Volatility Factors Research Articles

Volatility in GARCH Models of Business Tendency Index

This paper aims to obtain a model of business tendency index by considering volatility factor. Volatility factor detected by ARCH (Autoregressive Conditional Heteroscedasticity). The ARCH checking was performed using the Lagrange multiplier test. The modeling is Generalized Autoregressive Conditional Heteroscedasticity (GARCH) are able to overcome volatility problems by incorporating past residual elements and residual variants.

The Robustness of the Volatility Factor: Linear versus Nonlinear Factor Model

This article investigates the trade-off between an extension of the standard three-factor model including a new volatility factor compared to a parsimonious Markov switching model in the context of performance and risk analysis for a set of popular alternative beta strategies. The authors use Bayesian techniques to estimate a two-state (bull and bear) regime-switching model. Over the period of 1969–2014, they show that the inclusion of a time-varying feature in the standard model is as good as the extension of the volatility factor, at least in explaining the alphas for some alternative beta strategies.

A Solution to the Time-Scale Fractional Puzzle in the Implied Volatility

In the option pricing literature, it is well known that (i) the decrease in the smile amplitude is much slower than the standard stochastic volatility models and (ii) the term structure of the at-the-money volatility skew is approximated by a power-law function with the exponent close to zero. These stylized facts cannot be captured by standard models, and while (i) has been explained by using a fractional volatility model with Hurst index H > 1 / 2 , (ii) is proven to be satisfied by a rough volatility model with H < 1 / 2 under a risk-neutral measure. This paper provides a solution to this fractional puzzle in the implied volatility. Namely, we construct a two-factor fractional volatility model and develop an approximation formula for European option prices. It is shown through numerical examples that our model can resolve the fractional puzzle, when the correlations between the underlying asset process and the factors of rough volatility and persistence belong to a certain range. More specifically, depending on the three correlation values, the implied volatility surface is classified into four types: (1) the roughness exists, but the persistence does not; (2) the persistence exists, but the roughness does not; (3) both the roughness and the persistence exist; and (4) neither the roughness nor the persistence exist.

EMD-Based Study of the Volatility Mechanism in Economic Growth

In this paper, Empirical Mode Decomposition (EMD) is used for decomposing the quarterly data of year-on-year GDP growth rate from 2000 to 2016. Four intrinsic modes of different frequency scales and inclusive of economic growth volatility are obtained, together with one smooth residual term. Based on the validity information of the decomposed waveforms, the statistical method and the economic significance information are identified for exploring the inherent law of economic growth, before concluding that the economic growth volatility mechanism is comprised of the short-, medium- and long-term influential factors and a relatively stable basic element. Empirical analysis has found that the impacts of long-term volatility factors are dominant and tend to be determined by the business cycle.

Two asset-barrier option under stochastic volatility

ABSTRACTFinancial products which depend on hitting times for two underlying assets have become very popular in the last decade. Three common examples are double-digital barrier options, two-asset barrier spread options and double lookback options. Analytical expressions for the joint distribution of the endpoints and the maximum and/or minimum values of two assets are essential in order to obtain quasi-closed form solutions for the price of these derivatives. Earlier authors derived quasi-closed form pricing expressions in the context of constant volatility and correlation. More recently solutions were provided in the presence of a common stochastic volatility factor but with restricted correlations due to the use of a method of images. In this article, we generalize this finding by allowing any value for the correlation. In this context, we derive closed-form expressions for some two-asset barrier options.

MONETARY POLICY UNCERTAINTY AND ECONOMIC FLUCTUATIONS

AbstractWe investigate the relationship between uncertainty about monetary policy and its transmission mechanism, and economic fluctuations. We propose a new term structure model where the second moments of macroeconomic variables and yields can have a first‐order effect on their dynamics. The data favor a model with two unspanned volatility factors that capture uncertainty about monetary policy and the term premium. Uncertainty contributes negatively to economic activity. Two dimensions of uncertainty react in opposite directions to a shock to the real economy, and the response of inflation to uncertainty shocks varies across different historical episodes.

Asymptotics of Parisian ruin of Brownian motion risk model over an infinite-time horizon

Let be a standard Brownian motion. In this paper, we derive the asymptotics of the probability of Parisian ruin over an infinite time horizon for the following risk process (0.1) where is the initial reserve, is the force of interest, is the rate of premium and is a volatility factor. It turns out that the Parisian ruin probability decays exponentially as u tends to infinity and is a decreasing function of the force of interest for u large. Moreover, we obtain the approximations of Parisian ruin time.

