Partially Adaptive and Robust Estimation of Asset Models: Accommodating Skewness and Kurtosis in Returns

McDonald, James B.; Michelfelder, Richard A.

doi:10.4236/jmf.2017.71012

Cited by 12 publications

(4 citation statements)

References 21 publications

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“…Unlike the normal case where the mean of the distribution happens to be the location parameter µ, the mean of the EGB2 distribution is a function of both the location parameter a t,T and the scale parameter b t,T , as well as the shape parameters p t,T and q t,T . According to McDonald(1991), the mean of an EGB2 distribution can be obtained by its moment-generating function and the first moment in (5).…”

Section: Methodsmentioning

confidence: 99%

“…For example, investors underestimate left tail risk and under-insure against very low oil prices in crude oil derivative markets [2]. Motivated by the leptokurtic feature of asset returns and excessive losses caused by financial crises, the literature began to link tail risk management with derivative pricing [3][4][5]. In this regard, option-trading-based strategies were introduced, and novel options were designed for tail risk hedging.…”

Section: Introductionmentioning

confidence: 99%

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Tail Risk Signal Detection through a Novel EGB2 Option Pricing Model

2023

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Connecting derivative pricing with tail risk management has become urgent for financial practice and academia. This paper proposes a novel option pricing model based on the exponential generalized beta of the second kind (EGB2) distribution. The newly proposed model is of generality, simplicity, robustness, and financial interpretability. Most importantly, one can detect tail risk signals by calibrating the proposed model. The model includes the seminal Black–Scholes (B−S) formula as a limit case and can perfectly “replicate” the option prices from Merton’s jump-diffusion model. Based on the proposed pricing model, three tail risk warning measures are introduced for tail risk signals detection: the EGB2 implied tail index, the EGB2 implied Value-at-Risk (EGB2-VaR), and the EGB2 implied risk-neutral density (EGB2 R.N.D.). Empirical results show that the new pricing model can yield higher pricing accuracy than existing models in normal and crisis periods, and three model-based tail risk measures can perfectly detect tail risk signals before financial crises.

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Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Tail Risk Signal Detection through a Novel EGB2 Option Pricing Model

2023

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“…To generate our nonnormal error terms, we specified several conditions using the skewed generalized t distribution using the -sgt-package in R (Davis, 2015). This distributional package is attractive for our purposes because it allows us to simulate distributions with negative and positive values while also varying both skewness and kurtosis (McDonald & Michelfelder, 2017). The command in R includes five parameters: mu (i.e., mean), sigma (i.e., variance), lambda (i.e., skewness), and two parameters ( p and q ) to denote kurtosis.…”

Section: Study 2: Modeling Dependent Variables With Extremely Nonnor...mentioning

confidence: 99%

Out of Shape: The Implications of (Extremely) Nonnormal Dependent Variables

Certo,

Raney,

Albader

et al. 2023

Organizational Research Methods

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Organizational researchers have increasingly noted the problems associated with nonnormal dependent variable distributions. Most of this scholarship focuses on variables with positive values and long tails, such as employee performance, capital expenses, and assets. However, scholars frequently test organizational theories using dependent variables that include negative values, which is perhaps most prominently the case as it relates to measures of firm performance. Over the course of two studies, we investigate the implications of such nonnormally distributed dependent variables in organizational research. In Study 1, we examine the nonnormality of firm performance measures and uncover extreme levels of skewness and kurtosis that vary substantially across measures, samples, and years. We also illustrate that many transformations scholars use to address nonnormality are ineffective. In Study 2, we create simulations that seek to mirror these distributions, and we find that such extreme nonnormality reduces efficiency and increases Type II errors with most statistical approaches. Our analyses also reveal the effectiveness of quantile regression when modeling dependent variables that exhibit the nonnormal distributions often found in organizational research.

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“…Another example of DCS models is QAR (Harvey 2013), which is a nonlinear and outlier-robust alternative to the AR Moving Average (ARMA) model (Box and Jenkins 1970). An additional recent example of DCS models is QVAR (Blazsek et al , 2018b, which is a nonlinear and outlier-robust alternative to the VARMA model (see, for example, Lütkepohl 2005).…”

Section: Review Of the Literature On Dcs Modelsmentioning

confidence: 99%

Score-driven currency exchange rate seasonality as applied to the Guatemalan Quetzal/US Dollar

Ayala

Blazsek

2018

SERIEs

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In this paper we introduce new Dynamic Conditional Score (DCS) models for the Skew-Gent (Skewed Generalized t) and NIG (Normal-Inverse Gaussian) distributions as alternatives to the recent DCS models for the Student's-t and EGB2 (Exponential Generalized Beta of the second kind) distributions, respectively. The DCS models we propose include stochastic local level, stochastic seasonality, and irregular components with DCS-EGARCH (Exponential Generalized Autoregressive Conditional Heteroscedasticity) volatility dynamics. DCS models are robust to extreme observations, whereas standard financial time series models are not. We use data from the Guatemalan Quetzal (GTQ) to United States Dollar (USD) exchange rate for the period of 4th January 1994-30th June 2017. This dataset exhibits significant rises and falls in the GTQ/USD that lead to extreme observations, stochastic seasonality with dynamic amplitude, and volatility dynamics. These seasonality dynamics of the GTQ/USD are related to the Guatemalan trade-related currency movements, receipt and payment of foreign loans, and remittance payments of Guatemalans working abroad. We show that the in-sample statistical performance of the DCS-Skew-Gent and the DCS-NIG models is superior to that of the DCS-t and the DCS-EGB2 models, respectively. Furthermore, we show that the statistical performance of all DCS models is superior to that of the standard financial time series model. Keywords Dynamic Conditional Score (DCS) models • Guatemalan Quetzal (GTQ) to United States Dollar (USD) exchange rate • Stochastic seasonality component JEL Classification C22 • C52 • C58 • F31 B Szabolcs Blazsek

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Partially Adaptive and Robust Estimation of Asset Models: Accommodating Skewness and Kurtosis in Returns

Cited by 12 publications

References 21 publications

Tail Risk Signal Detection through a Novel EGB2 Option Pricing Model

Tail Risk Signal Detection through a Novel EGB2 Option Pricing Model

Out of Shape: The Implications of (Extremely) Nonnormal Dependent Variables

Score-driven currency exchange rate seasonality as applied to the Guatemalan Quetzal/US Dollar

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