Revisiting the Copula-Based Trading Method Using the Laplace Marginal Distribution Function

Nadaf, Tayyebeh; Lotfi, Taher; Shateyi, Stanford

doi:10.3390/math10050783

Cited by 4 publications

(3 citation statements)

References 15 publications

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“…Because classical Gaussian distribution models are frequently not supported by reallife data due to fat tails and asymmetry prevalent in financial data, the Laplace and related distributions are natural candidates to replace Gaussian models and processes in modeling these data [20]. Since Laplace distributions can account for leptokurtic and skewed data [21], it is also used to fit the marginal distribution function, which will then be used in a copula function [22]. Definition 3.…”

Section: Asymmetric Laplace Distributionmentioning

confidence: 99%

Asymmetric Laplace Distribution Models for Financial Data: VaR and CVaR

2022

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In the field of financial risk measurement, Asymmetric Laplace (AL) laws are used. The assumption of normalcy is used in traditional approaches for calculating financial risk. Asymmetric Laplace distribution, on the other hand, reveals the properties of empirical financial data sets much better than the normal model by leptokurtosis and skewness. According to recent financial data research, the regularity assumption is frequently broken. As a result, Asymmetric Laplace laws offer a simple, creative, and useful option to normal distributions when it comes to modeling financial data. We here engage AL distribution to explore specific formulas for the two commonly used risk measures, Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR). The currency exchange rates data are used to and worked out to illustrate the proposed methodologies.

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Section: Asymmetric Laplace Distributionmentioning

confidence: 99%

Asymmetric Laplace Distribution Models for Financial Data: VaR and CVaR

2022

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“…Copulas are a family of functions that construct the joint distribution of two or more random variables with an unidentified dependence among the variables [39,40]. The most widely used Copula functions include two categories: Elliptic Copulas and Archimedean Copulas.…”

Section: Analysis Of Hazard Probabilitymentioning

confidence: 99%

High-Resolution Hazard Assessment for Tropical Cyclone-Induced Wind and Precipitation: An Analytical Framework and Application

Tang

Liu

et al. 2022

Sustainability

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Intensified tropical cyclones (TCs) threaten the socioeconomic development of coastal cities. The coupling of strong wind and precipitation with the TC process usually amplifies the destructive effects of storms. Currently, an integrated analytical framework for TC hazard assessment at the city level that combines the joint statistical characteristics of multiple TC-induced hazards and local environmental features does not exist. In this study, we developed a novel hazard assessment framework with a high spatiotemporal resolution that includes a fine-tuned K-means algorithm for clustering TC tracks and a Copula model to depict the wind–precipitation joint probability distribution of different TC categories. High-resolution wind and precipitation data were used to conduct an empirical study in Shenzhen, a coastal megacity in Guangdong Province, China. The results show that the probabilities of TC-induced wind speed and precipitation exhibit significant spatial heterogeneity in Shenzhen, which can be explained by the characteristics of TC tracks and terrain environment factors. In general, the hazard intensity of TCs landing from the west side is higher than that from the east side, and the greatest TC intensity appears on the southeast coast of Shenzhen, implying that more disaster prevention efforts are needed. The proposed TC hazard assessment method provides a solid base for highly precise risk assessment at the city level.

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“…Laplace distributions are used to fit the marginal distribution function, which will then be employed in a copula function because they can account for leptokurtic and skewed data (Kotz et al 2001). Compared to the Gaussian distribution, it typically better describes stock return behavior while capturing the greater peak and heavy tails (Nadaf et al 2022). Recognizing the rarity of stock market data adhering strictly to a standard Laplace distribution, introducing the generalized Laplace distribution enhances flexibility for modeling real-life data.…”

Section: Introductionmentioning

confidence: 99%

Probability Distributions for Modeling Stock Market Returns—An Empirical Inquiry

Pokharel,

Aryal,

Khanal

et al. 2024

IJFS

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Investing in stocks and shares is a common strategy to pursue potential gains while considering future financial needs, such as retirement and children’s education. Effectively managing investment risk requires thoroughly analyzing stock market returns and making informed predictions. Traditional models often utilize normal variance distributions to describe these returns. However, stock market returns often deviate from normality, exhibiting skewness, higher kurtosis, heavier tails, and a more pronounced center. This paper investigates the Laplace distribution and its generalized forms, including asymmetric Laplace, skewed Laplace, and the Kumaraswamy Laplace distribution, for modeling stock market returns. Our analysis involves a comparative study with the widely-used Variance-Gamma distribution, assessing their fit with the weekly returns of the S&P 500 Index and its eleven business sectors, drawing parallel inferences from international stock market indices like IBOVESPA and KOSPI for emerging and developed economies, as well as the 20+ Years Treasury Bond ETFs and individual stocks across varied time horizons. The empirical findings indicate the superior performance of the Kumaraswamy Laplace distribution, which establishes it as a robust alternative for precise return predictions and efficient risk mitigation in investments.

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Revisiting the Copula-Based Trading Method Using the Laplace Marginal Distribution Function

Cited by 4 publications

References 15 publications

Asymmetric Laplace Distribution Models for Financial Data: VaR and CVaR

Asymmetric Laplace Distribution Models for Financial Data: VaR and CVaR

High-Resolution Hazard Assessment for Tropical Cyclone-Induced Wind and Precipitation: An Analytical Framework and Application

Probability Distributions for Modeling Stock Market Returns—An Empirical Inquiry

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