Volatility Estimation Research Articles

Volatility spillover and dynamic correlation between Islamic, conventional, cryptocurrency and precious metal markets during the immediate outbreak of COVID-19 pandemic

PurposeThis paper aims to investigate the immediate effect of the outbreak of the COVID-19 pandemic by investigating volatility transmission and dynamic correlation between stock (conventional and Islamic) markets, bitcoin and major commodities such as gold, oil and silver at different investment horizons before and after 161 trading days of the outbreak of the COVID-19 pandemic.Design/methodology/approachThe MGARCH-DCC and maximum overlap discrete wavelet transform -based cross-correlation were used in the estimation of the volatility spillover and continuous wavelet transform in the estimation of the time-varying volatility and correlation between the assets at different investment horizons.FindingsThe authors observed a sudden correlation breakdown following the COVID-19 shock. Oil (Bitcoin) was a major volatility transmitter before (during) COVID-19. Digital gold (Bitcoin), gold and silver became highly correlated during COVID-19. The highest co-movement between the assets was observed at medium and long-term investment horizons.Practical implicationsThe study findings have a financial implication for day traders, investors and policymakers in the understanding of volatility transmission and intercorrelation in a bid to actively manage stylized and well-diversified asset portfolios.Originality/valueThis study is unique for its employment in estimating the time-varying conditional volatility of the investable assets and cross-correlations between them at different investment horizons, particularly before and after COVID-19 outbreak.

The Fourier–Malliavin Volatility (FMVol) MATLAB® library

This paper presents the Fourier–Malliavin Volatility (FMVol) estimation library for MATLAB®. This library includes functions that implement Fourier–Malliavin estimators (see Malliavin and Mancino (2002, 2009)) of the volatility and co-volatility of continuous stochastic volatility processes and second-order quantities, like the quarticity (the squared volatility), the volatility of volatility and the leverage (the covariance between changes in the process and changes in its volatility). The Fourier–Malliavin method is fully non-parametric, does not require equally-spaced observations and is robust to measurement errors, or noise, without any preliminary bias correction or pre-treatment of the observations. Furthermore, in its multivariate version, it is intrinsically robust to irregular and asynchronous sampling. Although originally introduced for a specific application in financial econometrics, namely the estimation of asset volatilities, the Fourier–Malliavin method is a general method that can be applied whenever one is interested in reconstructing the latent volatility and second-order quantities of a continuous stochastic volatility process from discrete observations.

Volatility or higher moments: Which is more important in return density forecasts of stochastic volatility model?

Extensions of the stochastic volatility (SV) model focus on improving volatility inference or modeling higher moments of the return distribution. This study investigates which extension can better improve return density forecasts. By examining various specifications with S&P 500 daily returns for nearly 20 years, we find that a more accurate capture of volatility dynamics with realized volatility and implied volatility is more important than modeling higher moments for a conventional SV model in terms of both density and tail forecasts. The accuracy of volatility estimation and forecasts should be the precondition for higher moment extensions.

PERBANDINGAN ESTIMASI VOLATILITAS HARGA OPSI BELI SAHAM APPLE INC. (AAPL) DENGAN METODE BISECTION DAN SECANT

Stock price volatility is a measure of how far a stock price moves in a given Stock price volatility is a measure of how far a stock price moves in a given time. The theory developed by Black-Scholes states that every option price with the same 'underlying asset' and the same time to maturity but with different exercise values will have the same Implied Volatility value. However, this is not always the case in the market. Therefore, it is necessary to estimate volatility known as Implied Volatility, which is considered an appropriate method in estimating volatility values. This study compares the Bisection and Secant methods to estimate the volatility of Apple Inc. (Aapl) stock. This study uses data on the closing price of the stock in the period September 29, 2022 to September 29, 2023. Volatility estimation for the Bisection and Secant methods by determining the initial approximation and limiting it to a maximum of 100 simulations and iteration stops if it has produced a relative error smaller than = . The is an error tolerance limit, the smaller the error tolerance, the more accurate it is. According to the research results, the Bisection method produces an estimated volatility value of 0.498212 at the 9th iteration, while the Secant method produces an estimated value of 0.498590 at the 10th iteration. The Secant method produces a smaller relative error value of 0.000096, indicating that the Secant method is more accurate than the Bisection method.

