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     

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     

Option pricing under Markov‐switching GARCH processes

This study proposes an N ‐state Markov‐switching general autoregressive conditionally heteroskedastic (MS‐GARCH) option model and develops a new lattice algorithm to price derivatives under this framework. The MS‐GARCH option model allows volatility dynamics switching between different GARCH processes with a hidden Markov chain, thus exhibiting high flexibility in capturing the dynamics of financial variables. To measure the pricing performance of the MS‐GARCH lattice algorithm, we investigate the convergence of European option prices produced on the new lattice to their true values as conducted by the simulation. These results are very satisfactory. The empirical evidence also suggests that the MS‐GARCH model performs well in fitting the data in‐sample and one‐week‐ahead out‐of‐sample prediction. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 30:444–464, 2010     

A Markov regime‐switching ARMA approach for hedging stock indices

This study considers the hedging effectiveness of applying the N‐state Markov regime‐switching autoregressive moving‐average (MRS‐ARMA) model to the S&P‐500 and FTSE‐100 markets. The distinguishingfeature of this study is to incorporate the observations of serially correlated stockreturns into the hedging analysis. To resolve the problem of N^T possible routes induced by the presence of MA parameters associated with the algorithm of Hamilton JD ( 1989 ) and a sample of size T, we propose an algorithm by combining the ideas of Hamilton JD ( 1989 ) and Gray SF ( 1996 ). We find that the hedging performances of the three proposed MRS‐MA(1) strategies herein are superior to their corresponding MRS counterparts considered in Alizadeh A and Nomikos N ( 2004 ) over the out‐of‐sample periods, even when we realistically track the transaction costs generated from rebalancing the hedged portfolios. © 2010 Wiley Periodicals, Inc. Jrl Fut Mark 31:165–191, 2011     

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     

A Markov regime switching approach for hedging stock indices

In this paper we describe a new approach for determining time‐varying minimum variance hedge ratio in stock index futures markets by using Markov Regime Switching (MRS) models. The rationale behind the use of these models stems from the fact that the dynamic relationship between spot and futures returns may be characterized by regime shifts, which, in turn, suggests that by allowing the hedge ratio to be dependent upon the “state of the market,” one may obtain more efficient hedge ratios and hence, superior hedging performance compared to other methods in the literature. The performance of the MRS hedge ratios is compared to that of alternative models such as GARCH, Error Correction and OLS in the FTSE 100 and S&P 500 markets. In and out‐of‐sample tests indicate that MRS hedge ratios outperform the other models in reducing portfolio risk in the FTSE 100 market. In the S&P 500 market the MRS model outperforms the other hedging strategies only within sample. Overall, the results indicate that by using MRS models market agents may be able to increase the performance of their hedges, measured in terms of variance reduction and increase in their utility. © 2004 Wiley Periodicals, Inc. Jrl Fut Mark 24:649–674, 2004     

Switching asymmetric GARCH and options on a volatility index

Few proposed types of derivative securities have attracted as much attention and interest as option contracts on volatility. Grunbichler and Longstaff (1996) is the only study that proposes a model to value options written on a volatility index. Their model, which is based on modeling volatility as a GARCH process, does not take into account the switching regime and asymmetry properties of volatility. We show that the Grunbichler and Longstaff (1996) model underprices a three‐month option by about 10%. A Switching Regime Asymmetric GARCH is used to model the generating process of security returns. The comparison between the switching regime model and the traditional uni‐regime model among GARCH, EGARCH, and GJR‐GARCH demonstrates that a switching regime EGARCH model fits the data best. Next, the values of European call options written on a volatility index are computed using Monte Carlo integration. When comparing the values of the option based on the Switching Regime Asymmetric GARCH model and the traditional GARCH specification, it is found that the option values obtained from the different processes are very different. This clearly shows that the Grunbichler‐Longstaff model is too stylized to be used in pricing derivatives on a volatility index. © 2004 Wiley Periodicals, Inc. Jrl Fut Mark 24:251–282, 2004     

The Asymmetric Commodity Inventory Effect on the Optimal Hedge Ratio

Hedging strategies for commodity prices largely rely on dynamic models to compute optimal hedge ratios. This study illustrates the importance of considering the commodity inventory effect (effect by which the commodity price volatility increases more after a positive shock than after a negative shock of the same magnitude) in modeling the variance–covariance dynamics. We show by in‐sample and out‐of‐sample forecasts that a commodity price index portfolio optimized by an asymmetric BEKK–GARCH model outperforms the symmetric BEKK, static (OLS), or naïve models. Robustness checks on a set of commodities and by an alternative mean‐variance optimization framework confirm the relevance of taking into account the inventory effect in commodity hedging strategies.     

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     

Short Rate Dynamics and Regime Shifts*

We characterize the dynamics of the US short‐term interest rate using a Markov regime‐switching model. Using a test developed by Garcia, we show that there are two regimes in the data: In one regime, the short rate behaves like a random walk with low volatility; in another regime, it exhibits strong mean reversion and high volatility. In our model, the sensitivity of interest rate volatility to the level of interest rate is much lower than what is commonly found in the literature. We also show that the findings of nonlinear drift in Aït‐Sahalia and Stanton, using nonparametric methods, are consistent with our regime‐switching model.     

