Asymmetric Stochastic Volatility Research Articles

Test of Volatile Behaviors with the Asymmetric Stochastic Volatility Model: An Implementation on Nasdaq-100

The present study aimed to investigate the presence of asymmetric stochastic volatility and leverage effects within the Nasdaq-100 index. This index is widely regarded as an important indicator for investors. We focused on the nine leading stocks within the index, which are highly popular and hold significant weight in the investment world. These stocks are Netflix, PayPal, Google, Intel, Microsoft, Amazon, Tesla, Apple, and Meta. The study covered the period between 3 January 2017 and 30 January 2023, and we employed the EViews and WinBUGS applications to conduct the analysis. We began by calculating the logarithmic difference to obtain the return series. We then performed a sample test with 100,000 iterations, excluding the first 10,000 samples to eliminate the initial bias of the coefficients. This left us with 90,000 samples for analysis. Using the results of the asymmetric stochastic volatility model, we evaluated both the Nasdaq-100 index as a whole and the volatility persistence, predictability, and correlation levels of individual stocks. This allowed us to evaluate the ability of individual stocks to represent the characteristics of the Nasdaq-100 index. Our findings revealed a dense clustering of volatility, both for the Nasdaq-100 index and the nine individual stocks. We observed that this volatility is continuous but has a predictable impact on variability. Moreover, apart from Intel, all the stocks in the model exhibited both leverage effects and the presence of asymmetric relationships, as did the Nasdaq-100 index. Overall, our results show that the characteristics of stocks in the model are like the volatility characteristic of the Nasdaq-100 index and can represent it.

Iterative QML estimation for asymmetric stochastic volatility models

The paper illustrates a new procedure for estimating asymmetric stochastic volatility models. These models shape the asymmetric effect of negative and positive financial returns on the expected volatility, behaviour often observed in the stock prices, and known as “leverage effect”. The procedure is based on the iterative application of the quasi-maximum likelihood (QML) method and is proposed as an alternative to the procedure presented by Harvey and Shephard in 1996 and based on the application of the QML method on a modified auxiliary model. The estimation results generally converge to constant values after a few iterations. The volatility predictor provided by the new method is conceptually similar to the EGARCH predictor and different from the predictor of the other procedure. A simulation study shows that the iterative QML method provides parameter estimators with RMSEs decreasing as series length increases. The distribution of the estimates is approximately normal, and the approximation improves as the series size increases. Empirical applications of the method provide results similar to ones of the method known in literature. However, the two methods provide two different predictors and smoothers of volatility, which should be compared on a case-by-case basis.

Estimation of Realized Asymmetric Stochastic Volatility Models Using Kalman Filter

Despite the growing interest in realized stochastic volatility models, their estimation techniques, such as simulated maximum likelihood (SML), are computationally intensive. Based on the realized volatility equation, this study demonstrates that, in a finite sample, the quasi-maximum likelihood estimator based on the Kalman filter is competitive with the two-step SML estimator, which is less efficient than the SML estimator. Regarding empirical results for the S&P 500 index, the quasi-likelihood ratio tests favored the two-factor realized asymmetric stochastic volatility model with the standardized t distribution among alternative specifications, and an analysis on out-of-sample forecasts prefers the realized stochastic volatility models, rejecting the model without the realized volatility measure. Furthermore, the forecasts of alternative RSV models are statistically equivalent for the data covering the global financial crisis.

Modelling Asymmetric Dependence in Stochastic Volatility and Option Pricing: A Conditional Copula Approach

In this paper, stochastic volatility models with asymmetric dependence were presented and applied to pricing options. A dynamic conditional copula approach was proposed to capture this dependence asymmetry. This approach offered simplicity and flexibility, and yielded closed-form solutions for option pricing under different model constructions for the stochastic volatility based on a mean-reverting Gaussian, a square-root and a lognormal process. Empirical experimentation based on S&P 500 options showed that the developed dynamic option pricing models under asymmetric stochastic volatility significantly and consistently outperformed the basic Heston model across option maturities, strike prices and various copula function specifications. The square-root model combined with a Joe copula was the best ranked, having achieved 32.33% overall performance improvement. This superior empirical performance in option pricing, the unique flexibility to various dependence asymmetry considerations, and the analytical tractability added to the benefits of the proposed models framework.

