Market moves and the information content of option prices

In this paper we estimate risk-neutral returns distributions using the prices of options written on S&P 500 index futures and investigate whether or not specific characteristics of the returns distributions might be useful information for the purpose of predicting changes in market direction. The key distributional characteristics we focus on are skewness, kurtosis, and the probability weight in the extreme tails of the implied risk-neutral returns distributions. We find that, with one possible exception, the characteristics we considered are unlikely to improve a trader's ability to predict market moves.     

Controlling portfolio skewness and kurtosis without directly optimizing third and fourth moments

In spite of their importance, third or higher moments of portfolio returns are often neglected in portfolio construction problems due to the computational difficulties associated with them. In this paper, we propose a new robust mean–variance approach that can control portfolio skewness and kurtosis without imposing higher moment terms. The key idea is that, if the uncertainty sets are properly constructed, robust portfolios based on the worst-case approach within the mean–variance setting favor skewness and penalize kurtosis.     

Modeling of Income and Indicators of Poverty and Social Exclusion Using the Generalized Beta Distribution of the Second Kind

There are three reasons why estimation of parametric income distributions may be useful when empirical data and estimators are available: to stabilize estimation; to gain insight into the relationships between the characteristics of the theoretical distribution and a set of indicators, e.g. by sensitivity plots; and to deduce the whole distribution from known empirical indicators, when the raw data are not available. The European Union Statistics on Income and Living Conditions (EU‐SILC) survey is used to address these issues. In order to model the income distribution, we consider the generalized beta distribution of the second kind (GB2). A pseudo‐likelihood approach for fitting the distribution is considered, which takes into account the design features of the EU‐SILC survey. An ad‐hoc procedure for robustification of the sampling weights, which improves estimation, is presented. This method is compared to a non‐linear fit from the indicators. Variance estimation within a complex survey setting of the maximum pseudo‐likelihood estimates is done by linearization (a sandwich variance estimator), and a simplified formula for the sandwich variance, which accounts for clustering, is given. Performance of the fit and estimated indicators is evaluated graphically and numerically.     

On the Effect of Skewness and Kurtosis Misspecification on the Hedging Error

Using a result in Angelini and Herzel (2009a) , we measure, in terms of variance, the cost of hedging a contingent claim when the hedging portfolio is re‐balanced at a discrete set of dates. We analyse the dependence of the variance of the hedging error on the skewness and kurtosis as modeled by a Normal Inverse Gaussian model. We consider two types of strategies, the standard Black–Scholes Delta strategy and the locally variance‐optimal strategy, and we perform some robustness tests. In particular, we investigate the effect of different types of model misspecification on the performance of the hedging, like that of hedging without taking skewness into account. Computations are performed using a Fast Fourier Transform approach.     

Is the Pareto–Lévy law a good representation of income distributions?

Mandelbrot (Int Econ Rev 1:79–106, 1960) proposed using the so-called Pareto–Lévy class of distributions as a framework for representing income distributions. We argue in this article that the Pareto–Lévy distribution is an interesting candidate for representing income distributions because its parameters are easy to interpret and it satisfies a specific invariance-under-aggregation property. We also demonstrate that the Gini coefficient can be expressed as a simple formula of the parameters of the Pareto–Lévy distribution. We subsequently use income data for Norway and seven other OECD countries to fit the Pareto–Lévy distribution as well as the Generalized Beta type II (GB2) distribution. The results show that the Pareto–Lévy distribution fits the data better than the GB2 distribution for most countries, despite the fact that GB2 distribution has four parameters whereas the Pareto–Lévy distribution has only three.     

Modelling conditional moments and correlation with the continuous hidden-threshold-skew-normal distribution

A key issue in modelling conditional densities of returns of financial assets is the time-variation of conditional volatility. The classic econometric approach models volatility of returns with the generalized autoregressive conditional heteroscedasticity (GARCH) models where the conditional mean and the conditional volatility depend only on historical prices. We propose a new family of distributions in which the conditional distribution depends on a latent continuous factor with a continuum of states. The distribution has an interpretation in terms of a mixture distribution with time-varying mixing probabilities. The distribution parameters have economic interpretations in terms of conditional volatilities and correlations of the returns with the hidden continuous state. We show empirically that this distribution outperforms its main competitor, the mixed normal conditional distribution, in terms of capturing the stylized facts known for stock returns, namely, volatility clustering, leverage effect, skewness, kurtosis and regime dependence.     