Reading the Candlesticks: An OK Estimator for Volatility

Abstract We propose an Optimal candlesticK (OK) estimator for the spot volatility using high-frequency candlestick observations. Under a standard infill asymptotic setting, we show that the OK estimator is asymptotically unbiased and has minimal asymptotic variance within a class of linear estimators. Its estimation error can be coupled by a Brownian functional, which permits valid inference. Our theoretical and numerical results suggest that the proposed candlestick-based estimator is much more accurate than the conventional spot volatility estimator based on high-frequency returns. An empirical illustration documents the intraday volatility dynamics of various assets during the Fed chairman’s recent congressional testimony.

Advanced Statistical Analysis of the Predicted Volatility Levels in Crypto Markets

Our paper deals with an advanced statistical tool for the volatility prediction problem in financial (crypto) markets. First, we consider the conventional GARCH-based volatility models. Next, we extend the corresponding GARCH-based forecasting and calculate a specific probability associated with the predicted volatility levels. As the probability evaluation is based on a stochastic model, we develop an advanced data-driven estimation of this probability. The novel statistical estimation we propose uses real market data. The obtained analytical results for the statistical probability of the levels are also discussed in the framework of the integrated volatility concept. The possible application of the established probability estimation approach to the volatility clustering problem is also mentioned. Our paper includes a concrete implementation of the proposed volatility prediction tool and considers a novel trading and volatility estimation module for crypto markets recently developed by the 1ex Trading Board group in collaboration with GoldenGate Venture. We also briefly discuss the possible application of a model combined with the data-driven volatility prediction methodology to financial risk management.

An empirical analysis of the volume-volatility nexus in crude oil markets under structural breaks: Implications for forecasting

The present study investigates how volume impacts volatility in crude oil markets, focusing on the Mixture of Distribution Hypothesis (MDH). Our results reveal a positive and significant volatility-volume association in the case of WTI spot markets. However, we cannot draw similar conclusions for Brent crude oil. Furthermore, we find that the presence of volume leads to only a negligible drop in the volatility persistence, thereby rejecting the claims of the MDH. By incorporating volume as a predictor for volatility and modelling the innovations using heavy-tailed distributions, our estimates of volatility for both Brent and WTI crude oil improve significantly. Our findings reveal that volume contains important information that can impact volatility and prices for crude oil. This has significant implications for market participants, institutional investors, as well as regulators as they can design better strategies and policies based on the volume of trade. Also, from the perspective of risk management and hedging, the results provide interesting insights. Our findings are consistent across different time periods, forecasting horizons and robust to alternative methodologies.

Identifying jumps in high-frequency time series by wavelets

We discuss a volatility functional model and show that jumps asymptotically impact the volatility estimate. This result is useful because our model shows that significant variations affect the estimation of the volatility and historically price series have structures with this type of behavior. We also discuss a method for detecting and locating jumps at different levels and show that the jumps tend to be detected by wavelet coefficients at lower resolution levels accurately. By checking the wavelet coefficients on the different levels, we can find dyadic intervals in some levels, whose corresponding absolute value of the wavelet coefficient exceeds a threshold, and is significantly higher than the others. We applied the procedure in a simulation study and to a series of Google stocks.

Enhancing stock volatility prediction with the AO-GARCH-MIDAS model.

Research has substantiated that the presence of outliers in data usually introduces additional errors and biases, which typically leads to a degradation in the precision of volatility forecasts. However, correcting outliers can mitigate these adverse effects. This study corrects the additive outliers through a weighting method and let these corrected values to replace the original outliers. Then, the model parameters are re-estimated based on this new return series. This approach reduces the extent to which outliers distort volatility estimates, allowing the model to better adapt to market conditions and improving the accuracy of volatility forecasts. This study introduces this approach for the first time to generalized autoregressive conditional heteroskedasticity mixed data sampling (GARCH-MIDAS) models, so as to establish an additional outliers corrected GARCH-MIDAS model (AO-GARCH-MIDAS). This pioneering approach marks a unique innovation. The research employs a diverse array of evaluation methods to validate the model's robustness and consistently demonstrates its dependable performance. Findings unequivocally reveal the substantial influence of outliers on the model's predictive capacity, with the AO-GARCH-MIDAS model exhibiting consistent superiority across all evaluation criteria. Additionally, while the GARCH model showcases stronger estimation capabilities compared to the GARCH-MIDAS model, the latter demonstrates heightened predictive prowess. Notably, regarding variable selection, the results underscore the greater predictive informational value inherent in realized volatility over other low-frequency factors.

