基于高频数据的股指期货与现货市场波动溢出和信息传导研究

本文利用沪深300指数和当月股指期货连续合约的高频数据,采用非参数方法估计日度股票指数和股指期货的整体波动、连续性波动和跳跃,发现两个市场波动成分存在双向的格兰杰因果关系,但是期货市场的跳跃并不会影响后续股票市场的跳跃。此外,已实现相关系数在股指期货上市初期表现出了较大的变动,整体表现出了较强的联动趋势。最后,日内高频价格之间存在稳定的协整关系,两个市场存在双向的信息传导,股指期货的价格发现功能得到发挥。     

The Impact of Jumps in Volatility and Returns

This paper examines continuous‐time stochastic volatility models incorporating jumps in returns and volatility. We develop a likelihood‐based estimation strategy and provide estimates of parameters, spot volatility, jump times, and jump sizes using S&P 500 and Nasdaq 100 index returns. Estimates of jump times, jump sizes, and volatility are particularly useful for identifying the effects of these factors during periods of market stress, such as those in 1987, 1997, and 1998. Using formal and informal diagnostics, we find strong evidence for jumps in volatility and jumps in returns. Finally, we study how these factors and estimation risk impact option pricing.     

Financial and Economic Integration's Impact on Asian Equity Markets’ Sensitivity to External Shocks

This paper investigates the spillover effects from U.S. and regional stock markets on local stock markets in the Pacific Basin region and China. We also analyze if the spillover depends on countries’ financial and economic integration. We apply a stochastic volatility model with jumps in order to separate the spillover of extreme shocks from those of normal shocks. We find that the spillovers of both normal and extreme shocks are significant for almost all Asian countries except China. We also find that the time‐variation in stock market interdependence can largely be associated with economic integration.     

The anatomy of sovereign risk contagion

The channels for the cross-border propagation of sovereign risk in the international sovereign debt market are analysed. Identifying sovereign credit events as extraordinary jumps in CDS spreads, we distinguish between the immediate effects of such events and their longer term spillover effects. To analyse “fast and furious” contagion, we use daily CDS data to conduct event studies around a total of 89 identified credit events in a global country sample. To analyse “slow-burn” spillover effects, we apply a multifactor risk model, distinguishing between global and regional risk factors. We find that “fast and furious” contagion has been primarily a regional phenomenon, whilst “slow-burn” spillover effects can often be global in scope, especially those of the recent European debt crisis. The global risk factors are found to be driven by investor risk appetites and debt levels, whilst the regional factors depend on economic fundamentals of countries within a region.     

Systemic Risk and International Portfolio Choice

Returns on international equities are characterized by jumps; moreover, these jumps tend to occur at the same time across countries leading to systemic risk. We capture these stylized facts using a multivariate system of jump‐diffusion processes where the arrival of jumps is simultaneous across assets. We then determine an investor's optimal portfolio for this model of returns. Systemic risk has two effects: One, it reduces the gains from diversification and two, it penalizes investors for holding levered positions. We find that the loss resulting from diminished diversification is small, while that from holding very highly levered positions is large.     

Jump risk premia across major international equity markets

We decompose the non-diversifiable market risk into continuous and discontinuous components and jump systematic risks into positive vs. negative and small vs. large components. We examine their association with equity risk premia across major equity markets. We show that developed markets jumps are more closely linked to the aggregate market index than emerging and frontier ones. The reward for bearing both the continuous and downside jump risks is positive during the pre-crisis period whereas the reward for bearing the upside and large jump risks is negative during the crisis and post-crisis periods. We also provide evidence of significant continuous and discontinuous leverage effects during the pre-crisis period, suggesting that both continuous and discontinuous price and volatility risks share compensations for common underlying risk factors.     