Superstitious seasonality in precious metals markets? Evidence from GARCH models with time-varying skewness and kurtosis

In this article, we analyse whether the Friday the 13th effect documented by Kolb and Rodriguez (1987) can be observed in precious metals markets. Specifically, we use dummy-augmented GARCH models to investigate the impact of this specific calendar day on the conditional means of gold, silver, palladium and platinum returns. The specification of the GARCH model follows a flexible class recently proposed by León et al. (2005) that incorporates time-varying skewness and kurtosis by applying a Gram–Charlier series expansion of the normal density function. Our results for the period from July 1996 to August 2013 provide three important insights. First, there is no evidence that human superstition regarding bad luck Fridays affects precious metals markets in a negative way, i.e. returns on Fridays the 13th are not significantly lower than on regular Fridays. Second, besides showing robustness in a variety of settings, we can confirm this main result in a sensitivity check, where we replace the dummy variables by a new measure of investor attention, recently promoted by Da et al. (2011), that is based on Google search volumes. Third, as an important by-product of our study, we can show that there is significant evidence of time-varying skewness and kurtosis in precious metals returns.     

Score-driven Markov-switching EGARCH models: an application to systematic risk analysis

We introduce new Markov-switching (MS) dynamic conditional score (DCS) exponential generalized autoregressive conditional heteroscedasticity (EGARCH) models, to be used by practitioners for forecasting value-at-risk (VaR) and expected shortfall (ES) in systematic risk analysis. We use daily log-return data from the Standard & Poor’s 500 (S&P 500) index for the period 1950–2016. The analysis of the S&P 500 is useful, for example, for investors of (i) well-diversified US equity portfolios; (ii) S&P 500 futures and options traded at Chicago Mercantile Exchange Globex; (iii) exchange traded funds (ETFs) related to the S&P 500. The new MS DCS-EGARCH models are alternatives to of the recent MS Beta-t-EGARCH model that uses the symmetric Student’s t distribution for the error term. For the new models, we use more flexible asymmetric probability distributions for the error term: Skew-Gen-t (skewed generalized t), EGB2 (exponential generalized beta of the second kind) and NIG (normal-inverse Gaussian) distributions. For all MS DCS-EGARCH models, we identify high- and low-volatility periods for the S&P 500. We find that the statistical performance of the new MS DCS-EGARCH models is superior to that of the MS Beta-t-EGARCH model. As a practical application, we perform systematic risk analysis by forecasting VaR and ES.

Abbreviation Single regime (SR); Markov-switching (MS); dynamic conditional score (DCS); exponential generalized autoregressive conditional heteroscedasticity (EGARCH); value-at-risk (VaR); expected shortfall (ES); Standard & Poor's 500 (S&P 500); exchange traded funds (ETFs); Skew-Gen-t (skewed generalized t); EGB2 (exponential generalized beta of the second kind); NIG (normal-inverse Gaussian); log-likelihood (LL); standard deviation (SD); partial autocorrelation function (PACF); likelihood-ratio (LR); ordinary least squares (OLS); heteroscedasticity and autocorrelation consistent (HAC); Akaike information criterion (AIC); Bayesian information criterion (BIC); Hannan-Quinn criterion (HQC).     

An empirical re-examination of extreme tail behavior: testing the assumptions of the power laws and the generalized Pareto distribution on the financial series

This study investigates whether the power laws and the associated generalized Pareto distribution (GPD) exist in the extreme tail behavior of financial return series. We include 10 series of five major financial categories over the period 1971–2018 for empirical analysis. For the former assumption, we test three representative power-law distributions. For the latter, we employ an innovative bootstrap goodness-of-fit test of GPD modeling. We also discuss the relationship between both assumptions. The empirical outcomes indicate that both assumptions do not necessarily hold for all tail series due to the outlying observations. The rejection of the power laws assumption leads to the rejection of the GPD assumption. This rejection does not promise the non-rejection of power laws either. However, the non-rejection of either assumption does not imply non-rejection of the other assumption. Power-law distribution and exponential distribution outperform log-normal distribution in tail fitting. GPD fits better at the 1% quantile level than at the 5% level. Overall, we need to acknowledge the considerable gap between the goodness-of-fit testing outcomes of both the power laws and GPD assumptions.     