Observation-constrained kinetic modeling of isoprene SOA formation in the atmosphere

Abstract. Isoprene has the largest global non-methane hydrocarbon emission, and the oxidation of isoprene plays a crucial role in the formation of secondary organic aerosol (SOA). Two primary processes are known to contribute to SOA formation from isoprene oxidation: (1) the reactive uptake of isoprene-derived epoxides on acidic or aqueous particle surfaces and (2) the absorptive gas–particle partitioning of low-volatility oxidation products. In this study, we developed a new multiphase condensed isoprene oxidation mechanism that includes these processes with key molecular intermediates and products. The new mechanism was applied to simulate isoprene gas-phase oxidation products and SOA formation from previously published chamber experiments under a variety of conditions and atmospheric observations during the Southern Oxidant and Aerosol Studies (SOAS) field campaign. Our results show that SOA formation from most of the chamber experiments is reasonably reproduced using our mechanism, except when the concentration ratios of initial nitric oxide to isoprene exceed ∼ 2, the formed SOA is significantly underpredicted. The SOAS simulations also reasonably agree with the measurements regarding the diurnal pattern and concentrations of different product categories, while the total isoprene SOA remains underestimated. The molecular compositions of the modeled SOA indicate that multifunctional low-volatility products contribute to isoprene SOA more significantly than previously thought, with a median mass contribution of ∼ 57 % to the total modeled isoprene SOA. However, this contribution is intricately intertwined with IEPOX-derived SOA (IEPOX: isoprene-derived epoxydiols), posing challenges for their differentiation using bulk aerosol composition analysis (e.g., the aerosol mass spectrometer with positive matrix factorization). Furthermore, the SOA from these pathways may vary greatly, mainly dependent on the volatility estimation and treatment of particle-phase processes (i.e., photolysis and hydrolysis). Our findings emphasize that the various pathways to produce these low-volatility species should be considered in models to more accurately predict isoprene SOA formation. The new condensed isoprene chemical mechanism can be further incorporated into regional-scale air quality models, such as the Community Multiscale Air Quality Modelling System (CMAQ), to assess isoprene SOA formation on a larger scale.

Entropy as a Measure of Risk or a Source of Information to Mitigate Risk: A Comparison Across Various Financial Assets

Since the application of entropy in financial economics has been growing extensively as a measure of volatility, in portfolio selection and to detect anomalies in markets. It’s really complicated to establish that increase in entropy is a source of the useful information for the financial markets that tantamount to mitigate risk, or it is in fact an indicator of disorder reflecting the growing risk scenario in the financial market. To explore the more effective application of entropy in the field of financial economics, this study evaluates entropy in both contexts, as a source of information to mitigate risk and as an indicator of disorder reflecting volatility. Twelve years daily data of 29 financial assets have been used to measure the intrinsic entropy in addition to other eight volatility estimators and three GARCH models-based volatilities. Various assessment techniques are used to test the role of entropy in both contexts including, Run Test, Mean, Variance and Coefficients of Variation, Mean Squared Errors, Proportional Bias and Efficiency Estimator, in addition to spearman rank-order correlation. Results emphasis that entropy is more suitable as a volatility measure rather a source of information in the financial market.

The non-linear impact of monetary policy on shifts in economic policy uncertainty: evidence from the United States of America

A stochastic volatility estimation of VIX index’s latent volatility is used for the United States of America, as a proxy for the adjustments in the levels of investors’ uncertainty related to current and future economic policies. The impact of monetary policy stance on such measure is examined in the framework of the distributed lag non-linear models (DLNM). We place this analysis in the literature stream emphasizing the various sources of heterogeneity concerning investors’ expectations. The main finding is that the monetary policy does impact non-linearly the adjustments in investors’ predictions. While a tighter monetary policy does generally contribute to an increase in VIX’s latent volatility, the shape of such effect varies across different GLM and GAM specifications of DLNM. This outcome remains robust, even if: (1) we control for the global price of Brent crude and consumers’ confidence; (2) we use, instead of the stochastic framework, a Markov-switching GARCH-based estimator; or (3) we replace the monetary policy instrument with monetary policy uncertainty. We argue that accounting for its nonlinear effects on financial markets is of critical importance for the design of a monetary policy pursuing global financial stability.