Maximum Likelihood Inference for Asymmetric Stochastic Volatility Models

In this paper, we propose a new method for estimating and forecasting asymmetric stochastic volatility models. The proposal is based on dynamic linear models with Markov switching written as state space models. Then, the likelihood is calculated through Kalman filter outputs and the estimates are obtained by the maximum likelihood method. Monte Carlo experiments are performed to assess the quality of estimation. In addition, a backtesting exercise with the real-life time series illustrates that the proposed method is a quick and accurate alternative for forecasting value-at-risk.

Is Bitcoin really a currency? A viewpoint of a stochastic volatility model

ABSTRACT Using an asymmetric stochastic volatility model, this study investigates the day-of-the-week and holiday effects on the returns and volatility of Bitcoin from 1 January 2013 to 31 August 2019; in this context, we also discuss the characteristics of Bitcoin as a financial asset. The results of the estimation are threefold. First, the finding shows a small day-of-the week effect in volatility on Saturday and Sunday than in the rest of the week. Second, although the holiday effects are examined in active trading countries, namely Japan, China, Germany, and the United States, the positive post-holiday effect on the returns and weak positive pre-holiday effect on the volatility are only observed in the United States. Finally, the asymmetry effect is not observed. A comparison of Bitcoin to several assets such as stock, currency, and gold shows Bitcoin’s positioning between stock, currency, and gold in relation to the week and holiday effects, its reaction to federal funds and medium of exchange characteristics, and the lack of asymmetry effect.

Multivariate stochastic volatility for herding detection: Evidence from the energy sector

The paper proposes a multivariate asymmetric stochastic volatility approach, allowing for common factors that detect and measure herding behavior conditional on the stylized facts of asset returns and another factor that captures non-herding behavior. Applying our approach to the constituents of the S&P 500 energy sector in periods of high uncertainty, the findings reveal a wealth of information on herding detection related to asset returns' co-movements and volatility encountered by the energy sector. We also examine to what degree macroeconomic indicators' uncertainty influences the common factors on herding detection. We conclude that stylized facts of energy assets experience significant changes, arising from the increased systemic market risk and crude oil prices that are exposed to.

Improving the asymmetric stochastic volatility model with ex-post volatility: the identification of the asymmetry

Simulation studies show that the asymmetry stochastic volatility (ASV) models may infer erroneous correlation coefficients, due to their predetermined return-volatility specification. We propose identifying the correlation parameter by incorporating the ex-post volatility in the ASV framework. We obtain a significantly smaller magnitude in the estimated correlation coefficients between equity and volatility processes among major U.S. equity market indexes. Out-of-sample index return distribution forecasts demonstrate superior performance when jointly estimating the return and the ex-post volatility processes. The corrected return-volatility correlations by estimating proposed ASV models with subsample data further document the time-varying leverage effect.

Improving the Asymmetric Stochastic Volatility Model with Ex-Post Volatility: The Identification of the Return-Volatility Correlation

Simulation studies prove that the asymmetry stochastic volatility (ASV) models infer erroneous return-volatility correlation, due to the unobservability of the true volatility. We propose to incorporate the ex-post volatility in the ASV framework for the identification of the correlation coefficient. Comparing to the standard ASV model, we obtain a significantly smaller magnitude of the estimated return-volatility correlation on major U.S. equity market indexes. Out-of-sample return density forecasts demonstrate superior performance when jointly estimating the return and the ex-post volatility processes. The corrected returnvolatility correlations by estimating proposed ASV models with subsample data further document the time-varying leverage effect.

Multiscale Stochastic Volatility Model with Heavy Tails and Leverage Effects

This paper studies multiscale stochastic volatility models of financial asset returns. It specifies two components in the log-volatility process and allows for leverage/asymmetric effects from both components while return innovation terms follow a heavy/fat tailed Student t distribution. The two components are shown to be important in capturing persistent dependence in return volatility, which is often absent in applications of stochastic volatility models which incorporate leverage/asymmetric effects. The models are applied to asset returns from a foreign currency market and an equity market. The model fits are assessed, and the proposed models are shown to compare favorably to the one-component asymmetric stochastic volatility models with Gaussian and Student t distributed innovation terms.