QUANTILE FORECASTS OF FINANCIAL RETURNS USING REALIZED GARCH MODELS*

This article applies the realized generalized autoregressive conditional heteroskedasticity (GARCH) model, which incorporates the GARCH model with realized volatility, to quantile forecasts of financial returns, such as Value‐at‐Risk and expected shortfall. Student's t‐ and skewed Student's t‐distributions as well as normal distribution are used for the return distribution. The main results for the S&P 500 stock index are: (i) the realized GARCH model with the skewed Student's t‐distribution performs better than that with the normal and Student's t‐distributions and the exponential GARCH model using the daily returns only; and (ii) using the realized kernel to take account of microstructure noise does not improve the performance.     

Optimal hedge ratio estimation and hedge effectiveness with multivariate skew distributions

This article proposes to use the three multivariate skew distributions (generalized hyperbolic distribution, multivariate skew normal distribution, and multivariate skew Student-t distribution) for estimating the minimum variance hedge ratio in a dynamic setting. Three criteria for measuring hedge effectiveness are employed: hedging instrument effectiveness, overall hedge effectiveness, and relative-to-optimal hedge ratio effectiveness (RHRE). Three portfolios of spot and futures series are formed for empirical analysis. The outcomes confirm that the three multivariate skew distributions are more helpful in deciding the minimum variance hedge ratio, especially the generalized hyperbolic distribution, than the symmetrical normal and Student-t distributions. This outperformance is significant especially at critical market moments and it is indicated by three hedge effectiveness measures. This advantage is held without the cost of lowering portfolio return. In addition, there is speculation possibility existing in the portfolio hedged by the traditional optimal hedge ratio and this potential can be detected especially by RHRE.     

Accounting for the impact of higher order moments in foreign equity option pricing model

This paper investigates the pricing of foreign equity option whose value depends on foreign equity prices and exchange rate. We assume that the underlying asset returns of foreign equity option is not a Brownian motion, and use the Gram-Charlier series expansion to augment a normal density with two additional terms to capture the effects of skewness and kurtosis. The empirical study shows that the higher order moments (skewness and kurtosis) clearly affect the estimated prices of foreign equity options. This approach enables us to capture more accurately the foreign equity option prices.     

Empirical analysis of jump dynamics, heavy-tails and skewness on value-at-risk estimation

This study provides a comprehensive analysis of the possible influences of jump dynamics, heavy-tails, and skewness with regard to VaR estimates through the assessment of both accuracy and efficiency. To this end, the ARJI model, and its degenerative GARCH model with normal, GED, and skewed normal (SN) distributions were adopted to capture the properties of time-varying volatility, time-varying jump intensity, heavy-tails and skewness, for a range of stock indices across international stock markets during the period of the U.S. subprime mortgage crisis. Empirical results show that, with regard to the evaluation of accuracy, the role of jump dynamics is more substantial than heavy-tails or skewness as it pertains to VaR accuracy at the 90% and 95% levels, while heavy-tails become more important at the 99% level for a long position. However, the influence of the abovementioned properties on VaR estimation does not appear substantial for a short position. In addition, the properties of jump dynamics and skewness appear to be beneficial for the improvement of efficiency.     

宏观经济统计数据结构变化分析及其对中国的实证

对于宏观经济统计数据的结构变化进行分析已成为研究数据质量的核心内容之一。本文从经济系统的角度运用联合估计诊断模型对我国 3 6个宏观经济时间序列的结构变化进行了全面的分析 ,发现了数据异常的特点和规律。研究结论表明 :大部分异常点的出现或多或少都是以聚集成堆的形式出现的 ,它们之间存在深刻的内在联系 ,孤立的异常点不是我国宏观经济时间序列的主要特征 ;几乎所有的原始序列都有显著的偏度 ,过多的峰度也是明显的 ,因此它们被显著地拒绝认为服从正态分布 ;大部分变量的原始序列和异常点修正后序列虽然都呈现出非ARCH特征 ,但是ARCH2、ARCH4、ARCH8的P值却有一定程度的不同。     

Marginal risk aversion and preferences in a betting market

An individual's behavioural attitudes toward variance and non-symmetry in the payoff distributions of pari-mutuel gambles are empirically examined using the von Neumann - Morgenstern expected utility of wealth paradigm. Preferences over payoff distributions for a representative bettor are estimated from observed payoffs at a greyhound racetrack. The results indicate that the representative bettor exhibits increasing absolute risk aversion and, given that the representative bettor is locally non-satiated with regard to wealth, exhibits preference for variance and aversion to positive skewness in the payoff distributions of the gambles examined.     