EXCHANGE RATE VOLATILITY OF UKRAINE’S MAIN TRADING PARTNERS

Ukraine, as an open economy under conditions of Russian aggression, is highly vulnerable to the import of exogenous shocks. This is embodied in exchange rate volatility and the emergence of corresponding risks. Most studies are aimed at direct, explicit, or transactional risks. They reflect the negative impact of exchange rate fluctuations on economic entities' cash flows in foreign economic activities. However, changes in currency prices can also affect the subjects oriented to the local market and not carry out operations in foreign currencies by changing competitiveness. One speaks about the indirect, implicit, or economic currency risk in this case. The latter generally arises in the event of volatility in the exchange rates of currencies of importing countries or competitors. The study is devoted to the analysis of indirect currency risks, which reflect potential adaptations of competitiveness due to changes in exchange rates. For this purpose, the currencies of the countries that account for about 80% of Ukraine's trade turnover over the last 10 years, namely the euro, Japanese yen, British pound, Swiss franc, yuan, Indian rupee, Czech krona, Polish zloty, Hungarian forint, and Turkish lira were chosen. The article aims to assess the volatility of exchange rates of Ukraine's main trading partners as a stage of analyzing economic currency risks. The paper uses statistical methods for volatility estimation and distribution characteristics, namely standard deviation, skewness, and kurtosis. The obtained results show that some currencies have a high level of asymmetry and excess, indicating possible unpredictable rate changes. The calculated indicators' generalization allows identifying currencies with relatively high and low risk. The article complements the results of previous studies, as it covers both major reserve currencies and currencies of leading countries whose markets are developing globally and in Europe. Estimates of asymmetry and excess exchange rate distributions are essential for effective currency risk management.

The volatility of capital flows in emerging markets: Measures and determinants

Capital flow volatility is a concern for macroeconomic and financial stability. Nonetheless, literature is scarce in this topic. Our paper sheds light on this issue along two dimensions. First, using quarterly data for 33 emerging markets and developing economies, we introduce new estimates of volatility for total multilateral gross capital in- and outflows and key categories, based on the residuals of ARIMA models. We find that a combination of our proposed approach and the commonly used standard deviation best identifies sharp rises during episodes of heightened global risk aversion, thus underscoring the need for a multi-faceted approach to gauge capital flow volatility. Second, we perform panel regressions to understand the determinants of volatility using both ARIMA and standard deviation measures of volatility. While there are variations across different categories of capital flows, generally speaking we identify three main drivers: the US interest rates, global risk aversion, and domestic real GDP. Overall, our findings call for a richer set of volatility estimates, beyond standard deviation, and also show that the determinants of capital flow volatility could vary depending on the measurement approach and the category of flow under analysis.

Simmering tensions on the Russia–Ukraine border and natural gas futures prices: identifying the impact using new hybrid GARCH

Focusing on the Russia–Ukraine war, this paper investigates natural gas futures volatilities. Applying several hybrid GARCH and EGARCH models, which innovatively incorporate both fat-tailed distribution errors and structural breaks, we derive the following new evidence. First, our hybrid modeling approach is effective in timely capturing the natural gas futures volatility spike when tensions simmered on the Russia–Ukraine border. Second, the hybrid modeling approach is effective for not only GARCH modeling but also EGARCH modeling. Third, the volatility estimates from our hybrid models have predictive power for the volatilities of nonhybrid models. Fourth, the volatility estimates from the nonhybrid models lag behind the volatilities of our hybrid models.

Volatility estimation of hidden Markov processes and adaptive filtration

The partially observed linear Gaussian system of stochastic differential equations with low noise in observations is considered. The coefficients of this system are supposed to depend on some unknown parameter. The problem of estimation of these parameters is considered and the possibility of the approximation of the filtering equations is discussed. An estimators are used for estimation of the quadratic variation of the derivative of the limit of the observed process. Then this estimator is used for nonparametric estimation of the integral of the square of volatility of unobservable component. This estimator is also used for construction of method of moments estimators in the case where the drift in observable component and the volatility of the state component depend on some unknown parameter. Then this method of moments estimator and Fisher-score device allow us to introduce the One-step MLE-process and adaptive Kalman–Bucy filter. The asymptotic efficiency of the proposed filter is discussed.

