Asymmetric Laplace Distribution Models for Financial Data: VaR and CVaR

Jing, Huiting; Liu, Yang; Zhao, Jinghua

doi:10.3390/sym14040807

Cited by 3 publications

(1 citation statement)

References 21 publications

(22 reference statements)

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“…Laplace distribution, also known as double-exponential distribution, is a continuous probability distribution that is widely employed in various fields, including statistics, signal processing and power system analysis. Laplace distribution is characterized by its symmetric bell-shaped curve and usually exhibits heavy tails compared to the normal distribution [21]. This heavy-tailed property makes the Laplace distribution particularly suitable for modeling data with outliers or extreme values.…”

Section: Laplace Distribution and Observationmentioning

confidence: 99%

Laplace-Domain Hybrid Distribution Model Based FDIA Attack Sample Generation in Smart Grids

Wu,

Zu,

Guo

et al. 2023

Symmetry

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False data injection attack (FDIA) is a deliberate modification of measurement data collected by the power grid using vulnerabilities in power grid state estimation, resulting in erroneous judgments made by the power grid control center. As a symmetrical defense scheme, FDIA detection usually uses machine learning methods to detect attack samples. However, existing detection models for FDIA typically require large-scale training samples, which are difficult to obtain in practical scenarios, making it difficult for detection models to achieve effective detection performance. In light of this, this paper proposes a novel FDIA sample generation method to construct large-scale attack samples by introducing a hybrid Laplacian model capable of accurately fitting the distribution of data changes. First, we analyze the large-scale power system sensing measurement data and establish the data distribution model of symmetric Laplace distribution. Furthermore, a hybrid Laplace-domain symmetric distribution model with multi-dimensional component parameters is constructed, which can induce a deliberate deviation in the state estimation from its safe value by injecting into the power system measurement. Due to the influence of the multivariate parameters of the hybrid Laplace-domain distribution model, the sample deviation generated by this model can not only obtain an efficient attack effect, but also effectively avoid the recognition of the FDIA detection model. Extensive experiments are carried out over IEEE 14-bus and IEEE 118-bus test systems. The corresponding results unequivocally demonstrate that our proposed attack method can quickly construct large-scale FDIA attack samples and exhibit significantly higher resistance to detection by state-of-the-art detection models, while also offering superior concealment capabilities compared to traditional FDIA approaches.

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Section: Laplace Distribution and Observationmentioning

confidence: 99%

Laplace-Domain Hybrid Distribution Model Based FDIA Attack Sample Generation in Smart Grids

Wu,

Zu,

Guo

et al. 2023

Symmetry

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Linear asymmetric Laplace fuzzy information granule and its application in short-to-medium term prediction for financial time series

Yang,

Wang

2024

Information Sciences

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A capital asset pricing model based on the value at risk under asymmetric Laplace distribution

Wu,

2023

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PurposeFinancial asset return series usually exhibit nonnormal characteristics such as high peaks, heavy tails and asymmetry. Traditional risk measures like standard deviation or variance are inadequate for nonnormal distributions. Value at Risk (VaR) is consistent with people's psychological perception of risk. The asymmetric Laplace distribution (ALD) captures the heavy-tailed and biased features of the distribution. VaR is therefore used as a risk measure to explore the problem of VaR-based asset pricing. Assuming returns obey ALD, the study explores the impact of high peaks, heavy tails and asymmetric features of financial asset return data on asset pricing.Design/methodology/approachA VaR-based capital asset pricing model (CAPM) was constructed under the ALD that follows the logic of the classical CAPM and derive the corresponding VaR-β coefficients under ALD.FindingsALD-based VaR exhibits a minor tail risk than VaR under normal distribution as the mean increases. The theoretical derivation yields a more complex capital asset pricing formula involving β coefficients compared to the traditional CAPM.The empirical analysis shows that the CAPM under ALD can reflect the β-return relationship, and the results are robust. Finally, comparing the two CAPMs reveals that the β coefficients derived in this paper are smaller than those in the traditional CAPM in 69–80% of cases.Originality/valueThe paper uses VaR as a risk measure for financial time series data following ALD to explore asset pricing problems. The findings complement existing literature on the effects of high peaks, heavy tails and asymmetry on asset pricing, providing valuable insights for investors, policymakers and regulators.

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Asymmetric Laplace Distribution Models for Financial Data: VaR and CVaR

Cited by 3 publications

References 21 publications

Laplace-Domain Hybrid Distribution Model Based FDIA Attack Sample Generation in Smart Grids

Laplace-Domain Hybrid Distribution Model Based FDIA Attack Sample Generation in Smart Grids

Linear asymmetric Laplace fuzzy information granule and its application in short-to-medium term prediction for financial time series

A capital asset pricing model based on the value at risk under asymmetric Laplace distribution

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