Extreme Value Theory in Finance: A Way to Forecast Unexpected Circumstances

Aslanertik, Banu Esra; Erdem, Sabri; Gümüş, Gülüzar Kurt

doi:10.1007/978-3-319-47172-3_12

Cited by 2 publications

(1 citation statement)

References 23 publications

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“…In statistics, one of the methods used to identify extreme events is extreme value theory (EVT). EVT aims to estimate the probability of an extreme event by looking at the tail of a distribution based on the extreme values obtained [6]. The approaches used in identifying an extreme value using EVT are block maxima (BM) and peaks over threshold (POT) [7].…”

Section: Introductionmentioning

confidence: 99%

Value at Risk Estimation Using Extreme Value Theory Approach in Indonesia Stock Exchange

Najamuddin,

Herdiani,

Jaya

2024

BAREKENG: J. Math. & App.

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Extreme Value Theory (EVT) is a method used to identify extreme cases in heavy tail data such as financial time series data. This research aimed to obtain an estimate of stock risk through the EVT approach and compare the accuracy of the two EVT approaches, Block Maxima (BM) and Peaks Over Threshold (POT). The method used to estimate stock risk is VaR with the BM and POT approaches, and the Z statistic is used to compare the accuracy. The data used, and the limitation in this research is daily closing price data for non-cyclical consumer stocks included in LQ45 for the period February 01, 2017, to January 31, 2023. Other research limitations are using weekly blocks or 5 working days in dividing BM blocks, using the percentage method in determining threshold values in the POT approach, and using Maximum Likelihood Estimation (MLE) to estimate EVT parameter estimates. The results of the VaR analysis show that the risk level generated by the POT method is greater than the risk level from BM. The results of backtesting between the two EVT approaches in estimating VaR values show that the POT approach is more accurate than the BM approach.

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Section: Introductionmentioning

confidence: 99%

Value at Risk Estimation Using Extreme Value Theory Approach in Indonesia Stock Exchange

Najamuddin,

Herdiani,

Jaya

2024

BAREKENG: J. Math. & App.

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A 2D Lévy-flight model for the complex dynamics of real-life financial markets

Yarahmadi

Saberi

2022

Chaos: An Interdisciplinary Journal of Nonlinear Science

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We report on the emergence of scaling laws in the temporal evolution of the daily closing values of the S&P 500 index prices and its modeling based on the Lévy flights in two dimensions (2D). The efficacy of our proposed model is verified and validated by using the extreme value statistics in the random matrix theory. We find that the random evolution of each pair of stocks in a 2D price space is a scale-invariant complex trajectory whose tortuosity is governed by a [Formula: see text] geometric law between the gyration radius [Formula: see text] and the total length [Formula: see text] of the path, i.e., [Formula: see text]. We construct a Wishart matrix containing all stocks up to a specific variable period and look at its spectral properties for over 30 years. In contrast to the standard random matrix theory, we find that the distribution of eigenvalues has a power-law tail with a decreasing exponent over time—a quantitative indicator of the temporal correlations. We find that the time evolution of the distance of 2D Lévy flights with index [Formula: see text] from origin generates the same empirical spectral properties. The statistics of the largest eigenvalues of the model and the observations are in perfect agreement.

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Extreme Value Theory in Finance: A Way to Forecast Unexpected Circumstances

Cited by 2 publications

References 23 publications

Value at Risk Estimation Using Extreme Value Theory Approach in Indonesia Stock Exchange

Value at Risk Estimation Using Extreme Value Theory Approach in Indonesia Stock Exchange

A 2D Lévy-flight model for the complex dynamics of real-life financial markets

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