Modelling Inflation Dynamics and Global Oil Price Shocks in OAPEC Countries: TVP-VAR

This paper aims to examine the dynamic pass-through effect of oil price shocks on inflation in OAPEC countries using quarterly data ranging from 1990:Q1 to 2022:Q4. The incorporation of the TVP-VAR model along with the Markov Chain Monte Carlo method with stochastic volatility estimation offers a robust framework for capturing the time-varying nature of the relationship. Additionally, the analysis of the Impulse Response Function provides valuable insights into the short-term and long-term dynamics following oil price shocks. The results demonstrate a significant positive pass-through effect of oil prices on inflation in the sample member states, with heterogeneous magnitude and persistence. These variations are attributed to diversity in oil dependency, exchange rate regimes, monetary policy frameworks and the degree of openness to global markets. The study suggests the need for effective inflation management strategies and appropriate policy responses to oil price fluctuations. Furthermore, policymakers may consider adjusting exchange rates, interest rates, or trade policies to manage inflationary pressures effectively.

An Age–Period–Cohort Framework for Profit and Profit Volatility Modeling

The greatest source of failure in portfolio analytics is not individual models that perform poorly, but rather an inability to integrate models quantitatively across management functions. The separable components of age–period–cohort models provide a framework for integrated credit risk modeling across an organization. Using a panel data structure, credit risk scores can be integrated with an APC framework using either logistic regression or machine learning. Such APC scores for default, payoff, and other key rates fit naturally into forward-looking cash flow estimates. Given an economic scenario, every applicant at the time of origination can be assigned profit and profit volatility estimates so that underwriting can truly be account-level. This process optimizes the most fallible part of underwriting, which is setting cutoff scores and assigning loan pricing and terms. This article provides a summary of applications of APC models across portfolio management roles, with a description of how to create the models to be directly integrated. As a consequence, cash flow calculations are available for each account, and cutoff scores can be set directly from portfolio financial targets.

Oil price volatility prediction using out-of-sample analysis – Prediction efficiency of individual models, combination methods, and machine learning based shrinkage methods

In this study, we compare the efficacy of forecast combination methods against machine learning-based shrinkage techniques in predicting oil price volatility. Our analysis is based on heterogeneous autoregressive (HAR) model framework. We employ eight individual HAR models and their variations, alongside five distinct combination methods for aggregating forecasts derived from HAR models and their variants. Additionally, we incorporate two widely recognized machine learning-based shrinkage methods, namely the elastic net and the lasso. Machine learning (ML) techniques, including elastic net and lasso, exhibit promise in estimating individual extended HAR models and combination sampled approaches. Meanwhile, model confidence set (MCS) estimation techniques demonstrate notably superior out-of-sample forecasting performance for the chosen sample. Our empirical findings reveal that both the elastic net and the lasso exhibit superior out-of-sample prediction accuracy in comparison to the individual HAR models and their variants, as well as the five combination techniques. Furthermore, we provide statistical evidence demonstrating the notably higher directional accuracy achieved by the elastic net and lasso methodologies. Importantly, our results remain statistically consistent across a range of robustness analyses. These findings hold significance for investors and policymakers, as they suggest potential economic benefits derived from allocating portfolios in alignment with oil price volatility estimates.

Macroeconomic news, senior officials' speeches, and emerging currency markets: An intraday analysis of price jump reaction

We examine intraday emerging currency jumps in response to domestic and foreign macroeconomic news announcements, as well as US senior officials' speeches. We use the robust-to-jump volatility estimator to estimate currency jumps. We provide evidence that both emerging currency jumps and cojumps exhibit significant and pronounced responses to US monetary policy and real activity news releases. Moreover, we find that domestic monetary policy and economic real activity data, and senior Federal Reserve officials' speeches, trigger significant jumps in emerging currencies, leading to large currency fluctuations that would disrupt market stability, undermining economic resilience and potentially diminishing ESG ratings.