The effects of structural breaks and long memory on currency hedging

Empirical evidence suggests that unconditional variance of exchange rate return series is subject to occasional structural breaks that may induce spurious phenomenon of high persistence and long memory of volatility processes. In this study, we investigate the effects of such breaks on estimated risk-minimizing hedge strategies (ratios) and their performance in currency markets. Using bivariate GARCH (BGARCH) and fractionally integrated GARCH models, we estimate the hedge ratios for six foreign currencies in the full sample with and without controlling for breaks and each subsample of different unconditional variance regimes identified by a modified version of the Inclan C, and Tiao GC (1994) algorithm. Our findings suggest that daily currency risk can be better hedged with currency futures when controlling for unconditional variance breaks in the BGARCH model. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 30:607–632, 2010     

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     

Optimal hedging with a regime‐switching time‐varying correlation GARCH model

The authors develop a Markov regime‐switching time‐varying correlation generalized autoregressive conditional heteroscedasticity (RS‐TVC GARCH) model for estimating optimal hedge ratios. The RS‐TVC nests within it both the time‐varying correlation GARCH (TVC) and the constant correlation GARCH (CC). Point estimates based on the Nikkei 225 and the Hang Seng index futures data show that the RS‐TVC outperforms the CC and the TVC both in‐ and out‐of‐sample in terms of variance reduction. Based on H. White's (2000) reality check, the null hypothesis of no improvement of the RS‐TVC over the TVC is rejected for the Nikkei 225 index contract but is not rejected for the Hang Seng index contract. © 2007 Wiley Periodicals, Inc. Jrl Fut Mark 27:495–516, 2007     

Forecasting volatility

The forecasting ability of the most popular volatility forecasting models is examined and an alternative model developed. Existing models are compared in terms of four attributes: (1) the relative weighting of recent versus older observations, (2) the estimation criterion, (3) the trade‐off in terms of out‐of‐sample forecasting error between simple and complex models, and (4) the emphasis placed on large shocks. As in previous studies, we find that financial markets have longer memories than reflected in GARCH(1,1) model estimates, but find this has little impact on outofsample forecasting ability. While more complex models which allow a more flexible weighting pattern than the exponential model forecast better on an in‐sample basis, due to the additional estimation error introduced by additional parameters, they forecast poorly out‐of‐sample. With the exception of GARCH models, we find that models based on absolute return deviations generally forecast volatility better than otherwise equivalent models based on squared return deviations. Among the most popular time series models, we find that GARCH(1,1) generally yields better forecasts than the historical standard deviation and exponentially weighted moving average models, though between GARCH and EGARCH there is no clear favorite. However, in terms of forecast accuracy, all are dominated by a new, simple, nonlinear least squares model, based on historical absolute return deviations, that we develop and test here. © 2005 Wiley Periodicals, Inc. Jrl Fut Mark 25:465–490, 2005     

The finite sample properties of the GARCH option pricing model

The authors explore the finite sample properties of the generalized autoregressive conditional heteroscedasticity (GARCH) option pricing model proposed by S. L. Heston and S. Nandi (2000). Simulation results show that the maximum likelihood estimators of the GARCH process may contain substantial estimation biases, even when samples as large as 3,000 observations are used. However, it was found that these biases cause significant mispricings only for short‐term, out‐of‐the‐money options. It is shown that, given an adequate estimation sample, this bias can be reduced considerably by employing the jackknife resampling method. © 2007 Wiley Periodicals, Inc. Jrl Fut Mark 27:599–615, 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     

Stock return dynamics,option volume,and the information content of implied volatility

This article reports new empirical results on the information content of implied volatility, with respect to modeling and forecasting the volatility of individual firm returns. The 50 firms with the highest option volume on the Chicago Board Options Exchange between 1988 and 1995 are examined. First, the results indicate that the ability of implied volatility to subsume all relevant information about conditional variance depends on option trading volume. For the most active options in the sample, implied volatility reliably outperforms GARCH and subsumes all information in return shocks beyond the first lag. For these active options, implied volatility performs substantially better than indicated by the prior results of Lamoureux and Lastrapes ( 1993 ), despite significant methodological improvements in the time‐series volatility models in this study including the use of high‐frequency intraday return shocks. For the lower option‐volume firms in the sample, the performance of implied volatility deteriorates relative to time‐series volatility models. Finally, compared to a time‐series approach, the implied volatility of equity index options provides reliable incremental information about future firm‐level volatility. © 2003 Wiley Periodicals, Inc. Jrl Fut Mark 23:615–646, 2003     

A copula‐based regime‐switching GARCH model for optimal futures hedging

The article develops a regime‐switching Gumbel–Clayton (RSGC) copula GARCH model for optimal futures hedging. There are three major contributions of RSGC. First, the dependence of spot and futures return series in RSGC is modeled using switching copula instead of assuming bivariate normality. Second, RSGC adopts an independent switching Generalized Autoregressive Conditional Heteroscedasticity (GARCH) process to avoid the path‐dependency problem. Third, based on the assumption of independent switching, a formula is derived for calculating the minimum variance hedge ratio. Empirical investigation in agricultural commodity markets reveals that RSGC provides good out‐of‐sample hedging effectiveness, illustrating importance of modeling regime shift and asymmetric dependence for futures hedging. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 29:946–972, 2009     

The Cross‐Currency Hedging Performance of Implied Versus Statistical Forecasting Models

