The Relation between Physical and Risk‐neutral Cumulants

Variance swaps are natural instruments for investors taking directional bets on volatility and are often used for portfolio protection. The empirical observation on skewness research suggests that derivative professionals may also desire to hedge beyond volatility risk and there exists the need to hedge higher‐moment market risks, such as skewness and kurtosis risks. We study two derivative contracts – skewness swap and kurtosis swap – which trade the forward realized third and fourth cumulants. Using S&P 500 index options data from 1996 to 2005, we document the returns of these swap contracts, i.e., skewness risk premium and kurtosis risk premium. We find that the both skewness and kurtosis risk premiums are significantly negative.     

Smiling less at LIFFE

This study investigates the structure of the implied volatility smile, using the prices of equity options traded on the LIFFE. First, the slope of the implied volatility curve is significantly negative for both individual stocks and index options, and the slope is less negative for longer‐term options. The implied volatility skew can be described by risk‐neutral skewness and kurtosis, with the former having the first‐order effect. Moreover, the implied volatility skew for individual stock options is less severe than for index options. Finally, the relationship between the real and risk‐neutral moments implied in option prices is significant. The results indicate that, for equity options traded on the LIFFE, the slope of the implied volatility skew is flatter than that on the Chicago Board of Exchange (CBOE). © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 28:57–81, 2008     

中国证券市场波动的区制关联性

应用单变量和二元向量SW-ARCH模型,本文发现我国证券市场收益率波动具有明显的"区制转移"特征,可以将其分为"高波动"和"低波动"两个区制.在"高波动区制"下,沪深两市间具有明显的波动"溢出"和"传染"特征,市场整体风险强;相反,在"低波动区制"下,市场间主要表现"低系统风险"特征,负相关的波动关联性使证券市场具有较强的风险分散功能和较高的资金配置效率.     

Volatility and shock interactions and risk management implications: Evidence from the U.S. and frontier markets

The study affords comprehensive evidence of shock and volatility interactions between stock markets of each of the twenty four frontier markets and the U.S. for the period 2006:01 to 2015:07. The results from the recent EDCC-GARCH model of Nakatani and Teräsvirta (2009), which permits for concurrent estimation of shock and volatility interactions as well as dynamic conditional correlations (DCC) across assets, shows unidirectional shock and volatility transmissions from the U.S. to the frontier markets. The conditional correlation between the U.S. and each frontier market is very low or negative, offering diversification benefits to U.S. investors. The DCC exhibits slow decay and is insignificantly impacted by previous period's shocks. The results are very intuitive for optimal portfolio allocations using the traditional capital-based as well as the risk-based allocations. The risk parity approach to portfolio management increases (reduces) allocations to lower (higher) risk assets to improve portfolio diversification while increasing the risk-adjusted returns.     

Return and Volatility Dynamics in the Spot and Futures Markets in Australia: An Intervention Analysis in a Bivariate EGARCH‐X Framework

This article provides evidence of linkages between the equity market and the index futures market in Australia, where the futures market has experienced a major structural event due to the futures contract respecification. A bivariate Exponential Generalized Autoregressive Conditional Heteroskedasticity (EGARCH) model is developed that includes a cointegrating residual as an explanatory variable for both the conditional mean and the conditional variance. The conditional mean returns from both markets are influenced by the long‐run equilibrium relationship, and these markets are informationally linked through the second moments. The crossmarket spillovers exhibit asymmetric behavior in that the volatility responses to past standardized innovations are different for market advances and market retreats. An intervention analysis shows that some of the parameters describing the return‐generating process have shifted after the contract respecification by the futures exchange. © 2001 John Wiley & Sons, Inc. Jrl Fut Mark 21:833–850, 2001     

Information content of cross‐sectional option prices: A comparison of alternative currency option pricing models on the Japanese yen

