Volatility cascades in cryptocurrency trading

This paper studies volatility cascades across multiple trading horizons in cryptocurrency markets. Using one-minute data on Bitcoin, Ethereum and Ripple against the US dollar, we implement the wavelet Hidden Markov Tree model. This model allows us to estimate the transition probability of high or low volatility at one time scale (horizon) propagating to high or low volatility at the next time scale. We find that when moving from long to short horizons, volatility cascades tend to be symmetric: low volatility at long horizons is likely to be followed by low volatility at short horizons, and high volatility is likely to be followed by high volatility. In contrast, when moving from short to long horizons, volatility cascades are strongly asymmetric: high volatility at short horizons is now likely to be followed by low volatility at long horizons. These results are robust across time periods and cryptocurrencies.     

Portfolio allocation and the investment horizon: a multiscaling approach

A new approach is proposed for analysing portfolio allocation over various time scales. This new approach is based on wavelet analysis, which decomposes a given time series on a scale-by-scale basis. Empirical results indicate that, as the investment horizon lengthens, a greater weighting should be allocated to stocks. An explanation for this result is that the mean-reverting property of stock returns causes investors to perceive that stocks are less risky than bonds and T-bills at longer time scales compared with shorter time scales. When we include the effect of risk aversion, it is found that the higher the risk aversion, the less the Sharpe ratio, indicating that a more conservative investor prefers a smoother consumption stream.     

The term structure of S&P 100 model-free volatilities

We develop an improved method to obtain the model-free volatility more accurately despite the limitations of a finite number of options and large strike price intervals. Our method computes the model-free volatility from European-style S&P 100 index options over a horizon of up to 450 days, the first time that this has been attempted, as far as we are aware. With the estimated daily term structure over the long horizon, we find that (i) changes in model-free volatilities are asymmetrically more positively impacted by a decrease in the index level than negatively impacted by an increase in the index level; (ii) the negative relationship between the daily change in model-free volatility and the daily change in index level is stronger in the near term than in the far term; and (iii) the slope of the term structure is positively associated with the index level, having a tendency to display a negative slope during bear markets and a positive slope during bull markets. These significant results have important implications for pricing and hedging index derivatives and portfolios.     

Modelling changes in the unconditional variance of long stock return series

In this paper we develop a testing and modelling procedure for describing the long-term volatility movements over very long daily return series. For this purpose we assume that volatility is multiplicatively decomposed into a conditional and an unconditional component as in Amado and Teräsvirta (2012, 2013). The latter component is modelled such that the unconditional time-varying component evolves slowly over time. Statistical inference is used for specifying the parameterization of the time-varying component by applying a sequence of Lagrange multiplier tests. The model building procedure is illustrated with an application to 22,986 daily returns of the Dow Jones Industrial Average stock index covering a period of more than ninety years. The main conclusions are as follows. First, the LM tests strongly reject the assumption of constancy of the unconditional variance. Second, the results show that the apparent long memory property in volatility may be interpreted as changes in the unconditional variance of the long series. Finally, based on a formal statistical test we find evidence of the superiority of volatility forecasting accuracy of the new model over the GJR-GARCH model at all horizons for eight subsets of the long return series.     

A behavioural explanation to the asymmetric volatility phenomenon: Evidence from market volatility index

This study examines how the behavioural explanations, in particular loss aversion, can be used to explain the asymmetric volatility phenomenon by investigating the relationship between stock market returns and changes in investor perceptions of risk measured by the volatility index. We study the behaviour of India volatility index vis‐à‐vis Hong Kong, Australia and UK volatility index, and provide a comprehensive comparative analysis. Using Bai‐Perron test, we identify structural breaks and volatility regimes in the time series of volatility index, and investigate the volatility index‐return relation during high, medium and low volatility periods. Regardless of volatility regimes, we find that volatility index moves in opposite direction in response to stock index returns, and contemporaneous return is the most dominating across the four markets. The negative relation is strongest for UK followed by Australia, Hong Kong and India. Second, volatility index reacts significantly different to positive and negative returns; negative return has higher impact on changes in volatility index than positive return across the markets over full‐sample and sub‐sample periods. The asymmetric effect is stronger in low volatility regime than in high and medium volatility periods for all the markets except UK. The strength of asymmetric effect is strongest for Hong Kong and weakest for India. Finally, negative returns have exponentially increasing effect and positive returns have exponentially decreasing effect on the changes in volatility index.     

