The microstructural foundations of leverage effect and rough volatility

We show that typical behaviors of market participants at the high frequency scale generate leverage effect and rough volatility. To do so, we build a simple microscopic model for the price of an asset based on Hawkes processes. We encode in this model some of the main features of market microstructure in the context of high frequency trading: high degree of endogeneity of market, no-arbitrage property, buying/selling asymmetry and presence of metaorders. We prove that when the first three of these stylized facts are considered within the framework of our microscopic model, it behaves in the long run as a Heston stochastic volatility model, where a leverage effect is generated. Adding the last property enables us to obtain a rough Heston model in the limit, exhibiting both leverage effect and rough volatility. Hence we show that at least part of the foundations of leverage effect and rough volatility can be found in the microstructure of the asset.     

High-frequency financial data modeling using Hawkes processes

Intraday Value-at-Risk (VaR) is one of the risk measures used by market participants involved in high-frequency trading. High-frequency log-returns feature important kurtosis (fat tails) and volatility clustering (extreme log-returns appear in clusters) that VaR models should take into account. We propose a marked point process model for the excesses of the time series over a high threshold that combines Hawkes processes for the exceedances with a generalized Pareto distribution model for the marks (exceedance sizes). The conditional approach features intraday clustering of extremes and is used to calculate instantaneous conditional VaR. The models are backtested on real data and compared to a competitor approach that proposes a nonparametric extension of the classical peaks-over-threshold method. Maximum likelihood estimation is computationally intensive; we use a differential evolution genetic algorithm to find adequate starting values for the optimization process.     

Disagreement and equilibrium option trading volume

Using a complete market equilibrium model, we present results concerning the effect disagreement has on equilibrium option trading volume and positioning. We find that if agents agree on volatility, total option volume is independent of wealth distribution and average optimism. We also find option volume increasing in drift disagreement and decreasing in risk aversion and volatility. Pessimists are shown to write most options. With volatility disagreement, the results are less clear; however, we show agents with high volatility beliefs write deep out of the money options and buy close to the money options. Numerical comparative statics are also performed. This revised version was published online in June 2006 with corrections to the Cover Date.     

A slightly depressing jump model: intraday volatility pattern simulation

Hawkes processes have been finding more applications in diverse areas of science, engineering and quantitative finance. In multi-frequency finance various phenomena have been observed, such as shocks, crashes, volatility clustering, turbulent flows and contagion. Hawkes processes have been proposed to model those challenging phenomena appearing across asset prices in various exchanges. The original Hawkes process is an intensity-based model for series of events with path dependence and self-exciting or mutual-exciting mechanisms. This paper introduces a slightly depressing process to model the reverse phenomenon of self-exciting mechanisms. Such a process models the decline in the intensity of jumps observed in market regimes. The proposed birth-immigration-death process captures the decline in jump intensity observed at the start of a daily trading regime while the classical immigration-birth process models an increase in jump intensity towards the close of daily trading. Each of these processes can be expressed as a special case of a simple bivariate Hawkes process.     

Portfolio Returns,Market Volatility,and Seasonality

This paper examines three important issues related to the relationship between stock returns and volatility. First, are Duffee's (1995) findings of the relationship between individual stock returns and volatility valid at the portfolio level? Second, is there a seasonality of the market return volatility? Lastly, do size portfolio returns react symmetrically to the market volatility during business cycles? We find that the market volatility exhibits strong autocorrelation and small size portfolio returns exhibit seasonality. However, this phenomenon is not present in large size portfolios. For the entire sample period of 1962–1995, the highest average monthly volatility occurred in October, followed by November, and then January. Examining the two sub-sample periods, we find that the average market volatility increases by 15.4% in the second sample period of 1980–1995 compared to the first sample period of 1962–1979. During the contraction period, the average market volatility is 60.9% higher than that during the expansion period. Using a binary regression model, we find that size portfolio returns react asymmetrically with the market volatility during business cycles. This paper documents a strongly negative contemporaneous relationship between the size portfolio returns and the market volatility that is consistent with the previous findings at the aggregate level, but is inconsistent with the findings at the individual firm level. In contrast with the previous findings, however, we find an ambiguous relationship between the percentage change in the market volatility and the contemporaneous stock portfolio returns. This ambiguity is attributed to strongly negative contemporaneous and one-month ahead relationships between the market volatility and portfolio returns.

