Value at risk and conditional extreme value theory via markov regime switching models

This study develops a new conditional extreme value theory‐based (EVT) model that incorporates the Markov regime switching process to forecast extreme risks in the stock markets. The study combines the Markov switching ARCH (SWARCH) model (which uses different sets of parameters for various states to cope with the structural changes for measuring the time‐varying volatility of the return distribution) with the EVT to model the tail distribution of the SWARCH processed residuals. The model is compared with unconditional EVT and conditional EVT‐GARCH models to estimate the extreme losses in three leading stock indices: S&P 500 Index, Hang Seng Index and Hang Seng China Enterprise Index. The study found that the EVT‐SWARCH model outperformed both the GARCH and SWARCH models in capturing the non‐normality and in providing accurate value‐at‐risk forecasts in the in‐sample and out‐sample tests. The EVTSWARCH model, which exhibits the features of measuring the volatility of a heteroscedastic financial return series and coping with the non‐normality owing to structural changes, can be an alternative measure of the tail risk. © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 28:155–181, 2008     

Time‐varying jump risk premia in stock index futures returns

This study tests the presence of time‐varying risk premia associated with extreme news events or jumps in stock index futures return. The model allows for a dynamic jump component with autoregressive jump intensity, long‐range dependence in volatility dynamics, and a volatility in mean structure separately for the normal and extreme news events. The results show significant jump risk premia in four stock market index futures returns including the DAX, FTSE, Nikkei, and S&P500 indices. Our results are robust to various specifications of conditional variance including the plain GARCH, component GARCH, and Fractionally Integrated GARCH models. We also find the time‐varying risk premium associated with normal news events is not significant across all indices. © 2011 Wiley Periodicals, Inc. Jrl Fut Mark 32:639–659, 2012     

股指期货动态套期保值率研究——基于DCC-MVGARCH模型

本文利用传统的回归模型(OLS)、双变量向量自回归模型(VAR)、双变量向量误差修正模型(VECM)和动态条件自相关双变量GARCH模型(DCC-MVGARCH)对恒生指数期货、标准普尔500指数期货、日经225指数期货、我国的沪深300指数期货的最优套期保值比率进行了估计,并采用基于风险最小化的方法对4种模型的套期保值有效性进行了比较。结果双变量向量误差修正模型估计出的最优套期保值比率更大,对4种模型的套期保值有效性的检验表明,采用动态条件自相关双变量GARCH模型(DCC-MVGARCH)估计得到的最优套期保值比率进行套期保值的效果,并非优于采用传统回归模型、双变量向量自回归模型、双变量向量误差修正模型估计得到的套期保值比率进行套期保值的效果。     

Price discovery in the hang seng index markets: Index,futures, and the tracker fund

In this paper, price discovery among the Hang Seng Index markets is investigated using the Hasbrouck and Gonzalo and Granger common‐factor models and the multivariate generalized autoregressive conditional heteroskedasticity (M‐GARCH) model. Minute‐by‐minute data from the Hang Seng Index, Hang Seng Index futures, and the tracker fund show that the movements of the three markets are interrelated. The futures markets contain the most information, followed by the spot market. The tracker fund does not contribute to the price discovery process. The three markets exhibit spillover effects, indicating that their second moments are linked, even though the flow of information from the tracker fund to the other markets is minimal. Overall results suggest that the three markets have different degrees of information processing abilities, although they are governed by the same set of macroeconomic fundamentals. © 2004 Wiley Periodicals, Inc. Jrl Fut Mark 24:887–907, 2004     

Do small traders contribute to price discovery? Evidence from the Hong Kong Hang Seng Index markets

Using one‐contract‐size trades in the Mini Hang Seng Index futures to proxy the activities of small traders, this study empirically investigates the information contribution of small futures traders to price discovery on the Hang Seng Index (HSI) markets. Estimated with the models of Gonzalo, J., and Granger, C. W. J. ( 1995 ) and Hasbrouck, J. ( 1995 ), the results show that small traders contribute about 16.8% to price discovery, a disproportionately high share considering their relatively low trading volume. The results also indicate that the Hang Seng Index futures (HSIF) market still has the largest information share (about 71.0%), whereas the HSI spot market has a 12.2% share. Our results suggest that small traders are not uninformed in the HSIF markets, and play an important role in price discovery. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 30:156–174, 2010     