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     

Jumping hedges: An examination of movements in copper spot and futures markets

Price risk is an important factor for both copper purchasers, who use the commodity as a major input in their production process, and copper refiners, who must deal with cash‐flow volatility. Information from NYMEX cash and futures prices is used to examine optimal hedging behavior for agents in copper markets. A bivariate GARCH‐jump model with autoregressive jump intensity is proposed to capture the features of the joint distribution of cash and futures returns over two subperiods with different dominant pricing regimes. It is found that during the earlier producerpricing regime this specification is not needed, whereas for the later exchange pricing era jump dynamics stemming from a common jump across cash and futures series are significant in explaining the dynamics in both daily and weekly data sets. Results from the model are used to under‐take both within‐sample and out‐of‐sample hedging exercises. These results indicate that there are important gains to be made from a time‐varying optimal hedging strategy that incorporates the information from the common jump dynamics. © 2006 Wiley Periodicals, Inc. Jrl Fut Mark 26:169–188, 2006     

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 Tunisian stock market index volatility: Long memory vs. switching regime

This paper investigates the dilemma of long memory versus a switching regime for the Tunisian stock market index volatility. Precisely, different specifications of the Fractionally Integrated GARCH (FIGARCH) model of Baillie et al. (1996) and Switching ARCH (SWARCH) model of Hamilton and Susmel (1994) have been estimated under both Gaussian and Student error distributions.The empirical results show that the Student FIGARCH(1,d,1) specification outperforms the Markov switching ARCH model. In addition, the empirical results indicate that the long memory behavior observed in the Tunisian stock price (TUNINDEX) volatility is a true behavior and is not spuriously created by changes in regimes.     

Aggregate Australian Takeovers: A Review of Markov Regime Switching Models

This article reviews the case of modeling merger waves in the Australian market for the period 1972–2004. Three Markov switching models are examined, the Gaussian AR(1), Poisson AR(1), and State‐Space autoregressive moving average (ARMA) (1,1), to find which gives the best fit. The State‐Space Markov switching ARMA(1,1) model is found to be the best for describing Australian takeover activity as estimation results based on it have a lower Bayesian information criterion score than the other two models. Each model's ability to predict a ‘wave’ is then tested by including its estimated probability in a macroeconomic model to explain merger activity. The State‐Space model also performs better because the inclusion of its estimated probability substantially increases the explanatory power of the regression model (measured by the regression adjusted R²). In addition, it predicted a takeover wave in 2009, which was closer to the actual incidents of takeover activity in the market at that time than the predictions of the other two models. The results are robust when the measure of takeover activity is changed from the number of takeover bids to the proportion of takeover bids relatively to the number of exchange‐listed companies. JEL classification: G34, C32.     

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     

What explains default risk premium during the financial crisis? Evidence from Japan

As is well documented, subprime mortgage markets carried significant default risk. This paper investigates the relationship between default risk premium, stock market conditions and macroeconomic variables during the financial crisis. Using iTraxx Japan Credit Default Swap (CDS) index spreads covering the period from March 2006 to November 2009, we employ a time-varying dynamic factor model with Markov regime switching to generate regime probabilities for default risk. We analyze the sensitivity of default risk premium changes to stock market conditions and macroeconomic variables by using two-state Markov switching models: a crisis regime sparked by rising loan defaults in the sub-prime mortgage market, and a non-crisis regime. We found strong evidence that the relationship between default risk premium changes, stock market and macroeconomic variables is regime-dependent. Our results suggest that during periods of crisis, CDS indices behave as a higher-risk indicator and become more sensitive to stock market conditions and macroeconomic variables. This paper examines the effects of the financial crisis in explaining the default risk premium. Understanding the determinants of default risk premium is important for financial analysts, economic policy makers and credit risk management.     

Testing mean reversion in financial market volatility: Evidence from S&P 500 index futures

This article presents a comprehensive study of continuous time GARCH (generalized autoregressive conditional heteroskedastic) modeling with the thintailed normal and the fat‐tailed Student's‐t and generalized error distributions (GED). The study measures the degree of mean reversion in financial market volatility based on the relationship between discrete‐time GARCH and continuoustime diffusion models. The convergence results based on the aforementioned distribution functions are shown to have similar implications for testing mean reversion in stochastic volatility. Alternative models are compared in terms of their ability to capture mean‐reverting behavior of futures market volatility. The empirical evidence obtained from the S&P 500 index futures indicates that the conditional variance, log‐variance, and standard deviation of futures returns are pulled back to some long‐run average level over time. The study also compares the performance of alternative GARCH models with normal, Student's‐ t, and GED density in terms of their power to predict one‐day‐ahead realized volatility of index futures returns and provides some implications for pricing futures options. © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 28:1–33, 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     

Markov switching GARCH models of currency turmoil in Southeast Asia

This paper analyzes exchange rate turmoil with a Markov switching GARCH model. We distinguish between two different regimes in both the conditional mean and the conditional variance: “ordinary” regime, characterized by low exchange rate changes and low volatility, and “turbulent” regime, characterized by high exchange rate devaluation and high volatility. We also allow the transition probabilities to vary over time as functions of economic and financial indicators. We find that real effective exchange rates, money supply relative to reserves, stock index returns, and bank stock index returns and volatility contain valuable information for identifying turbulent and ordinary periods.