     

Concentration of the UK Stock Market

Abstract:  During 1999 and 2000 a large number of articles appeared in the financial press which argued that the concentration of the FTSE 100 had increased. Many of these reports suggested that stock market volatility in the UK had risen, because the concentration of its stock markets had increased. This study undertakes a comprehensive measurement of stock market concentration using the FTSE 100 index. We find that during 1999, 2000 and 2001 stock market concentration was noticeably higher than at any other time since the index was introduced. When we measure the volatility of the FTSE 100 index we do not find an association between concentration and its volatility. When we examine the variances and covariance's of the FTSE 100 constituents we find that security volatility appears to be positively related to concentration changes but concentration and the size of security covariances appear to be negatively related. We simulate the variance of four versions of the FTSE 100 index; in each version of the index the weighting structure reflects either an equally weighted index, or one with levels of low, intermediate or high concentration. We find that moving from low to high concentration has very little impact on the volatility of the index. To complete the study we estimate the minimum variance portfolio for the FTSE 100, we then compare concentration levels of this index to those formed on the basis of market weighting. We find that realised FTSE index weightings are higher than for the minimum variance index.     

Quadratic Hawkes processes for financial prices

We introduce and establish the main properties of QHawkes (‘Quadratic’ Hawkes) models. QHawkes models generalize the Hawkes price models introduced in Bacry and Muzy [Quant. Finance, 2014, 14(7), 1147–1166], by allowing feedback effects in the jump intensity that are linear and quadratic in past returns. Our model exhibits two main properties that we believe are crucial in the modelling and the understanding of the volatility process: first, the model is time-reversal asymmetric, similar to financial markets whose time evolution has a preferred direction. Second, it generates a multiplicative, fat-tailed volatility process, that we characterize in detail in the case of exponentially decaying kernels, and which is linked to Pearson diffusions in the continuous limit. Several other interesting properties of QHawkes processes are discussed, in particular the fact that they can generate long memory without necessarily being at the critical point. A non-parametric fit of the QHawkes model on NYSE stock data shows that the off-diagonal component of the quadratic kernel indeed has a structure that standard Hawkes models fail to reproduce. We provide numerical simulations of our calibrated QHawkes model which is indeed seen to reproduce, with only a small amount of quadratic non-linearity, the correct magnitude of fat-tails and time reversal asymmetry seen in empirical time series.     

The role of global economic conditions in forecasting gold market volatility: Evidence from a GARCH-MIDAS approach

In this study, we examine the role of global economic conditions in the predictability of gold market volatility using alternative measures. Based on the available data frequency for the relevant series, we adopt the GARCH-MIDAS approach which allows for mixed-data frequencies. We find that global economic conditions contribute significantly to gold market volatility, albeit with mixed outcomes. While the results also lend support to the safe-haven properties of the gold market, the outcome can be influenced by the choice of measure for global economic conditions. For completeness, we extend the analyses to other precious metals (palladium, platinum, rhodium and silver) and find that the global economic conditions forecast the return volatility of the gold market better than these other precious metals. Our results are robust to multiple forecast horizons and offer useful insights on the plausible investment choices in the precious metals market.     

Overconfidence among option traders

The investor overconfidence theory predicts a direct relationship between market‐wide turnover and lagged market return. However, previous research has examined this prediction in the equity market, we focus on trading in the options market. Controlling for stock market cross‐sectional volatility, stock idiosyncratic risk, and option market volatility, we find that option trading turnover is positively related to past stock market return. In addition, call option turnover and call to put ratio are also positively associated with the past stock market return. These findings are consistent with the overconfidence theory. We also find that overconfident investors trade more in the options market than in the equity market. We rule out explanations other than investor overconfidence, such as momentum trading and varying risk preferences, for our findings.     