Weak monotonicity and Bayes–Nash incentive compatibility

An allocation rule is called Bayes–Nash incentive compatible, if there exists a payment rule, such that truthful reports of agents' types form a Bayes–Nash equilibrium in the direct revelation mechanism consisting of the allocation rule and the payment rule. This paper provides a characterization of Bayes–Nash incentive compatible allocation rules in social choice settings where agents have multi-dimensional types, quasi-linear utility functions and interdependent valuations. The characterization is derived by constructing complete directed graphs on agents' type spaces with cost of manipulation as lengths of edges. Weak monotonicity of the allocation rule corresponds to the condition that all 2-cycles in these graphs have non-negative length. For the case that type spaces are convex and the valuation for each outcome is a linear function in the agent's type, we show that weak monotonicity of the allocation rule together with an integrability condition is a necessary and sufficient condition for Bayes–Nash incentive compatibility.     

India's gender bias in child population,female education and growing prosperity: 1951–2011

¹ 1. Professor D. P. Chaudhri sadly died before the publication of this paper. View all notesUsing Census and National Sample Survey (NSS) data, this paper studies the evolution of Gender Bias (GB) in the age group 0–6 in India and its association with education and higher prosperity. GB is pervasive and has grown over time with higher prosperity and resultant demographic transition and enhanced education. Large household size (associated with high fertility rates and low Monthly Per Capita Expenditure (MPCE)) are linked with low GB. However, with higher prosperity and lower Total Fertility Rate (TFR) GB rises sharply. Hence, the outlook for GB in the age group 0–6 appears bleak at least until 2026. There are wide variations in GB across various states, even districts. Both improved education of females in the age group 15–49 and higher prosperity lead to worsening of GB. However, at high values of the interaction of these two variables there is a turnaround in the trend of worsening GB. Policy conclusions are discussed.     

The Intensity and Shape of Inequality: The ABG Method of Distributional Analysis

Inequality is anisotropic: its intensity varies by income level. We here develop a new tool, the isograph, to focus on local inequality and illustrate these variations. This method yields three coefficients which summarize the shape of inequality: a main coefficient, α, which measures inequality at the median; and two correction coefficients, β and γ, which pick up any differential curvature at the top and bottom of the distribution. The analysis of a set of 232 microdata samples from 41 different countries in the LIS datacenter archive allows us to provide a systematic overview of the properties of the ABG (α β γ) coefficients, which are compared to a set of standard indices including Atkinson indices, generalized entropy, Wolfson polarization, and the GB2 distribution. This method also provides a smoothing tool that reveals the differences in the shape of distributions (the strobiloid) and how these have changed over time.     

International Trade and the Value of Time

I discuss a generalized Heckscher–Ohlin–Vanek (HOV) model in which consumption requires time as well as money (as in Becker's theory of the allocation of time) and the amount of work that a worker can do per unit of time—her “ability”—varies from country to country. High ability implies high income per hour, which implies a high value of time and, therefore, high consumption of the good that is more “time‐saving.” Therefore, if domestic production of this good is not commensurately high, it would have to be imported. In this way, I demonstrate that international differences in worker ability constitute an independent source of gains from trade. The model is able to explain several observed features of North–South trade that are not explained by the HOV model. The theoretical possibility of a Leontief paradox‐type trade pattern is also demonstrated.     

Beta trigonometric distributions

Beta distributions are popular models for economic data. In this paper, six new distributions are introduced which generalize the standard beta distribution. These distributions involve the trigonometric functions, sine and cosine. Expressions are derived for their analytical shapes, nth moments, method of moments estimators, maximum likelihood estimators and the associated Fisher information matrices. These calculations involve several special functions. A numerical study is performed to show the flexility of these distributions as compared to the standard beta distribution. An application to consumer expenditure data is illustrated to show that the proposed distributions are better models to economic data than one based on the standard beta distribution. Possible ways of extending the models are also discussed.