Asymmetric Variance Research Articles

Testing an Algorithm with Asymmetric Markov-Switching GARCH Models in US Stock Trading

In the present paper, we extend the current literature in algorithmic trading with Markov-switching models with generalized autoregressive conditional heteroskedastic (MS-GARCH) models. We performed this by using asymmetric log-likelihood functions (LLF) and variance models. From 2 January 2004 to 19 March 2021, we simulated 36 institutional investor’s portfolios. These used homogenous (either symmetric or asymmetric) Gaussian, Student’s t-distribution, or generalized error distribution (GED) and (symmetric or asymmetric) GARCH variance models. By including the impact of stock trading fees and taxes, we found that an institutional investor could outperform the S&P 500 stock index (SP500) if they used the suggested trading algorithm with symmetric homogeneous GED LLF and an asymmetric E-GARCH variance model. The trading algorithm had a simple rule, that is, to invest in the SP500 if the forecast probability of being in a calm or normal regime at t + 1 is higher than 50%. With this configuration in the MS-GARCH model, the simulated portfolios achieved a 324.43% accumulated return, of which the algorithm generated 168.48%. Our results contribute to the discussion on using MS-GARCH models in algorithmic trading with a combination of either symmetric or asymmetric pdfs and variance models.

ANALISIS VOLATILITAS DAN FORECAST SAHAM PT ANTAM (PERSERO) Tbk. DAN PT ADARO ENERGY Tbk. DENGAN GARCH, EGARCH DAN GJR

An extraordinary event that causes shock can affect volatility which causes asymmetric variance and error or commonly called asimetric shock / effect. This paper aims to analyze the volatility of stock returns of PT ANTAM (Persero) Tbk and PT Adaro Energy Tbk in the period of 2008 to 2016. The research results show that ANTM and ADRO have a GARCH effect and also have a leverage effect where the optimal model is found in the GJR model (0,1,1) for ANTM and GJR (1,1,1) for ADRO. Forecasting results shows that ADRO has higher volatility but in a relatively low percentage of volatility about 0.001 while ANTM have a tendency to decrease volatility with a fairly large percentage of volatility about 0.0025.

Bilateral multiple gamma returns: Their risks and rewards

The bilateral gamma model for returns is naturally derived from the lognormal model. Maximizing entropy in a random time change delivers the symmetric variance gamma model. The asymmetric variance gamma follows on incorporating skewness. Differential speeds for the upward and downward motions lead to the bilateral gamma. A further generalizations results in the bilateral double gamma model when the speed parameter of the bilateral gamma model is itself taken to be gamma distributed on entropy maximization. A rich five to seven parameter specification of preferences renders possible the extraction of physical densities from option prices. The quality of such extraction is measured by examining the uniformity of the estimated distribution functions evaluated at realized forward returns. The economic value of risky returns is seen to embed three/five risk premia for the bilateral gamma/bilateral double gamma. For the bilateral gamma they are up and down side volatilities compensated in up and down side drifts, and the down side drift compensated in the up side drift. For the bilateral double gamma one adds in addition compensations for skewness. Results reveal a drop in the down side risk premium since the crisis with an increase in the recent period.

Analisis Volatilitas Return Saham PT Antam (Persero) Tbk dan PT Adaro Energy Tbk Dengan Garch, Egarch Dan GJR

An extraordinary event that causes shock can affect volatility which causes asymmetric variance and error or commonly called asimetric shock / effect. This paper aims to analyze the volatility of stock returns of PT ANTAM (Persero) Tbk and PT Adaro Energy Tbk in the period of 2008 to 2016. The research results show that ANTM and ADRO have a GARCH effect and also have a leverage effect where the optimal model is found in the GJR model (0,1,1) for ANTM and GJR (1,1,1) for ADRO. Forecasting results shows that ADRO has higher volatility but in a relatively low percentage of volatility about 0.001 while ANTM have a tendency to decrease volatility with a fairly large percentage of volatility about 0.0025.
 
 Keywords: Volatility, GARCH, EGARCH, GJR

Three regime bivariate normal distribution: a new estimation method for co-value-at-risk, CoVaR

We propose a new distribution for estimation of co-value-at-risk, CoVaR, a financial system risk measure conditional on an institution in a financial distress: a three regime bivariate normal (3RN) distribution which is composed of three bivariate normal distributions with asymmetric variance matrices for the right-tail, left-tail and mid-part corresponding to the return of an institution. The distribution captures explicitly the asymmetric correlation of system return and institution return: usually stronger for bad times than for good times. The 3RN distribution allows simple evaluations of the CoVaR taking full advantage of asymmetric correlation. An implementation for the quasi maximum likelihood estimator (QMLE) is provided. The proposed estimation method is applied to stock price data sets consisting of one financial system and four financial institutions: the US S&P 500 index, Bank of America Corporation, JP Morgan Chase & Co., Goldman Sachs Group, Inc. and Citigroup Inc. The data analysis shows that the proposed method has better in-sample and out-of-sample violation performance than existing methods and some other possible candidates.