Quantification of the high level of endogeneity and of structural regime shifts in commodity markets

We propose a “reflexivity” index that quantifies the relative importance of short-term endogeneity for several commodity futures markets (corn, oil, soybean, sugar, and wheat) and a benchmark equity futures market (E-mini S&P 500), from mid-2000s to October 2012. Our reflexivity index is defined as the average ratio of the number of price moves that are due to endogenous interactions to the total number of all price changes, which also include exogenous events. It is obtained by calibrating the Hawkes self-excited conditional Poisson model on time series of price changes. The Hawkes model accounts simultaneously for the co-existence and interplay between the exogenous impact of news and the endogenous mechanism by which past price changes may influence future price changes. Our robustness tests show that our index provides a ‘pure’ measure of endogeneity that is independent of the rate of activity, order size, volume or volatility. We find an overall increase of the reflexivity index since the mid-2000s to October 2012, which implies that at least 60–70 percent of commodity price changes are now due to self-generated activities rather than novel information, compared to 20–30 percent earlier. While our reflexivity index is defined on short-time windows (10–30 min) and thus does not capture long-term memory, we discover striking coincidence between its dynamics and that of the price hikes and abrupt falls that developed since 2006 and culminated in early 2009.     

ON THE ROBUSTNESS OF RANGE‐BASED VOLATILITY ESTIMATORS

We empirically examine Parkinson's range‐based volatility estimate in the federal funds market, which is unique because institutional regulations create a predictable pattern in interday volatility. We find that range‐based volatility estimates and standard deviations produce the expected volatility pattern. We also find that at trading pressure points where microstructure noise should be greatest, range‐based estimates are less than the standard deviations. Thus, we support the argument that range‐based volatility estimates remove the upward bias created by microstructure noise. We find that the Parkinson method is the most efficient range‐based volatility measure among a set of alternates in this market.     

Asymmetric volatility spillovers between economic policy uncertainty and stock markets: Evidence from China

This study explores the spillovers between economic policy uncertainty (EPU) and stock market realized volatility (RV). The monthly index of Chinese and US EPU and RV are used to analyze the pairwise directional spillovers. We find that RV is a net receiver that is more vulnerable to shocks from U.S. EPU than to shocks from Chinese EPU. We further decompose the RV into good and bad volatility to test the asymmetric spillover effect between the stock market and EPU. The results suggest that EPU has a bigger effect on bad volatility in the stock market throughout most of the sample period. However, we find that good volatility spillovers become larger during periods of stimulated reform, whereas bad volatility spillovers become larger during periods of international disputes. We show that Chinese stock market volatility is sensitive to both U.S. and Chinese EPU and that the spillover is asymmetric in different periods.     

Interaction of investor trades and market volatility: Evidence from the Tokyo Stock Exchange

This paper examines the relation between market volatility and investor trades by identifying who supplies and demands market liquidity on the Tokyo Stock Exchange. Because the different trading patterns of various investor types such as individual investors, institutional investors, and foreign investors affect market liquidity differently, we find that market volatility fluctuates significantly depending on which investor types participate in trade. We show that market volatility increases by more than 50% from the average level when there are greater buy trades by momentum investors that demand liquidity and there are less sell trades by contrarian (or profit-taking) investors that supply liquidity. On the other hand, volatility dampens by more than 57% when there are greater sell trades by profit-taking investors, mostly by domestic investors, while there are less momentum buy trades.     

Stock market volatility and equity returns: Evidence from a two-state Markov-switching model with regressors

This paper proposes a two-state Markov-switching model for stock market returns in which the state-dependent expected returns, their variance and associated regime-switching dynamics are allowed to respond to market information. More specifically, we apply this model to examine the explanatory and predictive power of price range and trading volume for return volatility. Our findings indicate that a negative relation between equity market returns and volatility prevails even after having controlled for the time-varying determinants of conditional volatility within each regime. We also find an asymmetry in the effect of price range on intra- and inter-regime return volatility. While price range has a stronger effect in the high volatility state, it appears to significantly affect only the transition probabilities when the stock market is in the low volatility state but not in the high volatility state. Finally, we provide evidence consistent with the ‘rebound’ model of asset returns proposed by Samuelson (1991), suggesting that long-horizon investors are expected to invest more in risky assets than short-horizon investors.     

The Political Economy of Volatility Dynamics in the Hong Kong Stock Market

Despite its obvious importance, little empirical research has examined the impact of political risk on stock market volatility. This paper uses data on the Hong Kong stock market over a long sample period to investigate whether political risk has induced regime shifts in stock market volatility. Regime shifts are modelled via a Markov switching EGARCH model that allows for regime-dependent volatility asymmetry. We find strong evidence of regime shifts in conditional volatility as well as significant volatility asymmetry in high volatility periods. Major political uncertainties were reflected in a switch to the high-volatility regime. However, contrary to popular perceptions, we find no evidence that the Hong Kong stock market has become persistently more volatile since the start of Sino-British political negotiations in 1982.     