Combining long memory and level shifts in modelling and forecasting the volatility of asset returns

We propose a parametric state space model of asset return volatility with an accompanying estimation and forecasting framework that allows for ARFIMA dynamics, random level shifts and measurement errors. The Kalman filter is used to construct the state-augmented likelihood function and subsequently to generate forecasts, which are mean and path-corrected. We apply our model to eight daily volatility series constructed from both high-frequency and daily returns. Full sample parameter estimates reveal that random level shifts are present in all series. Genuine long memory is present in most high-frequency measures of volatility, whereas there is little remaining dynamics in the volatility measures constructed using daily returns. From extensive forecast evaluations, we find that our ARFIMA model with random level shifts consistently belongs to the 10% Model Confidence Set across a variety of forecast horizons, asset classes and volatility measures. The gains in forecast accuracy can be very pronounced, especially at longer horizons.     

Fundamentalists,chartists and asset pricing anomalies

This paper investigates whether excess volatility of asset prices and serial correlations of stock monthly returns may be explained by the interactions between fundamentalists and chartists. Fundamentalists forecast future prices cum dividends through an adaptive learning rule. In contrast, chartists forecast future prices based on the observation of past price movements. Numerical simulations reveal that the interplay of fundamentalists and chartists robustly generates excess volatility of asset prices, volatility clustering, trends in prices (i.e. positive serial correlations of returns) over short horizons and oscillations in prices (i.e. negative serial correlations of returns) over long horizons, often observed in financial data. Moreover, we find that the memory of the learning rule plays a key role in explaining the above-mentioned stylized facts. In particular, we establish that excess volatility of asset prices; volatility clustering and autocorrelation of returns at different horizons emerge when fundamentalists have short memory. However, volatility clustering as well as short-run and long-run dependencies, observed in financial time series, are more pronounced when fundamentalists have longer memory.     

The impact of transaction duration,volume and direction on price dynamics and volatility

We explore the role of trade volume, trade direction, and the duration between trades in explaining price dynamics and volatility using an Asymmetric Autoregressive Conditional Duration model applied to intraday transactions data. Our results suggest that volume, direction and duration are important determinants of price dynamics, while duration is also an important determinant of volatility. However, the impact of volume and direction on volatility is marginal after controlling for duration, and the impact of volume on volatility appears to be confined to periods of infrequent trading.     

INTRADAY MARKET BEHAVIOR AND THE EXTENT OF FEEDBACK BETWEEN S&P 500 FUTURES PRICES AND THE S&P 500 INDEX

In this study we empirically examine the intraday lead/lag relation between S&P 500 futures prices and the S&P 500 index, and whether daily market characteristics are associated with changes in the relation. We estimate daily Geweke measures of feedback and regress time series of these measures on daily price volatility and volume characteristics. Results indicate that the contemporaneous price relation is substantive and that measures of contemporaneous feedback are positively associated with the daily range of the futures price. The primary implication is that the relation between cash and futures prices becomes stronger as futures price volatility increases. As volatility increases, information is being impounded at a faster rate so that futures and equity markets operate more closely as one market. Large futures price moves, by themselves, are not responsible for breakdowns in the stock-futures price relation.     

Asymmetries of the intraday return-volatility relation

This study investigates the asymmetry of the intraday return-volatility relation at different return horizons ranging from 1, 5, 10, 15, up to 60 min and compares the empirical results with results for the daily return horizon. Using data on the S&P 500 (SPX) and the VIX from September 25, 2003 to December 30, 2011 and a Quantile-Regression approach, we observe strong negative return-volatility relation over all return horizons. However, this negative relation is asymmetric in three different aspects. First, the effects of positive and negative returns on volatility are different and more pronounced for negative returns. Second, for both positive and negative returns, the effect is conditional on the distribution of volatility changes. The absolute effect is up to five times larger in the extreme tails of the distribution. Third, at the intraday level, there is evidence of both autocorrelation in volatility changes and cross-autocorrelation with returns. This lead-lag relation with returns is also very asymmetric and more pronounced in the tails of the distribution. These effects are, however, not observed at the daily return horizon.     