Large-Scale Portfolio Allocation Under Transaction Costs and Model Uncertainty

We theoretically and empirically study large-scale portfolio allocation problems when transaction costs are taken into account in the optimization problem. We show that transaction costs act on the one hand as a turnover penalization and on the other hand as a regularization, which shrinks the covariance matrix. As an empirical framework, we propose a flexible econometric setting for portfolio optimization under transaction costs, which incorporates parameter uncertainty and combines predictive distributions of individual models using optimal prediction pooling. We consider predictive distributions resulting from highfrequency based covariance matrix estimates, daily stochastic volatility factor models and regularized rolling window covariance estimates, among others. Using data capturing several hundred Nasdaq stocks over more than 10 years, we illustrate that transaction cost regularization (even to small extent) is crucial in order to produce allocations with positive Sharpe ratios. We moreover show that performance differences between individual models decline when transaction costs are considered. Nevertheless, it turns out that adaptive mixtures based on high-frequency and low-frequency information yield the highest performance. Portfolio bootstrap reveals that naive 1=N-allocations and global minimum variance allocations (with and without short sales constraints) are significantly outperformed in terms of Sharpe ratios and utility gains.

Level and volatility factors in macroeconomic data

Macroeconomic models typically focus on innovations in the level of fundamentals as driver of business cycles because modeling of volatility can be demanding. This paper suggests a simple methodology that can separate the level from the volatility factors without directly estimating the volatility processes. This is made possible by exploiting features in the second order approximation of equilibrium models and using information in a large panel of data to estimate the factors. Augmenting the factors to a VAR shed light on the effects of the level and volatility shocks and their relative importance.

The idiosyncratic volatility puzzle and mergers and acquisitions activity

This paper examines whether the puzzling negative relationship between idiosyncratic volatility and next month performance is affected by the intensity of merger and acquisition (M&A) activity in the market. Our results show that the idiosyncratic volatility puzzle is stronger in periods of high M& A activity than in periods of low M&A activity. Further analysis shows that the negative relationship between idiosyncratic volatility and next month performance is the strongest in the high M&A activity sub-period spanning from 1982–1989. In contrast, M&A activity does not explain the negative relationship between the common factor in idiosyncratic volatility (CIV) and next month performance. M&A activity can in part explain the idiosyncratic volatility puzzle, but it does not subsume the negative relationship between CIV exposure and firm returns.

How Many Factors? Does Adding Momentum and Volatility Improve Performance

This paper considers whether adding two established anomalies, momentum and low volatility, will improve our understanding of asset pricing beyond the FF5 model. We do this by considering whether these factors provide economic, as opposed to statistical, significance within the asset pricing model. We measure economic significance in two ways, first, we consider whether the factor coefficient signs and values on the factors are economically meaningful, for example, do the coefficients distinguish between high and low risk portfolios. Second, we consider an out-of-sample trading rule based on expected returns derived from each asset pricing model. Our results suggest that the momentum and volatility factors provide no additional information over the FF5 model. Moreover, it is not clear that the FF5 model itself provides a noticeable improvement over the FF3 model. Of note, the momentum and low volatility factors exhibit limited statistical significance, have similar coefficients across high and low values of different anomalies and big and small firm portfolios. The trading performance of a seven-factor model, while reasonable itself, is worse than both the FF3 and FF5 models. Furthermore, based on the trading results, the FF5 model provides no noticeable contribution over the FF3 model, the latter of which could be regarded as preferred.

Option Valuation with Volatility Components, Fat Tails, and Nonmonotonic Pricing Kernels*

We nest multiple volatility components, fat tails and a U-shaped pricing kernel in a single option model and compare their contribution to describing returns and option data. All three features lead to statistically significant model improvements. A second volatility factor is economically most important and improves option fit by 18% on average. A U-shaped pricing kernel improves the option fit by 17% on average, and more so for two-factor models. Fat tails improve option fit by just over 3% on average, and more so when a U-shaped pricing kernel is applied. Our results suggest that the three features we investigate are complements rather than substitutes.

Latent Common Return Volatility Factors: Capturing Elusive Predictive Accuracy Gains When Forecasting Volatility

In this paper, we use factor-augmented HAR-type models to predict the daily integrated volatility of asset returns. Our approach is based on a proposed two-step dimension reduction procedure designed to extract latent common volatility factors from a large dimensional and high-frequency returns dataset with 267 constituents of the S&P 500 index. In the first step, we apply either LASSO or elastic net shrinkage on estimates of integrated volatility of all constituents in the dataset, in order to select a subset of asset return series for further processing. In the second step, we utilize (sparse) principal component analysis to estimate latent common asset return factors, from which latent integrated volatility factors are extracted. Although we find limited in-sample fit improvement, relative to a benchmark HAR model, all of our proposed factor-augmented models result in substantial out-of-sample predictive accuracy improvement. In particular, forecasting gains are observed at market, sector, and individual-stock levels, with the exception of the financial sector. Further investigation of the factor structures for non-financial assets shows that industrial and technology stocks are characterized by minimal exposure to financial assets, inasmuch as forecasting gains associated with factor-augmented models for these types of assets are largely attributable to the inclusion of non-financial stock price return volatility in our latent factors.

