Econometric modeling and value-at-risk using the Pearson type-IV distribution

Stavroyiannis, Stavros; Makris, Ilias A.; Nikolaidis, Vasilis N.; Zarangas, Leonidas

doi:10.1016/j.irfa.2012.02.003

Cited by 33 publications

(18 citation statements)

References 56 publications

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“…We use the AR(1)-GJR-GARCH(1, 1) approach (Bollerslev, 1986;Glosten et al, 1993) where the residuals follow the standardised Pearson type IV distribution, since in a series of papers it has been shown that it performs better than the skewed-t-student distribution especially at high confidence levels (Stavroyiannis et al, 2012(Stavroyiannis et al, , 2013Stavroyiannis and Zarangas, 2013;Stavroyiannis, 2014)…”

Section: The Modelmentioning

confidence: 99%

Expected shortfall and tail conditional expectation with the Pearson type IV distribution

Stavroyiannis

2016

GBER

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The Basel Committee of Banking Supervision has used value-at-risk as a measure of market risk in the trading book for two decades in several accords. After the global financial crisis of 2008-2009 value-at-risk was criticised on the grounds that as a measure of risk is not sub-additive, in the sense that it behaves very erratically when banks or regulators try to aggregate compartmentalised risk across all branches of a large diverse bank. Expected shortfall emerged as a natural alternative of value-at-risk fulfilling all four axioms of a coherent risk measure and belongs to the category of spectral risk measures which are not elicitable unless they reduce to minus the expected value. Another critical issue is that the Basel committee indicates that risk managers should conduct the risk measurement tests based on a dataset which is very small for high confidence levels calculations. In this work we calculate and apply the theoretical tail conditional expectation of the standardised Pearson type IV distribution. This is a coherent measure of risk and assuming it describes appropriately the data generation process it can provide the risk manager with reliable results.

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Section: The Modelmentioning

confidence: 99%

Expected shortfall and tail conditional expectation with the Pearson type IV distribution

Stavroyiannis

2016

GBER

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“…However, the advances in econometrics and computer science enable scholars tō t the data and produce advanced, but complex, mathematical models that present accurate VaR estimations, even when the data inputs are inappropriate: extreme value theory (Assaf 2009), nonparametric Kernel Estimators (Yi-Hou Huang & Tseng 2009), GARCH family models (Engle 2004, Angelidis et al 2004, Stavroyiannis et al 2012, Diamandis et al 2011, Mabrouk & Saadi 2012, Asymmetric Heterogeneous Autoregressive realized volatility model combined with Extreme Value Theory (Louzis et al 2014), Markov Switching Regime (Billio & Pelizzon 2000), Fuzzy VaR and Expected Shortfall models with elliptical distributions (Moussa et al 2014), Extreme Learning Machine (Zhang et al 2017), etc.…”

Section: Introductionmentioning

confidence: 99%

ACCURACY VERSUS COMPLEXITY TRADE-OFF IN VaR MODELING: COULD TECHNICAL ANALYSIS BE A SOLUTION?

Vasileiou

2019

J. Fin. Mngt. Mar. Inst.

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Accurate Value at Risk (VaR) estimations are crucial for the robustness and stability of a financial system. Even though significant advances have been made in the field of risk modeling, many crises have emerged during the same period, and an explanation for this is that the advanced models are not widely applied in the financial industry due to their mathematical complexity. In contrast to the mathematically complex models that torture the data in the output stage, we suggest a new approach that filters the data inputs, based on Technical Analysis (TA) signals. When the trading signals suggest that the conditions are positive (negative) for investments we use data from the previously documented positive (negative) periods in order to calculate the VaR. In this way, we use input data that are more representative of the financial conditions under examination and thus VaR estimations are more accurate and more representative (nonprocyclical) than the conventional models’ estimation that use the last nonfiltered [Formula: see text]-day observations. Testing our assumptions in the US stock market for the period 2000–2017, the empirical data confirmed our hypothesis. Moreover, we suggest specific legislative adjustments that contribute to more accurate and representative VaR estimations: (i) an extra backtesting procedure at a lower than the 99% confidence level as a procyclicality test and (ii) to ease the minimum requirement of 250 observations that is currently the input threshold because it leads to less accurate VaR estimations.

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“…Distributional schemes for the likelihood estimator include the standard normal distribution (Engle, 1982), the Student-t distribution (Bollerslev, 1987), the Generalized Error Distribution (GED) introduced by Subbotin (1923) and applied by Nelson (1991), the skewed GED (Hill et al, 2008;Theodossiou, 2002;Theodossiou and Trigeorgis, 2003), the skewed t-Student distribution (Fernandez and Steel, 1998;Lambert and Laurent, 2000) hereinafter referred to as SKST, and the Pearson type IV distribution (Stavroyiannis et al, 2012;Stavroyiannis and Zarangas, 2013).…”

Section: Introductionmentioning

confidence: 99%

A Note on the Nelson Cao Inequality Constraints in the GJR-GARCH Model: Is There a Leverage Effect?

Stavroyiannis

2017

SSRN Journal

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The majority of stylized facts of financial time series and several Value-at-Risk measures are modeled via univariate or multivariate GARCH processes. It is not rare that advanced GARCH models fail to converge for computational reasons, and a usual parsimonious approach is the GJR-GARCH model. There is a disagreement in the literature and the specialized econometric software, on which constraints should be used for the parameters, introducing indirectly the distinction between asymmetry and leverage. We show that the approach used by various software packages is not consistent with the Nelson-Cao inequality constraints. Implementing Monte Carlo simulations, despite of the results being empirically correct, the estimated parameters are not theoretically coherent with the Nelson-Cao constraints for ensuring positivity of conditional variances. On the other hand ruling out the leverage hypothesis, the asymmetry term in the GJR model can take negative values when typical constraints like the condition for the existence of the second and fourth moments, are imposed.

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Econometric modeling and value-at-risk using the Pearson type-IV distribution

Cited by 33 publications

References 56 publications

Expected shortfall and tail conditional expectation with the Pearson type IV distribution

Expected shortfall and tail conditional expectation with the Pearson type IV distribution

ACCURACY VERSUS COMPLEXITY TRADE-OFF IN VaR MODELING: COULD TECHNICAL ANALYSIS BE A SOLUTION?

A Note on the Nelson Cao Inequality Constraints in the GJR-GARCH Model: Is There a Leverage Effect?

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