Understanding How the Effects of Conditional Conservatism Measurement Bias Vary with the Research Context

While the asymmetric timeliness (AT) measure of Basu (1997) underpins a large body of empirical research on conditional conservatism (CC), prior studies have demonstrated that it is biased and could lead to Type 1 error. To assess how this bias could affect inferences from prior literature, we re-examine previous CC studies that apply the AT measure, and we compare the outcomes with those based on the asymmetric conditional variance (ACV) measure of Dutta & Patatoukas (2017) confirmed to be less influenced by similar bias. We draw two primary conclusions. First, both measures yield similar inferences in interrupted time-series settings that examine the impact of exogenous accounting policy changes on CC. Second, the inferences drawn from the AT measure are not supported by the ACV measure in seminal studies that model the determinants of CC in cross-sectional settings. In addition, we find that the conflicting results between the AT and ACV measures in the cross-sectional settings disappear when the AT measure is allowed to vary across firms. Our findings have implications for both past and future empirical studies of CC.

Speed and Biases of Fourier-Based Pricing Choices: Analysis of the Bastes and Asymmetric Variance Gamma Models

This paper compares the CPU effort and numerical biases of six Fourier-based implementations. Our analyses focus on two jump-related models that can consistently price options with different strikes and maturities: (i) the Bates jump-diffusion model, which combines jumps with stochastic volatility and (ii) the Asymmetric Variance Gamma (AVG) model, a pure-jump process where an infinite number of jumps can occur in any interval of time. We show that both truncation and discretization errors significantly increase as we move away from the diffusive Black-Scholes-Merton dynamics. While most pricing choices converge to the Bates reference values, Attari’s formula is the only Fourier-based method that does not completely blow up in any AVG problematic region. In terms of CPU speed, the strike vector computations proposed by Zhu (2010) significantly improve the computational burden, rendering the use of fast Fourier transforms and plain delta-probability decompositions inefficient.

Asymmetric effects of oil revenue shocks on government spending composition and productive sectors: new evidence from Nigeria

AbstractOil revenue plays an important role in meeting government obligations in Nigeria. It accounts for almost 90 per cent of the total export earnings and government spending. Given the high relevance of oil in Nigeria, this paper examines the asymmetric effects of oil revenue shocks on government spending and the real sectors from 1970 to 2017. We find no long‐run equilibrium relationships among oil revenue and the variables of interest. However, when we allow for non‐linear relationship, cointegration is found to exist only for negative oil revenue and the variable of interest. Both the asymmetric variance decomposition and the generalised asymmetric impulse response function show positive responses of agricultural output and capital expenditure to negative oil revenue shocks while only manufacturing output and recurrent expenditure respond negatively. We recommend that the government should not depend solely on oil exports as the major source of revenue but also create incentive in the non‐oil sectors for complementary revenue generation.

Bilateral Multiple Gamma Returns: Their Risks and Rewards

The bilateral gamma model for returns is naturally derived from the lognormal model. Maximizing entropy in a random time change delivers the symmetric variance gamma model. The asymmetric variance gamma follows on incorporating skewness. Differential speeds for the upward and downward motions lead to the bilateral gamma. A further generalizations results in the bilateral double gamma model when the speed parameter of the bilateral gamma model is itself taken to be gamma distributed on entropy maximization. A rich five to seven parameter specification of preferences renders possible the extraction of physical densities from option prices. The quality of such extraction is measured by examining the uniformity of the estimated distribution functions evaluated at realized forward returns.The economic value of risky returns is seen to embed three/five risk premia for the bilateral gamma/bilateral double gamma. For the bilateral gamma they are up and down side volatilities compensated in up and down side drifts, and the down side drift compensated in the up side drift. For the bilateral double gamma one adds in addition compensations for skewness. Results reveal a drop in the down side risk premium since the crisis with an increase in the recent period.

Asymmetric Variance Premium, Skewness Premium, and the Cross-Section of Stock Returns

We find a negative relationship between the individual stocks' semivariance premia, defined as the difference between the risk-neutral and physical expected downside semivariances, and future stock returns. The high-minus-low hedge portfolio earns the excess return of -64 (-46) basis points per month, the characteristic-adjusted return of -58 (-28) basis points per month, and the industry-adjusted return of -73 (-27) basis points per month in equal (value)-weighted returns. They are all economically substantial and statistically significant. Such a negative relationship can not be explained by risk-based asset pricing models. We find that the predictive power of semivariance premium is information-driven and reflects trading activity of informed investors who place large transactions on options.