Exploring Option Pricing and Hedging via Volatility Asymmetry

This paper evaluates the application of two well-known asymmetric stochastic volatility (ASV) models to option price forecasting and dynamic delta hedging. They are specified in discrete time in contrast to the classical stochastic volatility models used in option pricing. There is some related literature, but little is known about the empirical implications of volatility asymmetry on option pricing. The objectives of this paper are to estimate ASV option pricing models using a Bayesian approach unknown in this type of literature, and to investigate the effect of volatility asymmetry on option pricing for different size equity sectors and periods of volatility. Using the S&P MidCap 400 and S&P 500 European call option quotes, results show that volatility asymmetry benefits the accuracy of option price forecasting and hedging cost effectiveness in the large-cap equity sector. However, ASV models do not improve the option price forecasting and dynamic hedging in the mid-cap equity sector.

Data cloning estimation for asymmetric stochastic volatility models

The paper proposes the use of data cloning (DC) to the estimation of general univariate asymmetric stochastic volatility (ASV) models with flexible distributions for the standardized returns. These models are able to capture the asymmetric volatility, the leptokurtosis and the skewness of the distribution of returns. Data cloning is a general technique to compute maximum likelihood estimators, along with their asymptotic variances, by means of a Markov chain Monte Carlo (MCMC) methodology. The main aim of this paper is to illustrate how easily general univariate ASV models can be estimated and consequently studied via data cloning. Changes of specifications, priors and sampling error distributions are done with minor modifications of the code. Using an intensive simulation study, the finite sample properties of the estimators of the parameters are evaluated and compared to those of a benchmark estimator that is also user-friendly. The results show that the proposed estimator is computationally efficient, and can be an effective alternative to the existing estimation methods applied to ASV models. Finally, we use data cloning to estimate the parameters of general ASV models and forecast the one-step-ahead volatility of S&P 500 and FTSE-100 daily returns.

A Revisit to the Asymmetric Stochastic Volatility Models' Correlation Structures

The asymmetric stochastic volatility (ASV) models extend the stochastic volatility model (SV) by modeling the correlation between the asset return and its volatility. We prove by simulation studies that fitting the ASV models may infer erroneous estimations of the correlation coefficients. Even if the true return-volatility correlation structure is different from the ASV models' specifications, the ASV models constantly provide significant correlation coefficients far from zero. The misidentification of the correlation parameter can be a significant issue considering that in-conclusive empirical evidence regarding the asymmetry has been documented, and the ASV model can only represent the general asymmetry according to its return-volatility correlation specification. The incorporation of ex-post volatility helps the ASV model to identify the true return-volatility correlation. Empirical evidence on major U.S. equity market indexes verifies that ASV models with ex-post volatility obtain significantly different estimations of the correlation parameters compared to the benchmark ASV models. Moreover, the inclusion of the ex-post volatility also significantly improves the ASV models in return density forecasting. It is necessary to include the ex-post volatility when estimating the ASV model.

The Asymmetry of Shanghai Composite Index Volatility—Stochastic Volatility Models Based on GHST Distribution

In this paper, we analyzed how the asymmetric stochastic volatility models with GHST distribution capture the asymmetry of stock index volatility in China. Under the setting of fat-tail distribution, we introduced the correlation parameter ρ of two error terms to refine the classification of ASV model from two aspects of Contemporaneous correlation and Subsequent correlation. So we could compare the effect of ASV model in demonstrating the asymmetry of stock index volatility under the above different settings. Using the daily returns of Shanghai stock composite index, we concluded that the ASV model with GHST distribution and Subsequent correlation between error terms can better describe the asymmetry of the stock index in China. The DIC value and Kupiec test verified the adequacy and the effectiveness of risk measurement of the above model respectively.