Factor Analysis for Volatility

Factor models have become ubiquitous in finance for performing high dimensional analysis of returns and volatilities. Historical literature on the subject decomposes volatility into a factor component (systemic risk) and a remainder (idiosyncratic risk). However, recent work has suggested that a market shock to volatility may increase both systemic risk and idiosyncratic risk — specifically, that idiosyncratic volatility of US equities data has a factor structure, with the factor highly correlated with, and possibly precisely the market volatility. In this paper we attempt to characterize the underlying factor and find that it can be decomposed into a statistical (PCA) and structural (market volatility) factor. We also show that this feature is more common than expected, appearing in diverse sets of financial data. Lastly, we find that this dual- factor approach is slightly dominated in forecasting environments by a single statistical factor. Acknowledgments: For research support we thank the National Science Foundation. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

Effects of platform quality requirement on sellers

PurposeThe purpose of this paper is to study the effects of the requirement on product quality and refund (return service charge).Design/methodology/approachThe authors set a minimum product quality level for platform to study the effects of the minimum product quality level on product quality and refund for risk-neutral sellers and risk-averse sellers, respectively.FindingsFor the risk-neutral sellers whose optimal product quality level is lower than the minimum level will improve the product quality to the minimum required level. However, under a certain condition with the requirement the sellers will increase refund. Similar results are found when uncertainty is incorporated into demand and return quantity. In addition, how the sellers’ optimal refund is affected by market parameters and market volatile factors is discussed. Specially, the correlation between the uncertainty of the demand and the return quantity affects sellers’ optimal decision of return service charge in many ways.Originality/valueThe obtained results can provide operational managers in reality with valuable suggestions in quality management for platform.

Ancient village fire escape path planning based on improved ant colony algorithm

The roadways are narrow and perplexing in ancient villages, it brings challenges and difficulties for people to choose route to escape when a fire occurs. In this paper, a fire escape path planning method based on ant colony algorithm is presented according to the problem. The factors in the fire environment which influence the escape speed is introduced to improve the heuristic function of the algorithm, optimal transfer strategy, and adjustment pheromone volatile factor to improve pheromone update strategy adaptively, improve its dynamic search ability and search speed. Through simulation, the dynamic adjustment of the optimal escape path is obtained, and the method is proved to be feasible.

A New Look at the Efficiency & Volatility of Indian Agricultural Commodity Futures Markets

Indian agricultural commodity futures market is in the nascent stage. Since lifting of ban on futures trading in the beginning of this millennium, it is still facing serious threat from learned and the lay. Like any other futures market, Indian agricultural commodity futures markets are also expected to perform the role of price discovery and risk management. After having outlined the present status of Indian agricultural commodities market, a comprehensive study on the interrelationship between the spot and futures prices of 15 agricultural commodities is carried out to understand the dynamics of the co-integration, price causality and volatility factors which determine the efficiency of those markets for the period which stand different by various economical and market conditions, for arriving at relative conclusions. The Johansen’s co-integration test on the spot and futures data of the 15 agricultural commodities has shown that the spot and futures market were co-integrated). This proved that the market was efficient and the agriculture commodity futures exchanges provided efficient hedge against price risk emerging in respective commodities. The co-integration between spot price and future spot prices is the indication of efficiency and developed nature of the market. The Granger Causality Test results on the direction of flow of information between the spot and futures market shows that in majority (9 out of 15) of the commodities there were bi-directional flow of information. This shows that due to information flow from both sides, spot to future markets and future market to spot market, both were equally responsible for the price discovery process. The unidirectional causal relationship exhibited in six (6) commodities showed that futures market is leading the spot market. Whereas in terms of volatility, the GARCH test results show that there is volatility clustering and persistence throughout the study period. Even the Granger causality test on volatility revealed that the causation of volatility was bi-directional in 10 commodities. To be specific, we show that Indian agricultural commodities markets are highly efficient during the study period, including the period of price spikes and price distortions. The results of this study, stated above, shows that Indian agricultural commodity futures trading is highly efficient and playing the role it is supposed to play pretty good. The conclusions would certainly serve the concerned policy makers in decision making. Let us expect that the scenario of suspension and ban on futures trading in agricultural commodities is not repeated again, in the interest of Indian farmers. In-spite-of the above positive indications of the efficiency of Indian agriculture commodity market, it has witnessed massive and prolonged price escalations since 2007. The price spikes may be attributed to other fundamental factors not related to the scope of a futures exchange and call for further research.