Impact of portfolio flows and heterogeneous expectations on FX jumps: Evidence from an emerging market

Motivated by the recent currency crisis in Turkey, we investigate the role of portfolio flows and heterogeneous expectations on the high frequency stochastic jump behavior of the US dollar value against the Turkish lira, one of the most traded emerging market currencies in the world. We group the detected jumps into different types with respect to their direction (up and down) and timing (local and off-shore trading hours). For each type of jumps, we examine their relation with portfolio flows (in the form of equity and bond flows, and carry trade activity), and dispersion in beliefs for the future exchange rate level and key macroeconomic variables. We find that inflows to both equity and bond markets, and increasing carry trade activity significantly reduce the size of jumps and (partially) their intensity. On the other hand, heterogeneous expectations for the future exchange rate level, consumer price index and gross domestic product are found to increase the number of jumps and the average jump size.     

Risk contagion among international stock markets

We develop a stochastic volatility model with jumps in returns and volatility to analyze the risk spillover from the U.S. market and the regional market to a number of European countries’ equity markets. The key advantage of this approach compared to the earlier approaches is that it enables us to identify jumps and investigate spillover of extreme events across borders. We find that a large part of the jumps in the local markets are due to the U.S. market and the regional market. The U.S. contribution to the variances is in general below the contribution from the regional market. In general, we observe an increasing integration during the last two decades, which, to some extent, can be related to the advancement of the European Union. Furthermore, we show that the identification of the jumps can be used as a useful signal for portfolio reallocation.     

基于分位数关联的政策连续性跨国溢出研究

本文采用基于条件分位数的溢出指数方法,研究了不同冲击规模及方向下政策连续性的跨国溢出,考察相较于中间状态,极端上升与下降状态下的溢出变化及两者之间的非对称溢出效应,并构建相对溢入溢出指数,研究极端冲击对不同国家方向性溢出的异质性影响。研究发现:(1)政策连续性的总溢出以及各国溢入水平在不同条件分位数下呈U形结构,冲击规模对总溢出及各国溢入水平具有显著的正向影响。(2)在极端状态下,总溢出和大部分国家方向性溢出水平较中间状态显著提升,并且极端上升与下降状态具有非对称的溢出效应。其中,总溢出在极端下降状态涨幅更大,各国的溢出比溢入在两种极端状态下表现出更强烈的非对称性。(3)极端冲击的影响具有国别异质性,中国的方向性溢出水平大幅上升,对发达国家的左尾定向溢出加强,国际影响力显著增强。本文研究不仅对极端状态下保持经济系统稳定具有启示意义,也可为建设“双循环”新发展格局提供实证支持。     

The economic value of volatility timing with realized jumps

This paper comprehensively investigates the role of realized jumps detected from high frequency data in predicting future volatility from both statistical and economic perspectives. Using seven major jump tests, we show that separating jumps from diffusion improves volatility forecasting both in-sample and out-of-sample. Moreover, we show that these statistical improvements can be translated into economic value. We find that a risk-averse investor can significantly improve her portfolio performance by incorporating realized jumps into a volatility timing based portfolio strategy. Our results hold true across the majority of jump tests, and are robust to controlling for microstructure effects and transaction costs.     

Linear-quadratic term structure models – Toward the understanding of jumps in interest rates

We study linear-quadratic term structure models with random jumps in the short rate process where the jump arrival rate follows a stochastic process. Empirical results based on the US data show that incorporating stochastic jump intensity significantly improves model fit to the dynamics of both interest rate and volatility term structure. Our results also show that jump intensity is negatively correlated with interest rate changes and the average size is larger on the downside than upside. Examining the relation between jump intensity and macroeconomic shocks, we find that at monthly frequency, jumps are neither triggered by nor predictive of changes in macroeconomic variables. At daily frequency, however, we document interesting patterns for jumps associated with information shocks.     