Asymmetric stochastic volatility models: Properties and particle filter-based simulated maximum likelihood estimation

The statistical properties of a general family of asymmetric stochastic volatility (A-SV) models which capture the leverage effect in financial returns are derived providing analytical expressions of moments and autocorrelations of power-transformed absolute returns. The parameters of the A-SV model are estimated by a particle filter-based simulated maximum likelihood estimator and Monte Carlo simulations are carried out to validate it. It is shown empirically that standard SV models may significantly underestimate the value-at-risk of weekly S&P 500 returns at dates following negative returns and overestimate it after positive returns. By contrast, the general specification proposed provide reliable forecasts at all dates. Furthermore, based on daily S&P 500 returns, it is shown that the most adequate specification of the asymmetry can change over time.

Asymmetries in Volatility: An Empirical Study for the Peruvian Stock and Forex Markets

Asymmetric autoregressive conditional heteroskedasticity (EGARCH) models and asymmetric stochastic volatility (ASV) models are applied to daily data of Peruvian stock and Forex markets for the period of 5 January 1998–30 December 2011. Following the approach developed in [Omori, Y, S Chib, N Shephard and J Nakajima (2007). Stochastic volatility with leverage: Fast likelihood inference. Journal of Econometrics, 140, 425–449], Bayesian estimation tools are used with Normal and [Formula: see text]-Student errors in both models. The results suggest the significant presence of asymmetric effects in both markets. In the stock market, negative shocks generate higher volatility than positive shocks. In the Forex market, shocks related to episodes of depreciation create higher uncertainty in comparison with episodes of appreciation. Thus, the Central Reserve Bank faces relatively major difficulties in its intention of smoothing Forex volatility in times of depreciation. The model with the best fit in both markets is the ASV model with Normal errors. The stock market returns have greater periods of volatility; however, both markets react to shocks in the economy, as they display similar patterns and have a significant correlation for the sample period studied.

A new variant of estimation approach to asymmetric stochastic volatilitymodel

This paper proposes a novel simulation-based inference for an asymmetric stochastic volatility model. An acceptance-rejection Metropolis-Hastings algorithm is developed for the simulation of latent states of the model. A simple and e cient algorithm is also developed for estimation of a heavy-tailed stochastic volatility model. Simulation studies show that our proposed methods give rise to reasonable parameter estimates. Our proposed estimation methods are then used to analyze a benchmark data set of asset returns.

The semiparametric asymmetric stochastic volatility model with time-varying parameters: The case of US inflation

We propose a semiparametric extension of the time-varying parameter regression model with asymmetric stochastic volatility. For parameter estimation we use Bayesian methods. We illustrate our methods with an application to US inflation.

Comparison of asymmetric stochastic volatility models under different correlation structures

ABSTRACTThis paper conducts simulation-based comparison of several stochastic volatility models with leverage effects. Two new variants of asymmetric stochastic volatility models, which are subject to a logarithmic transformation on the squared asset returns, are proposed. The leverage effect is introduced into the model through correlation either between the innovations of the observation equation and the latent process, or between the logarithm of squared asset returns and the latent process. Suitable Markov Chain Monte Carlo algorithms are developed for parameter estimation and model comparison. Simulation results show that our proposed formulation of the leverage effect and the accompanying inference methods give rise to reasonable parameter estimates. Applications to two data sets uncover a negative correlation (which can be interpreted as a leverage effect) between the observed returns and volatilities, and a negative correlation between the logarithm of squared returns and volatilities.

Volatility and quantile forecasts by realized stochastic volatility models with generalized hyperbolic distribution

The predictive performance of the realized stochastic volatility model of Takahashi et al. (2009), which incorporates the asymmetric stochastic volatility model with the realized volatility, is investigated. Considering the well-known characteristics of financial returns, namely heavy tails and skewness, the model is extended by employing a wider class distribution, the generalized hyperbolic skew Student’s t-distribution, for financial returns. Using the Bayesian estimation scheme via a Markov chain Monte Carlo method, the model enables us to estimate the parameters in the return distribution and in the model jointly. It also makes it possible to forecast the volatility and return quantiles by sampling from their posterior distributions jointly. The model is applied to quantile forecasts of financial returns such as value-at-risk and expected shortfall, as well as to volatility forecasts, and the forecasts are evaluated using a range of tests and performance measures. The empirical results using the US and Japanese stock indices, the Dow Jones Industrial Average and Nikkei 225, show that the extended model improves the volatility and quantile forecasts, especially in some volatile periods.