A simplified approach to modeling the co‐movement of asset returns

The authors propose a simplified multivariate GARCH (generalized autoregressive conditional heteroscedasticity) model (the S‐GARCH model), which involves the estimation of only univariate GARCH models, both for the individual return series and for the sum and difference of each pair of series. The covariance between each pair of return series is then imputed from these variance estimates. The proposed model is considerably easier to estimate than existing multivariate GARCH models and does not suffer from the convergence problems that characterize many of these models. Moreover, the model can be easily extended to include more complex dynamics or alternative forms of the GARCH specification. The S‐GARCH model is used to estimate the minimum‐variance hedge ratio for the FTSE (Financial Times and the London Stock Exchange) 100 Index portfolio, hedged using index futures, and compared to four of the most widely used multivariate GARCH models. Using both statistical and economic evaluation criteria, it was found that the S‐GARCH model performs at least as well as the other models that were considered, and in some cases it was better. © 2007 Wiley Periodicals, Inc. Jrl Fut Mark 27:575–598, 2007     

Asymmetric covariance in spot‐futures markets

This article studies how the spot‐futures conditional covariance matrix responds to positive and negative innovations. The main results of the article are achieved by obtaining the Volatility Impulse Response Function (VIRF) for asymmetric multivariate GARCH structures, extending Lin (1997) findings for symmetric GARCH models. This theoretical result is general and can be applied to analyze covariance dynamics in any financial system. After testing how multivariate GARCH models clean up volatility asymmetries, the Asymmetric VIRF is computed for the Spanish stock index IBEX‐35 and its futures contract. The empirical results indicate that the spot‐futures variance system is more sensitive to negative than positive shocks, and that spot volatility shocks have much more impact on futures volatility than vice versa. Additionally, evidence is obtained showing that optimal hedge ratios are insensitive to the well‐known asymmetric volatility behavior in stock markets. © 2003 Wiley Periodicals, Inc. Jrl Fut Mark 23:1019–1046, 2003     

A random coefficient autoregressive Markov regime switching model for dynamic futures hedging

The random coefficient autoregressive Markov regime switching model (RCARRS) for estimating optimal hedge ratios, which generalizes the random coefficient autoregressive (RCAR) and Markov regime switching (MRS) models, is introduced. RCARRS, RCAR, MRS, BEKK‐GARCH, CC‐GARCH, and OLS are compared with the use of aluminum and lead futures data. RCARRS outperforms all models out‐of‐sample for lead and is second only to BEKK‐GARCH for aluminum in terms of variancereduction point estimates. White's data‐snooping reality check null hypothesis of no superiority is rejected for BEKK‐GARCH and RCARRS for aluminum, but not for lead. © 2006 Wiley Periodicals, Inc. Jrl Fut Mark 26:103–129, 2006     

Dynamic hedging with futures: A copula‐based GARCH model

In a number of earlier studies it has been demonstrated that the traditional regression‐based static approach is inappropriate for hedging with futures, with the result that a variety of alternative dynamic hedging strategies have emerged. In this study the authors propose a class of new copula‐based GARCH models for the estimation of the optimal hedge ratio and compare their effectiveness with that of other hedging models, including the conventional static, the constant conditional correlation (CCC) GARCH, and the dynamic conditional correlation (DCC) GARCH models. With regard to the reduction of variance in the returns of hedged portfolios, the empirical results show that in both the in‐sample and out‐of‐sample tests, with full flexibility in the distribution specifications, the copula‐based GARCH models perform more effectively than other dynamic hedging models. © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 28:1095–1116, 2008     

Pricing dynamics of index options and index futures in Hong Kong before and during the Asian financial crisis

