Random matrix models for datasets with fixed time horizons

This paper examines the use of random matrix theory as it has been applied to model large financial datasets, especially for the purpose of estimating the bias inherent in Mean-Variance portfolio allocation when a sample covariance matrix is substituted for the true underlying covariance. Such problems were observed and modeled in the seminal work of Laloux et al. [Noise dressing of financial correlation matrices. Phys. Rev. Lett., 1999, 83, 1467] and rigorously proved by Bai et al. [Enhancement of the applicability of Markowitz's portfolio optimization by utilizing random matrix theory. Math. Finance, 2009, 19, 639–667] under minimal assumptions. If the returns on assets to be held in the portfolio are assumed independent and stationary, then these results are universal in that they do not depend on the precise distribution of returns. This universality has been somewhat misrepresented in the literature, however, as asymptotic results require that an arbitrarily long time horizon be available before such predictions necessarily become accurate. In order to reconcile these models with the highly non-Gaussian returns observed in real financial data, a new ensemble of random rectangular matrices is introduced, modeled on the observations of independent Lévy processes over a fixed time horizon.     

The importance of the volatility risk premium for volatility forecasting

In this paper, we study the role of the volatility risk premium for the forecasting performance of implied volatility. We introduce a non-parametric and parsimonious approach to adjust the model-free implied volatility for the volatility risk premium and implement this methodology using more than 20 years of options and futures data on three major energy markets. Using regression models and statistical loss functions, we find compelling evidence to suggest that the risk premium adjusted implied volatility significantly outperforms other models, including its unadjusted counterpart. Our main finding holds for different choices of volatility estimators and competing time-series models, underlying the robustness of our results.     

Applying free random variables to random matrix analysis of financial data. Part I: The Gaussian case

We apply the concept of free random variables to doubly correlated (Gaussian) Wishart random matrix models, appearing, for example, in a multivariate analysis of financial time series, and displaying both inter-asset cross-covariances and temporal auto-covariances. We give a comprehensive introduction to the rich financial reality behind such models. We explain in an elementary way the main techniques of free random variables calculus, with a view to promoting them in the quantitative finance community. We apply our findings to tackle several financially relevant problems, such as a universe of assets displaying exponentially decaying temporal covariances, or the exponentially weighted moving average, both with an arbitrary structure of cross-covariances.     

Can financial innovation help to explain the reduced volatility of economic activity?

The stabilization of economic activity in the mid 1980s has received considerable attention. Research has focused primarily on the role played by milder economic shocks, improved inventory management, and better monetary policy. This paper explores another potential explanation: financial innovation. Examples of such innovation include developments in lending practices and loan markets that have enhanced the ability of households and firms to borrow and changes in government policy such as the demise of Regulation Q. We employ a variety of simple empirical techniques to identify links between the observed moderation in economic activity and the influence of financial innovation on consumer spending, housing investment, and business fixed investment. Our results suggest that financial innovation should be added to the list of likely contributors to the mid-1980s stabilization.     

Understanding the price of volatility risk in carry trades

This paper investigates the cross-sectional pricing ability of the short- and long-run components of global foreign exchange (FX) volatility for carry trade returns. We find a negative and statistically significant factor risk price for the long-run component, but no significant pricing effect due to the short-run volatility component. We also document that the dynamics of the long-run component of global FX volatility are related to US macroeconomic fundamentals. Our results are robust to various parametrizations of the volatility models used to obtain the volatility components and they are invariant to alternative asset pricing testing methodologies and sample periods.     

Stock market volatility, excess returns, and the role of investor sentiment

Using the Investors' Intelligence sentiment index, we employ a generalized autoregressive conditional heteroscedasticity-in-mean specification to test the impact of noise trader risk on both the formation of conditional volatility and expected return as suggested by De Long et al. [Journal of Political Economy 98 (1990) 703]. Our empirical results show that sentiment is a systematic risk that is priced. Excess returns are contemporaneously positively correlated with shifts in sentiment. Moreover, the magnitude of bullish (bearish) changes in sentiment leads to downward (upward) revisions in volatility and higher (lower) future excess returns.     

Computing the market price of volatility risk in the energy commodity markets

In this paper, we demonstrate the need for a negative market price of volatility risk to recover the difference between Black–Scholes [Black, F., Scholes, M., 1973. The pricing of options and corporate liabilities. Journal of Political Economy 81, 637–654]/Black [Black, F., 1976. Studies of stock price volatility changes. In: Proceedings of the 1976 Meetings of the Business and Economics Statistics Section, American Statistical Association, pp. 177–181] implied volatility and realized-term volatility. Initially, using quasi-Monte Carlo simulation, we demonstrate numerically that a negative market price of volatility risk is the key risk premium in explaining the disparity between risk-neutral and statistical volatility in both equity and commodity-energy markets. This is robust to multiple specifications that also incorporate jumps. Next, using futures and options data from natural gas, heating oil and crude oil contracts over a 10 year period, we estimate the volatility risk premium and demonstrate that the premium is negative and significant for all three commodities. Additionally, there appear distinct seasonality patterns for natural gas and heating oil, where winter/withdrawal months have higher volatility risk premiums. Computing such a negative market price of volatility risk highlights the importance of volatility risk in understanding priced volatility in these financial markets.     