Earning the right premium on the right factor in portfolio planning

The optimal portfolio as well as the utility from trading stocks and derivatives depends on the risk factors and on their market prices of risk. We analyze this dependence for a CRRA investor in models with stochastic volatility, jumps in the stock price, and jumps in volatility. We find that the compartment of the total variance into diffusion risk and jump risk has a small impact on the utility in an incomplete market only. In contrast, the decomposition of the equity risk premium into a diffusion component and a jump risk component and the compartment of the latter into its various elements has a huge impact on the utility in a complete market. The more extreme the market prices of risk, i.e. the more they deviate from their equilibrium values, the larger the utility of the investor. Additionally, we show that the structure of the optimal exposures to jump risk crucially depends on which elements of jump risk are priced.     

Cojumps in stock prices: Empirical evidence

We examine contemporaneous jumps (cojumps) among individual stocks and a proxy for the market portfolio. We show, through a Monte Carlo study, that using intraday jump tests and a coexceedance criterion to detect cojumps has a power similar to the cojump test proposed by Bollerslev et al. (2008). However, we also show that we should not expect to detect all common jumps comprising a cojump when using such coexceedance based detection methods. Empirically, we provide evidence of an association between jumps in the market portfolio and cojumps in the underlying stocks. Consistent with our Monte Carlo evidence, moderate numbers of stocks are often detected to be involved in these (systematic) cojumps. Importantly, the results suggest that market-level news is able to generate simultaneous large jumps in individual stocks. We also find evidence of an association between systematic cojumps and Federal Funds Target Rate announcements.     

When do jumps matter for portfolio optimization?

We consider the continuous-time portfolio optimization problem of an investor with constant relative risk aversion who maximizes expected utility of terminal wealth. The risky asset follows a jump-diffusion model with a diffusion state variable. We propose an approximation method that replaces the jumps by a diffusion and solve the resulting problem analytically. Furthermore, we provide explicit bounds on the true optimal strategy and the relative wealth equivalent loss that do not rely on quantities known only in the true model. We apply our method to a calibrated affine model. Our findings are threefold: Jumps matter more, i.e. our approximation is less accurate, if (i) the expected jump size or (ii) the jump intensity is large. Fixing the average impact of jumps, we find that (iii) rare, but severe jumps matter more than frequent, but small jumps.     

European equity markets volatility spillover: Destabilizing energy risk is the new normal

While energy risk is increasingly recognized as a systemic risk, there is limited comprehensive analysis of the risk propagation in regional contexts. In this study, we examine oil and natural gas price changes and shocks in relation to equity market returns and volatility for 24 European Economic Area (EEA) countries. In addition to traditional panel regressions, we also deploy the Diebold-Yilmaz (2014) spillover index for a closed network analysis. We differentiate in the cross-section across the core EU block, PIIGS countries, EU enlargement countries joining after 2004, and other non-EU countries, to provide insights into the ongoing debates on the European energy market stability. While we find evidence of the manifestation of energy risk throughout the sample period, we find that until 2019 the primary sources of volatility spillover in the EEA economic network arose from economic or political uncertainty. Energy risks, measured by large crude oil and natural gas price shocks also significantly contributed to equity market volatility, with increasing volatility risk arising from natural gas, a green labelled energy source after 2019. Last, we show that CEEC equity markets are more sensitive to oil and natural gas price shocks when domestic currencies depreciate against the Euro.     

Contingent Claims on Foreign Assets Following Jump-Diffusion Processes

In this paper we price contingent claims on several foreign assetsthat follow jump-diffusion processes. Discontinuities (jumps) arise dueto the assets' movement in the respective countries, or the exchangerates, or both. We assume the existence of multiple classes (sources)of jumps. Each jump can affect one or more state-variables and is definedby its intensity of arrival and by the joint probability distributionof its magnitude. The existence of jumps gives rise to significant deviationsfrom the joint lognormality assumptions of the multivariate geometricBrownian motion, and affords more flexibility in capturing the empiricallyobserved asymmetry and fat tails in asset returns. Analytic solutionsare provided for the European option on the best of several assets withoutor with exchange rate (quanto-type) protection. A Markov-chainnumerical method that can also handle American claims is given and itsaccuracy is demonstrated. Neglecting the effect of jumps causes seriousmisspricing and leads to erroneous decision-making when purchasing orexercising such options.     