This article implements a currency option pricing model for the general case of stochastic volatility, stochastic interest rates, and jumps in an attempt to reconcile levels of risk‐neutral skewness and kurtosis with observed option prices on the Japanese yen and to analyze the information content of the cross section of option prices by investigating the hedging and pricing performance of various currency option pricing models. The study makes use of both a method of moments and a more traditional generalized‐least‐squares (GLS) estimation technique, taking advantage of the fact that methods of moments do not specifically require the use of cross‐sectional option prices, whereas GLS does. Results centered around the Asia economic crisis of 1997 and 1998 indicate that the cross section of option prices surprisingly does not appear to contain superior information as the two estimation techniques yield relatively similar results once idiosyncratic differences between them are acknowledged. Extensions of the G. Bakshi, C. Cao, and Z. Chen (1997) results to currencies are also provided. © 2006Wiley Periodicals, Inc. Jrl Fut Mark 26:33–59, 2006     

Half-day trading and spillovers

This paper investigates the linkage of returns and volatilities between the United States and Chinese stock markets from January 2010 to March 2020. We use the dynamic conditional correlation (DCC) and asymmetric Baba–Engle–Kraft–Kroner (BEKK) GARCH models to calculate the time-varying correlations of these two markets and examine the return and volatility spillover effects between these two markets. The empirical results show that there are only unidirectional return spillovers from the U.S. stock market to the Chinese stock market. The U.S. stock market has a consistently positive spillover to China’s next day’s morning trading, but its impact on China’s next day’s afternoon trading appears to be insignificant. This finding implies that information in the U.S. stock market impacts the performance of the Chinese stock market differently in distinct semi-day trading. Moreover, with respect to the volatility, there are significant bidirectional spillover effects between these two markets.     

Interdependence of international equity variances: Evidence from East Asian markets

This paper investigates the interdependence of volatility in six East Asian markets. We first model the returns in a VAR-BEKK framework to obtain the conditional variances, and then apply the vector-autoregressive model (VAR) to the six-market variances. The results of VAR estimation show that the interdependence of equity market conditional variances is high. The Japanese market, while being the most exogenous and the least susceptible to volatility stimuli from other markets, is the most influential in transmitting volatility to the other East Asian markets.     

Power arch modelling of the volatility of emerging equity markets

In developed equity markets the APARCH model of Ding, Granger and Engle [Ding, Z., Granger, C. and Engle, R., 1993. A long memory property of stock market returns and a new model. Journal of Empirical Finance 1, 83–106] has proven to be useful in modelling the leverage and asymmetry effects; power transformations and long memory; and non-normal conditional error distributions that characterise the data. Extending the analysis of Jayasuriya, Shambora and Rossiter [Jayasuriya, S., Shambora, W. and Rossiter, R., 2005. Asymmetric volatility in mature and emerging markets, Working Paper, Ohio University.] to a wider set of emerging markets this paper explores the applicability of the model to emerging markets. The key findings are as follows. First, unlike developed markets where a power term of unity and a conditional standard deviation model appears to be appropriate, emerging markets demonstrate a considerably greater range of power values. Second, unlike developed markets where non-normal conditional error distributions appear to fit the data well, there are a set of emerging markets for which estimation problems arise with a conditional t distribution, and a conditional normal distribution appears to be the preferred option. Third, the degree of volatility asymmetry appears to vary across the set of emerging markets, with the Middle Eastern and African markets having very different volatility asymmetry characteristics to those of the Latin American markets.     

The impact of volatility derivatives on S&P500 volatility

This study investigates whether the newly cultivated platform of volatility derivatives has altered the volatility of the underlying S&P500 index. The findings suggest that the onset of the volatility derivatives trading has lowered the volatility of both the cash market volatility and the cash market index, and significantly reduced the impact of shocks to volatility. When big sudden events hit financial markets, however, the volatility of volatility seems to elevate in the U.S. equity market as a result of increased global correlations. Regardless of the period under examination and the estimator employed, long‐run volatility persistence is present. The latter drops significantly when the credit crunch period is excluded from the post‐event date sample period. The correlation between the broad equity index and the return volatility remains low, which in turn strengthens the role of volatility derivatives to facilitate portfolio diversification. The analysis also shows that volatility is mean reverting, whereas market data support the impact of information asymmetries on conditional volatility. In the post‐event date phase, no asymmetries are found when the recent crisis is not accounted for. Finally, comparisons with other international equity indices, with no volatility derivatives listed, unveil that these indices exhibit higher volatility and slower recovery from shocks than the S&P500 index. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 29:1190–1213, 2009     