Forecasting stock market volatility and the informational efficiency of the DAX-index options market

Alternative strategies for predicting stock market volatility are examined. In out-of-sample forecasting experiments implied-volatility information, derived from contemporaneously observed option prices or history-based volatility predictors, such as GARCH models, are investigated to determine if they are more appropriate for predicting future return volatility. Employing German DAX-index return data it is found that past returns do not contain useful information beyond the volatility expectations already reflected in option prices. This supports the efficient market hypothesis for the DAX-index options market.     

Exchange rate volatility,macroeconomic announcements and the choice of intraday periodicity filtering method

Filtering out the intraday periodicity of volatility is crucial for using high frequency data in econometric analysis. This paper studies the effects of filtering on statistical inference as regards the impact of news on exchange rate volatility. The properties of different methods are studied using a five-minute frequency EUR/USD data set and simulated returns. The simulation results suggest that all the methods tend to produce downward-biased estimates of news coefficients, some more biased than others. The study supports the Flexible Fourier Form method as the best for seasonality filtering.     

Time-varying co-movements and volatility spillovers among financial sector CDS indexes in the UK

This article investigates co-movements and volatility spillovers between the three UK financial sector CDS indexes over time. We find sharp increases in the dynamic conditional correlations for all pairs after the Lehman shock, indicating evidence of contagion, and decreases for two pairs (banking-life insurance and life insurance-other financial) after the zenith of the European debt crisis, implying the emergence of diversification opportunities. Dynamic spillover index measures suggest that, although the banking sector was a dominant net transmitter of volatility, other financial sectors also became net transmitters for some periods, highlighting the importance of appropriate regulation of these two sector areas.     

Day of the week effect on foreign exchange market volatility: Evidence from Turkey

This paper assesses the day of the week effect of the daily depreciation of the Turkish lira (TL) against the US dollar (USD) and its volatility. The empirical evidence from Turkey presented here suggests that Thursdays are associated with higher and Mondays with lower depreciation rates compared to those of Wednesdays. Moreover, Mondays and Tuesdays are associated with higher volatility than Wednesdays.     

Distilling private information from plain-vanilla options to predict future underlying stock price volatility: Evidence from the H-shares of Chinese banks

Deviations from put-call parity may arise in response to private information that a select group of investors possess. From a practical perspective, if one possesses private information, using options to speculate or hedge amplifies potential gains given the leverage embedded in options with respect to price changes in the underlying asset. In light of this, and if we assume that the average investor does not possess private information, it is perhaps possible though to infer such information through implied variance spreads and use it to predict future volatility in the underlying asset. In this piece I examine the extent to which such information is economically informative in predicting the intraday return variability of H-shares issued by China's state and joint-stock banks, respectively. Generally speaking, I uncover the following; firstly, call-put implied variance spreads are mean-reverting across time. Secondly, at any given point in time, the magnitude of the deviation from put-call parity is informative in predicting rises in future spot price volatility. Thirdly, straddle/strangle trades predict, at times one week in advance, rises in future spot price volatility. These findings hold after controlling for market-wide implied volatility, the flow and shock in information disseminating to the market, and implicit transactions costs.     

Return and volatility co-movement in commodity futures markets: the effects of liquidity risk

Commodity markets are a widely researched topic in the field of finance. In this paper, we investigate the co-movement of return and volatility measures in different commodity futures markets and how these measures are affected by liquidity risk. First, we find that commodity returns display co-movement and that liquidity risk plays a key role in shaping asset return patterns. Moreover, we show that the volatilities of commodity returns co-move, and we demonstrate the role of liquidity risk in this joint pattern. We also find that the commodity markets we investigated share a common volatility factor that determines their joint volatility co-movement. Because liquidity risk affects both commodity returns and volatility shocks, it might be interpreted as the common causal factor driving both measures simultaneously. Therefore, we affirm the view that liquidity shocks are firmly related to two residual risks originating from both market return and market volatility. Finally, we also show that liquidity spillovers can significantly drive cross-sectional correlation dynamics.     