Sovereign CDS Spreads,Volatility, and Liquidity: Evidence from 2010 German Short Sale Ban

The paper examines global impact of 2010 German short sale ban on sovereign credit default swap (CDS) spreads, volatility, and liquidity across 54 countries. We find that CDS spreads continue rising after the ban in the debt crisis region, which suggests that the short selling ban is incapable of suppressing soaring borrowing costs in these countries. However, we find that the ban helps stabilize the CDS market by reducing CDS volatility. The reduction in CDS volatility is greater in the eurozone than that in the non‐eurozone. Furthermore, we find that the CDS market liquidity has been impaired during the ban for the PIIGS (Portugal, Ireland, Italy, Greece, and Spain) countries. In contrast, there are no dramatic changes in the market liquidity for non‐PIIGS eurozone and non‐eurozone samples. The findings suggest that the short sale ban is ineffective to reduce sovereign borrowing costs in the debt crisis region if the underlying economy has not been significantly improved.     

Stock volatility predictability in bull and bear markets

The recent literature on stock return predictability suggests that it varies substantially across economic states, being strongest during bad economic times. In line with this evidence, we document that stock volatility predictability is also state dependent. In particular, in this paper, we use a large data set of high-frequency data on individual stocks and a few popular time-series volatility models to comprehensively examine how volatility forecastability varies across bull and bear states of the stock market. We find that the volatility forecast horizon is substantially longer when the market is in a bear state than when it is in a bull state. In addition, over all but the shortest horizons, the volatility forecast accuracy is higher when the market is in a bear state. This difference increases as the forecast horizon lengthens. Our study concludes that stock volatility predictability is strongest during bad economic times, proxied by bear market states.     

The calming effects of conflict: The impact of partisan conflict on market volatility

In recent decades, an increasing divide in political ideologies between Republicans and Democrats has had a notable impact on financial markets. In this paper, we investigate the effect of political conflict, as measured by the partisan conflict index (PCI), on both market and industry-level volatility. We find that PCI has a significant negative impact on market volatility, robust to different regression models. We provide evidence that such impact is not driven by dramatic political events, namely wars and presidential elections, or by presidential party. When controlling for market cycles, we show that PCI reduces volatility during expansionary periods but increases volatility during recessions. Furthermore, at the industry level, we find that PCI decreases volatility overall. We also find that PCI decreases the volatility of politically-sensitive industries significantly more that it does with other industries. These results can inform government policy makers, analysts, investors, and academics alike.     

Does reporting position affect the pricing of the volatility of comprehensive income?

The FASB changed the reporting policy for comprehensive income (CI) by issuing ASU No. 2011-05, which requires CI be reported in performance statements (i.e., either a single income statement with net income or a separate statement of CI following the income statement) rather than the previously allowed equity statements. We examine whether the change in reporting position of CI led to higher market pricing of CI volatility incremental to NI volatility (“incremental CI volatility”), as measured by the price-earnings relationship. We find that the market pricing of incremental CI volatility increased from the pre- to the post-ASU period for non-financial firms forced to change the reporting position of CI from equity to performance statements. The increase is more prominent for firms that switched to the income statement than for firms that switched to a separate statement of CI. Further, we find that the increased market pricing of incremental CI volatility translates into lower valuation weights on other comprehensive income.     

A global approach to mutual funds market timing ability

In this paper, we globally investigate market timing abilities of mutual fund managers from the three perspectives: market return, market-wide volatility and aggregate liquidity. We propose a new specification to study market timing. Instead of considering an average market exposure for mutual funds, we allow mutual fund market betas to follow a random walk in the absence of market timing ability. As a consequence, we capture market exposure dynamics which is really due to manager market timing skills while allowing dynamics to come from other sources than market timing. We find that on average 6% of mutual funds display return market timing abilities while this percentage amounts to respectively 13% and 14% for volatility and liquidity market timing. We also analyze market timing by investment strategies and for surviving and dead funds. Dead funds exhibit lower volatility and liquidity timing skills than live funds.