Volume and Volatility in Foreign Currency Futures Markets

In this paper we propose and test several hypotheses concerning time series properties of trading volume, price, short and long-term relationships between price and volume and the determinants of trading volume in forcign currency futures. The nearby contracts for British Pound, Canadian Dollar, Japanese Yen, German Mark and Swiss Franc are analyzed in three frequencies i.e. daily, weekly and monthly.We find supportive evidence for all the five currencies that the price volatility is a determinant of the trading volume changes. Furthermore, the volatility of the price process is a determinant of the unexpected component of the changes in trading volume. Also, there is a significant relationship between the volatility of price and the volatility of trading volume changes for three of the five currencies in the daily frequency and for one currency in the monthly frequency.     

我国货币政策对股票市场非对称影响的实证研究——基于马尔可夫区制转换VAR模型

本文基于1997年1月至2012年4月的数据,使用三区制滞后两阶的MS（3）-VAR（2）模型,对三种区制下货币政策对股票市场的影响进行分析。研究发现,在不同状态下,货币政策变量的变动对上址综指收益的影响在时间、方向和效果上是非对称的。在高收益、低波动状态与低亏损、低波动状态下,利率的变动对股票市场并不存在显著的影响;在高亏损、高波动状态下,利率的变动滞后一期对股票市场有较小的正向影响,但滞后二期时存在较大的负向影响。货币供应量变动对股票市场的影响在高亏损、高波动行情时比在高收益、低波动和低亏损、低波动行情时更加显著。总体来看,利率和货币供应量对股票市场的影响任高亏损、高波动行情下是显著的。     

Optimal hedge ratio and hedging effectiveness of stock index futures: evidence from India

In a free capital mobile world with increased volatility, the need for an optimal hedge ratio and its effectiveness is warranted to design a better hedging strategy with future contracts. This study analyses four competing time series econometric models with daily data on NSE Stock Index Futures and S&P CNX Nifty Index. The effectiveness of the optimal hedge ratios is examined through the mean returns and the average variance reduction between the hedged and the unhedged positions for 1-, 5-, 10- and 20-day horizons. The results clearly show that the time-varying hedge ratio derived from the multivariate GARCH model has higher mean return and higher average variance reduction across hedged and unhedged positions. Even though not outperforming the GARCH model, the simple OLS-based strategy performs well at shorter time horizons. The potential use of this multivariate GARCH model cannot be sublined because of its estimation complexities. However, from a cost of computation point of view, one can equally consider the simple OLS strategy that performs well at the shorter time horizons.     

Is more finance better? Disentangling intermediation and size effects of financial systems

Financial systems all over the world have grown dramatically over recent decades. But is more finance necessarily better? And what concept of financial system – a focus on its size, including both intermediation and other auxiliary “non-intermediation” activities, or a focus on traditional intermediation activity – is relevant for its impact on real sector outcomes? This paper assesses the relationship between the size of the financial system and intermediation, on the one hand, and GDP per capita growth and growth volatility, on the other hand. Based on a sample of 77 countries for the period 1980–2007, we find that intermediation activities increase growth and reduce volatility in the long run. An expansion of the financial sectors along other dimensions has no long-run effect on real sector outcomes. Over shorter time horizons a large financial sector stimulates growth at the cost of higher volatility in high-income countries. Intermediation activities stabilize the economy in the medium run especially in low-income countries. As this is an initial exploration of the link between financial system indicators and growth and volatility, we focus on OLS regressions, leaving issues of endogeneity and omitted variable biases for future research.     

A class of stochastic volatility models and the q-optimal martingale measure

This paper proposes an approach under which the q-optimal martingale measure, for the case where continuous processes describe the evolution of the asset price and its stochastic volatility, exists for all finite time horizons. More precisely, it is assumed that while the ‘mean–variance trade-off process’ is uniformly bounded, the volatility and asset are imperfectly correlated. As a result, under some regularity conditions for the parameters of the corresponding Cauchy problem, one obtains that the qth moment of the corresponding Radon–Nikodym derivative does not explode in finite time.     