PSEUDODIFFUSIONS AND QUADRATIC TERM STRUCTURE MODELS

The non-Gaussianity of processes observed in financial markets and the relatively good performance of Gaussian models can be reconciled by replacing the Brownian motion with Lévy processes whose Lévy densities decay as  exp(−λ| x |)  or faster, where  λ > 0  is large. This leads to asymptotic pricing models. The leading term, P ₀, is the price in the Gaussian model with the same instantaneous drift and variance. The first correction term depends on the instantaneous moments of order up to 3, that is, the skewness is taken into account, the next term depends on moments of order 4 (kurtosis) as well, etc. In empirical studies, the asymptotic formula can be applied without explicit specification of the underlying process: it suffices to assume that the instantaneous moments of order greater than 2 are small w.r.t. moments of order 1 and 2, and use empirical data on moments of order up to 3 or 4. As an application, the bond-pricing problem in the non-Gaussian quadratic term structure model is solved. For pricing of options near expiry, a different set of asymptotic formulas is developed; they require more detailed specification of the process, especially of its jump part. The leading terms of these formulas depend on the jump part of the process only, so that they can be used in empirical studies to identify the jump characteristics of the process.     

我国股票市场收益、交易量、波动性动态关系的实证分析

本文对我国股票市场上证指数和深圳成指的收益、交易量、波动性之间的动态关系进行了实证研究,研究结果表明:收益和绝对收益与交易量之间均存在正相关关系;收益与交易量以及绝对收益与交易量之间存在双向Granger因果关系(线性或非线性);深圳成指收益的波动方差对收益具有正向作用,而上证指数收益的波动方差对收益没有直接的影响;上证指数和深圳成指的成交量对股指收益的波动方差不具有解释作用.     

Return Dynamics when Persistence is Unobservable

This paper proposes a new theory of the sources of time-varying second (and higher) moments in financial time series. The key idea is that fully rational agents must infer the stochastic degree of persistence of fundamental shocks. Endogenous changes in their uncertainty determine the evolution of conditional moments of returns. The model accounts for the principal observed features of volatility dynamics and implies some new ones. Most strikingly, it implies a relationship between ex post trends, or momentum, and changes in volatility.     

The roles of news and volatility in stock market correlations during the global financial crisis

The global financial crisis has again brought the interdependencies of international financial markets to the fore, particularly during times of financial crises. This paper explores the relative roles of news and volatility in explaining the changes in correlations between national stock markets during the global financial crisis. Our results show that the majority of the correlations are more strongly explained by volatility rather than news. However as the global financial crisis evolves the relative role of news grows in importance.     

Contemporary and long-run correlations: A covariance component model and studies on the S&P 500 cash and futures markets

In this article, a multivariate component model for conditional asset return covariance is developed as an extension to the univariate volatility component model of Engle & Lee (1999). The conditional covariance now is decomposed into a long-run (trend) component and a short-run (transitory) component. Through the decomposition, relationships like the long-run correlation and volatility copersistence can be studied solely upon examining the long-run trend of the conditional covariance. The decomposition also has important implications in studying portfolio hedging problems such as the multi-period minimum-variance hedging for long-term portfolio management. The empirical study in this article focuses on estimating the covariance component structure between the S&P 500 cash and futures markets and their contemporary and long-run correlation relationship and the volatility copersistence relationship. © John Wiley & Sons, Inc. Jrl Fut Mark 19: 877–894, 1999     