主权债务风险跨国溢出研究——来自频域的新证据

本文从国家间主权债务风险溢出的持续期角度出发,采用基于广义方差分解谱表示的BK溢出指数方法,首次从频域视角对短期和长期下的主权债务风险跨国溢出效应进行研究。研究发现:第一,短期和长期下的主权债务风险跨国溢出效应均较为显著,并且时域下的总溢出主要由短期的风险溢出主导。第二,14个国家的短期和长期风险输出水平呈线性关系,但对于风险输入,不同类型国家出现分化并形成两个聚类,新兴市场国家的短期风险输入水平远高于长期,其具有较强的“短期脆弱性”。第三,风险输出国的自身风险越大,对他国的长期溢出水平越高,风险输入国的自身风险越大,接收他国的短期溢出水平越高,并且两两国家间的进出口规模、金融市场一体化水平和经济周期协同性与其长期风险溢出水平呈正相关关系,而与其短期风险溢出水平的关系并不显著。第四,短期和长期的主权债务风险溢出网络都呈现明显的区域聚集特征,并且各国在短期溢出网络中主要与同区域以及经济金融环境相似的国家连接,在长期溢出网络中则通过经贸关系将连接范围扩大至不同区域甚至经济金融环境差异较大的国家。     

Double-jump diffusion model for VIX: evidence from VVIX

This paper studies the continuous-time dynamics of VIX with stochastic volatility and jumps in VIX and volatility. Built on the general parametric affine model with stochastic volatility and jumps in the logarithm of VIX, we derive a linear relationship between the stochastic volatility factor and the VVIX index. We detect the existence of a co-jump of VIX and VVIX and put forward a double-jump stochastic volatility model for VIX through its joint property with VVIX. Using the VVIX index as a proxy for stochastic volatility, we use the MCMC method to estimate the dynamics of VIX. Comparing nested models of VIX, we show that the jump in VIX and the volatility factor are statistically significant. The jump intensity is also stochastic. We analyse the impact of the jump factor on VIX dynamics.     

Modeling Mortality With Jumps: Applications to Mortality Securitization

In this article, we incorporate a jump process into the original Lee–Carter model, and use it to forecast mortality rates and analyze mortality securitization. We explore alternative models with transitory versus permanent jump effects and find that modeling mortality via transitory jump effects may be more appropriate in mortality securitization. We use the Swiss Re mortality bond in 2003 as an example to show how to apply our model together with the distortion measure approach to value mortality-linked securities. Pricing the Swiss Re mortality bond is challenging because the mortality index is correlated across countries and over time. Cox, Lin, and Wang (2006) employ the normalized multivariate exponential tilting to take into account correlations across countries, but the problem of correlation over time remains unsolved. We show in this article how to account for the correlations of the mortality index over time by simulating the mortality index and changing the measure on paths.     

Using implied volatility jumps for realized volatility forecasting: Evidence from the Chinese market

This study examines the Chinese implied volatility index (iVIX) to determine whether jump information from the index is useful for volatility forecasting of the Shanghai Stock Exchange 50ETF. Specifically, we consider the jump sizes and intensities of the 50ETF and iVIX as well as cojumps. The findings show that both the jump size and intensity of the 50ETF can improve the forecasting accuracy of the 50ETF volatility. Moreover, we find that the jump size and intensity of the iVIX provide no significant predictive ability in any forecasting horizon. The cojump intensity of the 50ETF and iVIX is a powerful predictor for volatility forecasting of the 50ETF in all forecasting horizons, and the cojump size is helpful for forecasting in short forecasting horizon. In addition, for a one-day forecasting horizon, the iVIX jump size in the cojump is more predictive of future volatility than that of the 50ETF when simultaneous jumps occur. Our empirical results are robust and consistent. This work provides new insights into predicting asset volatility with greater accuracy.