This article examines the ability of several models to generate optimal hedge ratios. Statistical models employed include univariate and multivariate generalized autoregressive conditionally heteroscedastic (GARCH) models, and exponentially weighted and simple moving averages. The variances of the hedged portfolios derived using these hedge ratios are compared with those based on market expectations implied by the prices of traded options. One‐month and three‐month hedging horizons are considered for four currency pairs. Overall, it has been found that an exponentially weighted moving‐average model leads to lower portfolio variances than any of the GARCH‐based, implied or time‐invariant approaches. © 2001 John Wiley & Sons, Inc. Jrl Fut Mark 21:1043–1069, 2001     

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     

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     

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     

The bias in time series volatility forecasts

By Jensen's inequality, a model's forecasts of the variance and standard deviation of returns cannot both be unbiased. This study explores the bias in GARCH type model forecasts of the standard deviation of returns, which we argue is the more appropriate volatility measure for most financial applications. For a wide variety of markets, the GARCH, EGARCH, and GJR (or TGARCH) models tend to persistently over‐estimate the standard deviation of returns, whereas the ARLS model of L. Ederington and W. Guan (2005a) does not. Furthermore, the GARCH and GJR forecasts are especially biased following high volatility days, which cause a large jump in forecast volatility, which is rarely fully realized. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 30:305–323, 2010     

Volatility Spillovers and the Risk-Return Relation Between Stock and Foreign Exchange Markets in Brazil

We examine the evidence of mean and volatility spillovers between stock and foreign exchange markets in Brazil with multivariate GARCH models and nonlinear Granger causality tests. We also use a multivariate GARCH-in-mean model to assess the relationship between risk and return in these markets. The results indicate that the stock market leads the foreign exchange market in price formation and that nonlinear Granger causalities from the exchange market to the stock market do occur. Part of these nonlinear causalities are explained by volatility spillovers. We show that exchange rate volatility affects not only stock market volatility but also stock returns.     

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.     

Asymmetrical reaction to US stock-return news: evidence from major stock markets based on a double-threshold model

This paper examines the hypothesis that both stock returns and volatility are asymmetrical functions of past information from the US market. By employing a double-threshold GARCH model to investigate six major index-return series, we find strong evidence supporting the asymmetrical hypothesis of stock returns. Specifically, negative news from the US market will cause a larger decline in a national stock return than an equal magnitude of good news. This holds true for the volatility series. The variance appears to be more volatile when bad news impacts the market than when good news does.     

Optimal Futures Hedging Under Multichain Markov Regime Switching

Most of the existing Markov regime switching GARCH‐hedging models assume a common switching dynamic for spot and futures returns. In this study, we release this assumption and suggest a multichain Markov regime switching GARCH (MCSG) model for estimating state‐dependent time‐varying minimum variance hedge ratios. Empirical results from commodity futures hedging show that MCSG creates hedging gains, compared with single‐state‐variable regime‐switching GARCH models. Moreover, we find an average of 24% cross‐regime probability, indicating the importance of modeling cross‐regime dynamic in developing optimal futures hedging strategies. © 2012 Wiley Periodicals, Inc. Jrl Fut Mark 34:173–202, 2014     

Pricing VIX futures: Evidence from integrated physical and risk‐neutral probability measures

This study derives closed‐form solutions to the fair value of VIX (volatility index) futures under alternate stochastic variance models with simultaneous jumps both in the asset price and variance processes. Model parameters are estimated using an integrated analysis of integrated volatility and VIX time series from April 21, 2004 to April 18, 2006. The stochastic volatility model with price jumps outperforms for the short‐dated futures, whereas additionally including a state‐dependent volatility jump can further reduce out‐of‐sample pricing errors for other futures maturities. Finally, adding volatility jumps enhances hedging performance except for the short‐dated futures on a daily‐rebalanced basis. © 2007 Wiley Periodicals, Inc. Jrl Fut Mark 27:1175–1217, 2007     

Long memory in commodity futures volatility: A wavelet perspective

The authors reexamine the volatility of agricultural commodity futures for evidence of fractional integration, providing new empirical results and extending the extant literature in important dimensions. First, they utilize two relatively new estimators based on wavelets, which are generally superior to, for example, the popular estimator by J. Geweke and S. Porter‐Hudak (GPH; 1983) and exact maximum likelihood estimators (MLEs) on the basis of mean squared error (MSE). Second, they provide simulations to contrast their point estimates with those obtained by a fractionally integrated GARCH (generalized autoregressive conditional heteroscedasticity) model. Third, they conduct a wavelet coef.cient decomposition of futures volatility. They .nd that futures volatilities display the self‐similarity property consistent with long memory and that futures volatilities exhibit persistent long memory with .nite unconditional variance. © 2007 Wiley Periodicals, Inc. Jrl Fut Mark 27:411–437, 2007     

Revisiting the risk/return relations in the Asian Pacific markets: New evidence from alternative models

This paper examines the risk/return relations in eleven Asian Pacific stock markets and explores if the 1997 Asian financial crisis significantly influenced market behavior in the region. We use a plain vanilla time-series regression approach as well as various GARCH models. Although results significantly vary across model specifications, the overall evidence from GARCH models supports a significantly positive risk/return relation in several markets but only prior to the Asian financial crisis. These results accord with Glosten et al. (1993) and Harvey (2001) and suggest that the relative risk aversion is sensitive to both model specifications and structural breaks.