This article studies the impact of the Asian financial crisis on index options and index futures markets in Hong Kong. We employed a time‐stamped transaction data set of the Hang Seng Index options and futures contracts that were traded on the Hong Kong Futures Exchange. The results show that during the crisis period, the arbitrage profits, and the standard deviations of these profits increased in both ex‐post and ex‐ante analyses. In a market turbulent time, market volatility brings a higher arbitrage profit level. However, despite the increased market volatility, the profitability of the arbitrage trades declined substantially with longer execution time lags in the ex‐ante analysis. This suggests that the HSI futures and options markets are mature and resilient. A multiple regression analysis on the ex‐post arbitrage profit also suggests that there were structural changes during the Asian financial crisis and the Hong Kong government intervention periods. © 2000 John Wiley & Sons, Inc. Jrl Fut Mark 20: 145–166, 2000     

Nonlinear asymmetric models of the short‐term interest rate

This study introduces a generalized discrete time framework to evaluate the empirical performance of a wide variety of well‐known models in capturing the dynamic behavior of short‐term interest rates. A new class of models that displays nonlinearity and asymmetry in the drift, and incorporates the level effect and stochastic volatility in the diffusion function is introduced in discrete time and tested against the popular diffusion, GARCH, and level‐GARCH models. Based on the statistical test results, the existing models are strongly rejected in favor of the newly proposed models because of the nonlinear asymmetric drift of the short rate, and the presence of nonlinearity, GARCH, and level effects in its volatility. The empirical results indicate that the nonlinear asymmetric models are better than the existing models in forecasting the future level and volatility of interest rate changes. © 2006 Wiley Periodicals, Inc. Jrl Fut Mark 26:869–894, 2006     

Regime‐switching in stock index and Treasury futures returns and measures of stock market stress

We investigate bivariate regime‐switching in daily futures‐contract returns for the US stock index and ten‐year Treasury notes over the crisis‐rich 1997–2005 period. We allow the return means, volatilities, and correlation to all vary across regimes. We document a striking contrast between regimes, with a high‐stress regime that exhibits a much higher stock volatility, a much lower stock–bond correlation, and a higher mean bond return. The high‐stress regime is associated with higher average values of stock‐implied volatility, stock illiquidity, and stock and bond futures trading volume. The lagged implied volatility from equity‐index options is useful in modeling the time‐varying transition probabilities of the regime‐switching process. Our findings support the notions that: (1) stock market stress can have a material influence on Treasury bond pricing, and (2) the diversification benefits of combined stock–bond holdings tend to be greater during times with relatively high stock market stress. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 30:753–779, 2010     

Futures hedging when the structure of the underlying asset changes: The case of the BIFFEX contract

This article is concerned with the hedging effectiveness of futures contracts whose underlying asset is an index, when the structure of this index is changing. The case of the freight futures (BIFFEX) contract is examined here. Investigation of this issue is particularly interesting as the composition of its underlying asset, the Baltic Freight Index (BFI), has been revised on a number of occasions in order to improve the hedging performance of the market; previous empirical evidence on the market indicates substantially lower variance reduction (4–19%), compared to other markets (up to 98%). The BFI is a weighted average dry‐cargo freight rate index, compiled from actual freight rates on 11 shipping routes that are dissimilar in terms of vessel sizes and transported commodities. The hedging effectiveness of the market is investigated using both constant and time‐varying hedge ratios, estimated through bivariate error correction GARCH models. Our results indicate that the effectiveness of the BIFFEX contract as a centre for risk management has strengthened over the recent years as a result of the more homogeneous composition of the index. This by itself indicates that the latest restructuring of the index, in November 1999, which is aimed at increasing its homogeneity even further, is likely to have a beneficial impact on the market. © 2000 John Wiley & Sons, Inc. Jrl Fut Mark 20:775–801, 2000     

Volatility and maturity effects in the Nikkei index futures

Many financial data series are found to exhibit stochastic volatility. Some of these time series are constructed from contracts with time-varying maturities. In this paper, we focus on index futures, an important subclass of such time series. We propose a bivariate GARCH model with the maturity effect to describe the joint dynamics of the spot index and the futures-spot basis. The setup makes it possible to examine the Samuelson effect as well as to compare the hedge ratios under scenarios with and without the maturity effect. The Nikkei-225 index and its futures are used in our empirical analysis. Contrary to the Samuelson effect, we find that the volatility of the futures price decreases when the contract is closer to its maturity. We also apply our model to futures hedging, and find that both the optimal hedge ratio and the hedging effectiveness critically depend on both the maturity and GARCH effects. © 1999 John Wiley & Sons, Inc. Jrl Fut Mark 19: 895–909, 1999     