International financial integration: Stock return linkages and volatility transmission between Vietnam and advanced countries

This paper investigates the interdependence between the Vietnamese stock market and other influential equity markets in terms of return linkage and volatility transmission covering the period including pre, during and post the 2008 Global Financial Crisis. A VAR model is utilized to estimate the conditional return linkage among these indices and a GARCH-BEKK model is employed to investigate the volatility transmission. We find evidence of statistically significant correlation, return spillover and volatility linkage between Vietnamese stock market with other leading equity markets of the US, Hong Kong and Japan. Moreover, we find that during the financial crisis, stock markets become more interrelated.     

The Changing Role of Financial Stress,Oil Price,and Gold Price in Financial Contagion among US and BRIC Markets

The objective of this paper is to explore the determining factors behind financial contagion between US and BRIC (Brazil, Russia, India, and China) equity markets. To this end, we investigate the effects of global macroeconomic factors on the time‐varying correlations among these markets obtained by asymmetric dynamic conditional correlation method. Utilizing quantile regression analysis, we examine the determinants of financial contagion at different levels of time‐varying correlations. The results of quantile regression analyses reveal that global financial crisis (GFC) (2008) leads to changes in the dependence structure between dynamic conditional correlations among equity markets and global macroeconomic factors, such as global financial stress, oil prices, and gold prices. Following the GFC, monetary, and fiscal policy changes in the BRIC markets and hence changing macroeconomic risks of these markets are conducive to these changes. Our findings also demonstrate the importance of cross‐market rebalancing channel for information transmission across US and BRIC markets.     

The information content of implied volatility in agricultural commodity markets

In this article we compare the incremental information content of lagged implied volatility to GARCH models of conditional volatility for a collection of agricultural commodities traded on the New York Board of Trade. We also assess the relevance of the additional information provided by the implied volatility in a risk management framework. It is first shown that past squared returns only marginally improve the information content provided by the lagged implied volatility. Secondly, value‐at‐risk (VaR) models that rely exclusively on lagged implied volatility perform as well as VaR models where the conditional variance is modelled according to GARCH type processes. These results indicate that the implied volatility for options on futures contracts in agricultural commodity markets provides relevant volatility information that can be used as an input to VaR models. © 2003 Wiley Periodicals, Inc. Jrl Fut Mark 23:441–454, 2003     

波动率风险溢酬:基于香港和美国期权市场的研究

文章运用方差互换合约的思想,从香港恒生指数和美国S&P500指数现货和期权的价格中提炼出无模型波动率风险溢酬,并对其特征进行了考察。研究结果表明,香港股市和美国股市中的波动率风险的确被定价,且风险溢酬显著为负,说明两市投资者均体现出风险厌恶。但同时我们也发现两个市场投资者的行为模式存在差异。此外,香港和美国市场的波动率风险相关度很高,且存在明显的溢出效应。     

Emerging Equity Market Volatility

Abstract

This paper considers two emerging markets that are under-researched, Kenya and Nigeria. It offers a comprehensive view of four time properties that emerged from the empirical time series literature on asset returns: (1) the predictability of returns from past observations; (2) the auto-regressive behavior of conditional volatility; (3) the asymmetric response of conditional volatility to innovations; and (4) the conditional variance risk premium. Results of the exponential GARCH (EGARCH) model indicate that asymmetric volatility found in the U.S. and other developed markets also characterized the Nigerian stock exchange. In Kenya, however, the asymmetric volatility coefficient is significant and positive, suggesting that positive shocks increase volatility more than negative shocks of an equal magnitude. The Nairobi Stock Exchange (KSE) returns series report negative but insignificant risk-premium parameters. In Nigeria (NSE), return series exhibit a significant and positive time-varying risk premium. The results also show that expected returns are predictable, that the auto-regressive return parameters (? ₁ ) are significant in both Kenya and Nigeria. Finally, the GARCH parameter (b) is statistically significant, indicating that volatility persistence is present in the two emerging markets studied.