The Relative Efficiency and Volatility of Indian Agricultural Commodity Futures Markets

Indian agricultural commodity futures market is in the nascent stage. Since lifting of ban on futures trading in the beginning of this millennium, it is still facing serious threat from learned and the lay. Like any other futures market, Indian agricultural commodity futures markets are also expected to perform the role of price discovery and risk management. After having outlined the present status of Indian agricultural commodities market, a comprehensive study on the interrelationship between the spot and futures prices of 15 agricultural commodities is carried out to understand the dynamics of the co-integration, price causality and volatility factors which determine the efficiency of those markets for the period which stand different by various economical and market conditions, for arriving at relative conclusions. The Johansen’s co-integration test on the spot and futures data of the 15 agricultural commodities has shown that the spot and futures market were co-integrated). This proved that the market was efficient and the agriculture commodity futures exchanges provided efficient hedge against price risk emerging in respective commodities. The co-integration between spot price and future spot prices is the indication of efficiency and developed nature of the market. The Granger Causality Test results on the direction of flow of information between the spot and futures market shows that in majority (9 out of 15) of the commodities there were bi-directional flow of information. This shows that due to information flow from both sides, spot to future markets and future market to spot market, both were equally responsible for the price discovery process. The unidirectional causal relationship exhibited in six (6) commodities showed that futures market is leading the spot market. Whereas in terms of volatility, the GARCH test results show that there is volatility clustering and persistence throughout the study period. Even the Granger causality test on volatility revealed that the causation of volatility was bi-directional in 10 commodities. To be specific, we show that Indian agricultural commodities markets are highly efficient during the study period, including the period of price spikes and price distortions. The results of this study, stated above, shows that Indian agricultural commodity futures trading is highly efficient and playing the role it is supposed to play pretty good. The conclusions would certainly serve the concerned policy makers in decision making. Let us expect that the scenario of suspension and ban on futures trading in agricultural commodities is not repeated again, in the interest of Indian farmers. In-spite-of the above positive indications of the efficiency of Indian agriculture commodity market, it has witnessed massive and prolonged price escalations since 2007. The price spikes may be attributed to other fundamental factors not related to the scope of a futures exchange and call for further research.

Volatility Spillovers between Spot and Futures Markets: An Empirical Study on U.S. Agricultural Commodities

In well-established and matured agricultural commodity futures market, like U.S., the futures markets are expected to serve as a central exchange for both domestic and international information and thus function as a primary mechanism for price discovery and reduce price variability through hedging activities. After having outlined the present status of U.S. agricultural commodities market, a comprehensive study on the volatility spillover between the spot and futures markets of 12 agricultural commodities is carried out to understand the dynamics of volatility factors which hinder the efficiency of those markets, by comparing two different time periods which stand different by various economical and market conditions, for arriving at relative conclusions. The Granger Causality Test results on the direction of flow of volatility between the spot and futures market shows that in majority of the commodities (6 commodities during 1995-2005 & 7 commodities during 2006-2011) there were unidirectional flow of from futures to spot markets, meaning that futures markets has significantly contributed to the volatility of spot market. There were bidirectional relationship in 5 commodities in 1995-2005 & 3 commodities in 2006-2011. This shows that due to information flow from both sides, spot to future markets and future market to spot market, both were equally responsible for causing volatility. Overall there is no evidence of abnormal volatility in the sub-period 2006-2011, compared to1995-2005. Abnormality of non-directional flow is identified in CBOT wheat during 2005-2011 which means that factors beyond futures market were responsible. Whereas, from the GARCH (1, 1) results, in terms of volatility, there is volatility clustering and persistence throughout the study period, with no abnormality during post 2006 period alone. To be specific, we show that volatility in U.S. agricultural commodities markets were prevalent during 1995-2005 and during 2006-2011, which experienced price spikes and price distortions. Hence, we conclude that huge in-flow of funds into the agricultural commodity futures market since 2006 is not the reason for volatility in US agricultural commodity market.

Factor Exposures of Foreign Equity Capital in a Domestic Stock Market: Evidence from Korea

AbstractIn this paper, we examine the factor exposures of foreign equity capital in a domestic stock market in order to understand its risk‐taking behavior and sources of returns in the market. Using data from Korea for the 1999–2013 period, we find that foreigners are strongly exposed to the idiosyncratic volatility (IVOL) factor, which is long on low‐IVOL stocks and short on high‐IVOL stocks. That is, foreign equity capital is typically allocated to low‐IVOL stocks and profits from the return differential between low‐IVOL and high‐IVOL stocks. We also find that foreign equity capital moves in a way that it is loaded more on the IVOL factor when the IVOL factor premium is larger. We discuss the comparative advantage of foreign equity capital in bearing the IVOL factor risk and the role of information asymmetry between locals and foreigners in this risk sharing. We also provide additional empirical results that support our interpretation.