Inferring future volatility from the information in implied volatility in Eurodollar options: a new approach

We study the information content of implied volatility fromseveral volatility specifications of the Heath-Jarrow-Morton(1992) (HJM) models relative to popular historical volatilitymodels in the Eurodollar options market. The implied volatilityfrom the HJM models explains much of the variation of realizedinterest rate volatility over both daily and monthly horizons.The implied volatility dominates the GARCH terms, the Glostenet al. (1993) type asymmetric volatility terms, and the interestrate level. However, it cannot explain that the impact of interestrate shocks on the volatility is lower when interest rates arelow than when they are high.     

A Better Asymmetric Model of Changing Volatility in Stock and Exchange Rate Returns: Trend-GARCH

Abstract

The impact of short run price trending on the conditional volatility is tested empirically. A new family of conditionally heteroscedastic models with a trend-dependent conditional variance equation: The Trend-GARCH model is described. Modern microeconomic theory often suggests the connection between the past behaviour of time series, the subsequent reaction of market individuals, and thereon changes in the future characteristics of the time series. Results reveal important properties of these models, which are consistent with stylized facts found in financial data sets. They can also be employed for model identification, estimation, and testing. The empirical analysis supports the existence of trend effects. The Trend-GARCH model proves to be superior to alternative models such as EGARCH, AGARCH, TGARCH OR GARCH-in-Mean in replicating the leverage effect in the conditional variance, in fitting the news impact curve and in fitting the volatility estimates from high frequency data. In addition, we show that the leverage effect is dependent on the current trend, i.e. it differentiates between bullish and bearish markets. Furthermore, trend effects can account for a significant part of the long memory property of asset price volatilities.     

The Impact of Trades on Daily Volatility

This article proposes a trading-based explanation for the asymmetriceffect in daily volatility of individual stock returns. Previousstudies propose two major hypotheses for this phenomenon: leverageeffect and time-varying expected returns. However, leveragehas no impact on asymmetric volatility at the daily frequencyand, moreover, we observe asymmetric volatility for stocks withno leverage. Also, expected returns may vary with the businesscycle, that is, at a lower than daily frequency. Trading activityof contrarian and herding investors has a robust effect on therelationship between daily volatility and lagged return. Consistentwith the predictions of the rational expectation models, thenon-informational liquidity-driven (herding) trades increasevolatility following stock price declines, and the informed(contrarian) trades reduce volatility following stock priceincreases. The results are robust to different measures of volatilityand trading activity. (JEL C30, G11, G12)     

Characteristics of permanent and transitory returns in oil-sensitive emerging stock markets: The case of GCC countries

The estimates suggest that for both return components there exists a statistically significant high volatility regime for all the Gulf Cooperation Council (GCC) stock markets and the oil market. On the other hand, the results for the low volatility state of both components are mixed. The individual GCC markets vary in terms of sensitivity to volatility and its duration; with Saudi Arabia and Oman having the highest overall return volatility. All the GCC markets are much less volatile than that of the more open, crisis-ridden, oil-exporting Mexico. All GCC returns move in the same direction, whether in terms of total return, fundamentals or fads under both volatility regimes. The correlations between themselves and with Mexico, the oil price and the Morgan Stanley Capital International Index (MSCI) returns are weak compared to the correlations among stock returns of Germany, Japan UK and the US [Bhar, R., Hamori, S., 2004. Empirical characteristics of the permanent and transitory components of stock returns: analysis in a Markov-switching heteroscedasticity framework. Economics Letters 82, 157–165]. Mexico has considerably higher correlation with both MSCI and the oil price than all the GCC countries.     

MaxVaR for non-normal and heteroskedastic returns¶

In this work we propose Monte Carlo simulation models for dynamically computing MaxVaR for a financial return series. This dynamic MaxVaR takes into account the time-varying volatility as well as non-normality of returns or innovations. We apply this methodology to five stock market indices. To validate the proposed methods we compute the number of MaxVaR violations and compare them with the expected number. We also compute the MaxVaR-to-VaR ratio and find that, on average, dynamic MaxVaR exceeds dynamic VaR by 5–7% at the 1% significance level, and by 12–14% at the 5% significance level for the selected indices.