR), Value-at-Risk (VaR), Tail Value-at-Risk (TVaR), and the Mean of Order PP (MOP). Notably, PORT-VaR enhances risk assessments by allowing randomness in threshold selection, while VaR and TVaR measure potential losses at defined confidence levels, with TVaR providing insights into severe tail risks. The MOP approach helps balance financial objectives when optimizing portfolios amid uncertainty.