Speed and Biases of Fourier-Based Pricing Choices: A Numerical Analysis

This paper compares the CPU effort and numerical biases of six Fourier-based implementations. Our analyses focus on two jump-related models that can consistently price options with different strikes and maturities: (i) the Bates jump-diffusion model, which combines jumps with stochastic volatility and (ii) the Asymmetric Variance Gamma (AVG) model, a pure-jump process where an infinite number of jumps can occur in any interval of time. We show that both truncation and discretization errors significantly increase as we move away from the diffusive Black-Scholes-Merton dynamics. While most pricing choices converge to the Bates reference values, Attari’s formula is the only Fourier-based method that does not completely blow up in any AVG problematic region. In terms of CPU speed, the strike vector computations proposed by Zhu (2010) significantly improve the computational burden, rendering the use of fast Fourier transforms and plain delta-probability decompositions inefficient.

On the interaction between government spending and economic performance in Sweden: an asymmetric approach

This article applies newly developed asymmetric impulse response functions and asymmetric variance decompositions to investigate the dynamic relationship between government spending and the GDP at constant prices in Sweden. The estimated results show that an innovation in the government spending does not lead to a significant response in the GDP regardless of whether or not the asymmetric property is taken into account in the estimation of the impulses. The asymmetric variance decompositions also provide support for this conclusion. This might support the view that the Ricardo equivalence theorem is valid in the case of Sweden.

A Simple Approach for Monitoring Business Service Time Variation

Control charts are effective tools for signal detection in both manufacturing processes and service processes. Much of the data in service industries comes from processes having nonnormal or unknown distributions. The commonly used Shewhart variable control charts, which depend heavily on the normality assumption, are not appropriately used here. In this paper, we propose a new asymmetric EWMA variance chart (EWMA-AV chart) and an asymmetric EWMA mean chart (EWMA-AM chart) based on two simple statistics to monitor process variance and mean shifts simultaneously. Further, we explore the sampling properties of the new monitoring statistics and calculate the average run lengths when using both the EWMA-AV chart and the EWMA-AM chart. The performance of the EWMA-AV and EWMA-AM charts and that of some existing variance and mean charts are compared. A numerical example involving nonnormal service times from the service system of a bank branch in Taiwan is used to illustrate the applications of the EWMA-AV and EWMA-AM charts and to compare them with the existing variance (or standard deviation) and mean charts. The proposed EWMA-AV chart and EWMA-AM charts show superior detection performance compared to the existing variance and mean charts. The EWMA-AV chart and EWMA-AM chart are thus recommended.

Experimental verification of dose calculation using the simplified Monte Carlo method with an improved initial beam model for a beam-wobbling system

A beam delivery system using a single-radius-beam-wobbling method has been used to form a conformal irradiation field for proton radiotherapy in Japan. A proton beam broadened by the beam-wobbling system provides a non-Gaussian distribution of projection angle different in two mutually orthogonal planes with a common beam central axis, at a certain position. However, the conventional initial beam model for dose calculations has been using an approximation of symmetric Gaussian angular distribution with the same variance in both planes (called here a Gaussian model with symmetric variance (GMSV)), instead of the accurate one. We have developed a more accurate initial beam model defined as a non-Gaussian model with asymmetric variance (NonGMAV), and applied it to dose calculations using the simplified Monte Carlo (SMC) method. The initial beam model takes into account the different distances of two beam-wobbling magnets from the iso-center and also the different amplitudes of kick angle given by each magnet. We have confirmed that the calculation using the SMC with NonGMAV reproduced the measured dose distribution formed in air by a mono-energetic proton beam passing through a square aperture collimator better than with the GMSV and with a Gaussian model with asymmetric variance (GMAV) in which different variances of angular distributions are used in the two mutually orthogonal planes. Measured dose distributions in a homogeneous phantom formed by a modulated proton beam passing through a range shifter and an L-shaped range compensator, were consistent with calculations using the SMC with GMAV and NonGMAV, but in disagreement with calculations using the SMC with GMSV. Measured lateral penumbrae in a lateral direction were reproduced better by calculations using the SMC with NonGMAV than by those with GMAV, when an aperture collimator with a smaller opening was used. We found that such a difference can be attributed to the non-Gaussian angular distribution of the initial beam at a lateral position for the beam-wobbling system. Calculations using the SMC with NonGMAV are effective to reproduce dose distributions formed by a beam-wobbling system more accurately than that with GMSV or that with GMAV.