A note on the performance of regime switching hedge strategy

We characterize conditions under which the regime switching (RS) hedge strategy will perform better than the ordinary least squares (OLS) hedge strategy. The result can be extended to the case where the GARCH effects prevail. Specifically, these conditions would allow the RS‐GARCH hedge strategy to dominate both OLS and GARCH hedge strategies. © 2011 Wiley Periodicals, Inc. Jrl Fut Mark     

The contribution of a satellite market to price discovery: Evidence from the Singapore exchange

The Singapore Exchange (SGX), a small satellite market, successfully competes with a large home market, the Osaka Securities Exchange (OSE), in trading the Nikkei 225 futures index. In this paper, we investigate the contribution of the SGX to price discovery and shed light on the reasons for its continued success. Evidence is provided from information revelation and price discovery of three competing but informationally linked markets of the Nikkei 225 index—domestic spot (Tokyo Stock Exchange), domestic futures (OSE), and foreign futures (SGX), which represents the satellite market. Overall, the futures market contributes 77% to price discovery, with the satellite market contributing 42% of the futures and 33% of the total price discovery. These figures, surprisingly, far exceed the satellite market's share of trading volume. Support is provided for the extended trading hours on the SGX for three of the four non‐overlapping trading sub‐periods. © 2004 Wiley Periodicals, Inc. Jrl Fut Mark 24:981–1004, 2004     

Information content of extended trading for index futures

The recent extension of trading hours for Hang Seng Index Futures provides an opportunity to examine whether extended futures trading contains useful information about spot returns. Using the weighted price contribution measure, we find that pre‐open futures trades are associated with significant price discovery. We extend the model from T. Hiraki, E. D. Maberly, and N. Takezawa (1995) and adjust for the existence of a pre‐open trading session and the overnight trading of cross‐listed shares in London. Our results indicate that extended trading for index futures contains useful information in explaining subsequent spot returns during the trading day. © 2004 Wiley Periodicals, Inc. Jrl Fut Mark 24:861–886, 2004     

Variance risk premiums and predictive power of alternative forward variances in the corn market

We propose a fear index for corn using the variance swap rate synthesized from out‐of‐the‐money call and put options as a measure of implied variance. We find negative and time‐varying variance risk premiums (realized variance minus implied variance) in the corn market from 1987 to 2009. Our results contrast with Egelkraut, Garcia, and Sherrick (2007), but are in line with the findings of Simon (2002). We conclude that our synthesized model‐free implied variance estimation procedure contains superior information about future realized variance relative to traditional model‐dependent estimating procedures: the implied variance model by Black (1976) and the seasonal GARCH(1, 1) forecasted variance model. © 2011 Wiley Periodicals, Inc. Jrl Fut Mark 32:587–608, 2012     

Price discovery and investor structure in stock index futures

Previous literature on price discovery in stock index futures and spot markets neglects the role of different investor groups. This study relates time‐varying spot‐futures linkages studied within a VECM‐DCC‐GARCH framework to changes in the investor structure of the futures market over time. Empirical results suggest that during the dominance of presumably uninformed private investors, the futures market does not contribute to price discovery. By contrast, there is evidence of information flows from futures to spot markets and a significant increase in conditional correlation between both markets as institutional investors' share in trading volume increases. We derive implications for the design of emerging futures markets. © 2010 Wiley Periodicals, Inc. Jrl Fut Mark31:282–306, 2011     

VIX futures and its closed‐form pricing through an affine GARCH model with realized variance

This paper studies the forecasting of volatility index (VIX) and the pricing of its futures by a generalized affine realized volatility model proposed by Christoffersen et al. This model is a weighted average of a GARCH and a pure realized variance (RV) model that incorporates each volatility component into the new dynamics. We rewrite the VIX in terms of both volatility components and then derive closed‐form formulas for the VIX forecasting and its futures pricing. Our empirical studies find that a unification of the GARCH and the RV in the modeling substantially improves the forecasting of this index and the pricing of its futures.