Harnessing jump component for crude oil volatility forecasting in the presence of extreme shocks

Oil markets are subject to extreme shocks (e.g. Iraq’s invasion of Kuwait), causing the oil market price exhibits extreme movements, called jumps (or spikes). These jumps pose challenges on oil market volatility forecasting using conventional volatility dynamic models (e.g. GARCH model) This paper characterizes dynamics of jumps in oil market price using high frequency data from three perspectives: the probability (or intensity) of jump occurrence, the sign (e.g. positive or negative) of jumps, and the concurrence with stock market jumps. And then, the paper exploits predictive ability of these jump-related information for oil market volatility forecasting under the mixed data sampling (MIDAS) modeling framework. Our empirical results show that augmenting standard MIDAS model using the three jump-related information significantly improves the accuracy of oil market volatility forecasting. The jump intensity and negative jump size are particularly useful for predicting future oil volatility. These results are widely consistent across a variety of robustness tests. This work provides new insights on how to forecast oil market volatility in the presence of extreme shocks.     

Improved estimation of the covariance matrix of stock returns with an application to portfolio selection

This paper proposes to estimate the covariance matrix of stock returns by an optimally weighted average of two existing estimators: the sample covariance matrix and single-index covariance matrix. This method is generally known as shrinkage, and it is standard in decision theory and in empirical Bayesian statistics. Our shrinkage estimator can be seen as a way to account for extra-market covariance without having to specify an arbitrary multifactor structure. For NYSE and AMEX stock returns from 1972 to 1995, it can be used to select portfolios with significantly lower out-of-sample variance than a set of existing estimators, including multifactor models.     

股票市场非线性随机游走检验

中国股票市场指数收益率不服从正态分布假设，基本符合随机游走的特征，具有弱式有效性的市场特征，沪市指数收益率的时间序殊随机性略大于深市。造成这一现象的原因包括市场结构的非理性与投资行为的非理性等因素。     

A comparison principle between rough and non-rough Heston models—with applications to the volatility surface

We present a number of related comparison results, which allow one to compare moment explosion times, moment generating functions and critical moments between rough and non-rough Heston models of stochastic volatility. All results are based on a comparison principle for certain non-linear Volterra integral equations. Our upper bound for the moment explosion time is different from the bound introduced by Gerhold, Gerstenecker and Pinter [Moment explosions in the rough Heston model. Decisions in Economics and Finance, 2019, 42, 575–608] and tighter for typical parameter values. The results can be directly transferred to a comparison principle for the asymptotic slope of implied variance between rough and non-rough Heston models. This principle shows that the ratio of implied variance slopes in the rough versus non-rough Heston model increases at least with power-law behavior for small maturities.     

The Eurozone banking sector in the time of COVID-19: Measuring volatility connectedness

This article investigates the volatility connectedness of the Eurozone banking system over the last 15 years (from 2005 to 2020). Applying the Diebold-Yilmaz Connectedness Index model to the daily stock return volatilities of 30 major Eurozone banks, we are able to measure the risk spillover effects and to capture the COVID-19 outbreak's impact on banking stability. The empirical findings show that the 30 banks are highly interconnected. Furthermore, we show the strong impact of the COVID-19 pandemic on the volatility dynamics, i.e., on the structure of the Eurozone banking system. Dynamically, we find that volatility connectedness increases during crises, reaching its maximum peak at the time of COVID-19. The analysis points out the critical role of volatility transmission played by large banks, highlighting the “too-big-to-fail” characteristic of this banking system. However, we find that small-medium banks are important actors of contagion, supporting the thesis that the Eurozone banking system is also “too-interconnected to fail.” Finally, we document the heterogeneity effect of the COVID-19 pandemic between Eurozone banking systems. This heterogeneity impact could be a future source of financial instability within the Eurozone.     

Forecasting volatility of the U.S. oil market

We examine the information content of the CBOE Crude Oil Volatility Index (OVX) when forecasting realized volatility in the WTI futures market. Additionally, we study whether other market variables, such as volume, open interest, daily returns, bid-ask spread and the slope of the futures curve, contain predictive power beyond what is embedded in the implied volatility. In out-of-sample forecasting we find that econometric models based on realized volatility can be improved by including implied volatility and other variables. Our results show that including implied volatility significantly improves daily and weekly volatility forecasts; however, including other market variables significantly improves daily, weekly and monthly volatility forecasts.     

A cluster driven log-volatility factor model: a deepening on the source of the volatility clustering

We introduce a new factor model for log volatilities that considers contributions, and performs dimensionality reduction, at a global level through the market, and at a local level through clusters and their interactions. We do not assume a-priori the number of clusters in the data, instead using the Directed Bubble Hierarchical Tree algorithm to fix the number of factors. We use the factor model to study how the log volatility contributes to volatility clustering, quantifying the strength of the volatility clustering using a new nonparametric integrated proxy. Indeed finding a link between volatility and volatility clustering, we find that a global analysis reveals that only the market contributes to the volatility clustering. A local analysis reveals that for some clusters, the cluster itself contributes statistically to the volatility clustering effect. This is significantly advantageous over other factor models, since it offers a way of selecting factors in a statistical way, whilst also keeping economically relevant factors. Finally, we show that the log volatility factor model explains a similar amount of memory to a principal components analysis factor model and an exploratory factor model.