Stock, Energy and Currency Effects on the Asymmetric Wheat Market

The purpose of this paper is to explore the effects of financial and currency indicators on wheat futures prices. The results suggest that the stock market, and particularly the S&P 500, positively influence the wheat market, a fact that is attributed to the wealth effect and the modern portfolio management in the context of international markets’ integration. There is also evidence that the energy markets affecting the supply and demand side exert significant impact on the wheat market. Furthermore, the results show that the shocks of the U.S. dollar/yen exchange rate are transmitted to the wheat market. Finally, the structural analysis of wheat prices’ volatility support the hypothesis of the asymmetric conditional variance, as it appears to be more volatile in response to positive shocks caused by higher wheat prices, contrary to the respective results of the equities market.

Accuracy of Molecular Dating with the Rho Statistic: Deviations from Coalescent Expectations Under a Range of Demographic Models

Abstract The ρ statistic is commonly used to infer chronological dates for molecular lineages, especially from mitochondrial DNA sequences obtained in anthropological contexts. Since this approach was described 12 years ago, it has been applied to estimate molecular dates in more than 200 studies, including some published in top-tier journals. However, this method has not been well evaluated, and the accuracy of dates obtained from the ρ statistic remains unknown, especially for genetic data collected from populations with complex demographic histories. Here, molecular dates inferred from ρ are compared against coalescent expectations from a range of demographic models. This exercise reveals considerable inaccuracy. Molecular dates based on ρ have a slight downward bias with large asymmetric variance and commonly exhibit substantial type I error rates, where the true age of a lineage falls outside the 95% confidence bounds derived from the variance of ρ. Furthermore, demography proves to be a strong confo...

Accuracy of Molecular Dating with the Rho Statistic: Deviations from Coalescent Expectations Under a Range of Demographic Models

The ρ statistic is commonly used to infer chronological dates for molecular lineages, especially from mitochondrial DNA sequences obtained in anthropological contexts. Since this approachwas described 12 years ago, it has been applied to estimate molecular dates in more than 200 studies, including some published in top-tier journals. However, this method has not been well evaluated, and the accuracy of dates obtained from the ρ statistic remains unknown, especially for genetic data collected from populations with complex demographic histories. Here, molecular dates inferred from ρ are compared against coalescent expectations from a range of demographic models. This exercise reveals considerable inaccuracy. Molecular dates based on ρ have a slight downward bias with large asymmetric variance and commonly exhibit substantial type I error rates, where the true age of a lineage falls outside the 95% confidence bounds derived from the variance of ρ. Furthermore, demography proves to be a strong confounding factor in estimating molecular dates accurately, especially for populations in which bottlenecks, founder events, and size changes have played important historical roles. Therefore considerable caution should be applied to inferences made from molecular dates based on the ρ statistic, many of which may be misleading and warrant considerable skepticism.

Multiple Regimes and Volatility Transmission in Securitized Real Estate Markets

We examine the dynamics and transmission of conditional volatilities with multiple structural changes in return volatility using Bai and Perron (2003)’s methodology, across five major securitized real estate markets as well as employing a multivariate regime-dependent asymmetric dynamic covariance methodology (MRDADC) that allows the conditional matrix to be both time- and state-varying. Our results imply that a multiple-regime time varying asymmetric variance and covariance approach is important in modeling real estate securities valuation and selection and portfolio optimization, and is consistent with popular beliefs that market volatility changes over time. Our MRDADC models detect the presence of significant mean-volatility linkages across the five major securitized real estate markets under different volatility regimes and would have implications for global investor in terms of estimating a dynamic risk-minimizing hedge ratio in international portfolio management.

On discrete stochastic processes with long-lasting time dependence in the variance

In this manuscript, we analytically and numerically study statistical properties of an heteroskedastic process based on the celebrated ARCH generator of random variables whose variance is defined by a memory of qm-exponencial, form (eqm=1 x=ex). Specifically, we inspect the self-correlation function of squared random variables as well as the kurtosis. In addition, by numerical procedures, we infer the stationary probability density function of both of the heteroskedastic random variables and the variance, the multiscaling properties, the first-passage times distribution, and the dependence degree. Finally, we introduce an asymmetric variance version of the model that enables us to reproduce the so-called leverage effect in financial markets.

Dynamic correlations and volatility effects in the Balkan equity markets

This paper investigates the presence of time-varying comovements, volatility implications and dynamic correlations in major Balkan and leading mature equity markets, in order to provide quantified responses to international asset allocation decisions. Since asset returns and correlation dynamics are critical inputs in asset pricing, portfolio management and risk hedging, emphasis is placed on the respective (constant and dynamic) equity market correlations produced by alternative multivariate GARCH forms, the Constant Conditional Correlation and the Asymmetric Dynamic Conditional Correlation models. The Balkan stock markets are seen to exhibit time-varying correlations as a peer group, although correlations with the mature markets remain relatively modest. In conjunction with sensitivity analysis on the asymmetric variance–covariance matrix, active portfolio diversification to the Balkan equity markets indicates to potentially improve investors’ risk-return trade-off.