Yiu Kuen Tse

A Multivariate Generalized Autoregressive Conditional Heteroscedasticity Model with Time-Varying Correlations

In this article we propose a new multivariate generalized autoregressive conditional heteroscedasticity (MGARCH) model with time-varying correlations. We adopt the vech representation based on the conditional variances and the conditional correlations. Whereas each conditional-variance term is assumed to follow a univariate GARCH formulation, the conditional-correlation matrix is postulated to follow an autoregressive moving average type of analog. Our new model retains the intuition and interpretation of the univariate GARCH model and yet satisfies the positive-definite condition as found in the constant-correlation and Baba–Engle–Kraft–Kroner models. We report some Monte Carlo results on the finite-sample distributions of the maximum likelihood estimate of the varying-correlation MGARCH model. The new model is applied to some real data sets.

A test for constant correlations in a multivariate GARCH model

We introduce a Lagrange Multiplier (LM) test for the constant-correlation hypothesis in a multivariate GARCH model. The test examines the restrictions imposed on a model which encompasses the constant-correlation multivariate GARCH model. It requires the estimates of the constant-correlation model only and is computationally convenient. We report some Monte Carlo results on the finite-sample properties of the LM statistic. The LM test is compared against the Information Matrix (IM) test due to Bera and Kim (1996). The LM test appears to have good power against the alternatives considered and is more robust to nonnormality. We apply the test to three data sets, namely, spot-futures prices, foreign exchange rates and stock market returns. The results show that the spot-futures and foreign exchange data have constant correlations, while the correlations across national stock market returns are time varying.

The conditional heteroscedasticity of the yen–dollar exchange rate

This paper examines the conditional heteroscedasticity of the yen-dollar exchange rate. A model is constructed by extending the asymmetric power autoregressive conditional heteroscedasticity model to a process that is fractionally integrated. It is found that, unlike the equity markets, the appreciation and depreciation shocks of the yen against the dollar have similar effects on future volatilities. Although the results reject both the stable and the integrated models, our analysis of the response coefficients of the past shocks and the application of the models to the estimation of the capital requirements for trading the currencies show that there are no substantial differences between the fractionally integrated models and the stable models.

Some Recent Developments in Futures Hedging

The use of futures contracts as a hedging instrument has been the focus of much research. At the theoretical level, an optimal hedge strategy is traditionally based on the expected-utility maximization paradigm. A simplification of this paradigm leads to the minimum-variance criterion. Although this paradigm is quite well accepted, alternative approaches have been sought. At the empirical level, research on futures hedging has benefited from the recent developments in the econometrics literature. Much research has been done on improving the estimation of the optimal hedge ratio. As more is known about the statistical properties of financial time series, more sophisticated estimation methods are proposed. In this survey we review some recent developments in futures hedging. We delineate the theoretical underpinning of various methods and discuss the econometric implementation of the methods. Copyright 2002 by Blackwell Publishers Ltd

Evaluating the hedging performance of the constant-correlation GARCH model

This paper compares the performances of the hedge ratios estimated from the OLS (ordinary least squares) method and the constant-correlation VGARCH (vector generalized autoregressive conditional heteroscedasticity) model. These methods are evaluated based on the out-of-sample optimal hedge ratio forecasts. A systematic comparison is provided by examining ten spot and futures markets covering currency futures, commodity futures and stock index futures. Using a recently proposed test (Tse, 2000) for the constant-correlation assumption, it is found that the assumption cannot be rejected for eight of the ten series. To gain the maximum benefit of a time-varying hedging strategy the estimation data is kept up-to-date for the re-estimation of the hedge ratios. Both the constant hedge ratio (using OLS) and the timevarying hedge ratio (using constant-correlation VGARCH) are re-estimated on a day-by-day rollover, and the post-sample variances of the hedged portfolios are examined. It is found that the OLS hedge ratio performs better than the VGARCH hedge ratio. This result may be another indication that the forecasts generated by the VGARCH models are too variable.

A Monte Carlo investigation of some tests for stochastic dominance

This paper compares the performance of several tests for stochastic dominance up to order three using Monte Carlo methods. The tests considered are the Davidson and Duclos (2000) test, the Anderson test (1996) and the Kaur, Rao and Singh (1994) test. Only unpaired samples of independent observations are considered, as this is a restriction for both the Anderson and Kaur–Rao–Singh tests. We find that the Davidson–Duclos test appears to be the best. The Kaur–Rao–Singh test is overly conservative and does not compare favorably against the Davidson–Duclos and Anderson tests in terms of power.

Hedging downside risk with futures contracts

This paper considers a futures hedge strategy that minimizes the lower partial moments; such a strategy minimizes the downside risk and is consistent with the expected utility hypothesis. Two statistical methods are adopted to estimate the optimal hedge ratios: the empirical distribution function method and the kernel density estimation method. Both methods are applied to the Nikkei Stock Average (NSA) spot and futures markets. It is found that, for a hedger who is willing to absorb small losses but otherwise extremely cautious about large losses, the optimal hedge strategy that minimizes the lower partial moments may be sharply different from the minimum variance hedge strategy. If a hedger cares for downside-only risk, then the conventional minimum variance hedge strategy is inappropriate. The methods presented in this paper will be useful in these scenarios.

Stock returns volatility in the Tokyo stock exchange

Abstract This paper examines the stock returns volatility in the Tokyo Stock Exchange in the period 1986 through 1989. Structures of returns volatility are estimated and forecasted. Models of autoregressive conditional heteroscedasticity (ARCH) are fitted to the stock returns. It is found that the returns series exhibit significant ARCH and GARCH effects with nonnormality. Based on fitted ARCH and GARCH models in the period 1986 through 1987 we forecast the volatility of returns in 1988 through 1989. The ARCH/GARCH forecast are compared with a benchmark value, a naive forecast and an exponential weighted moving average (EWMA) forecast. The results show that the EWMA method gives the best forecasts. These findings have implications in forecasting movements of market volatility, with applications to option pricing and control for variation margin risk in stock index futures.

Fractional cointegration and futures hedging

This article examines the performance of various hedge ratios estimated from different econometric models: The FIEC model is introduced as a new model for estimating the hedge ratio. Utilized in this study are NSA futures data, along with the ARFIMA‐GARCH approach, the EC model, and the VAR model. Our analysis identifies the prevalence of a fractional cointegration relationship. The effects of incorporating such a relationship into futures hedging are investigated, as is the relative performance of various models with respect to different hedge horizons. Findings include: (i) Incorporation of conditional heteroskedasticity improves hedging performance; (ii) the hedge ratio of the EC model is consistently larger than that of the FIEC model, with the EC providing better post‐sample hedging performance in the return–risk context; (iii) the EC hedging strategy (for longer hedge horizons of ten days or more) incorporating conditional heteroskedasticty is the dominant strategy; (iv) incorporating the fractional cointegration relationship does not improve the hedging performance over the EC model; (v) the conventional regression method provides the worst hedging outcomes for hedge horizons of five days or more. Whether these results (based on the NSA index) can be generalized to other cases is proposed as a topic for further research.

Conditional Volatility in Foreign Exchange Rates: Evidence from the Malaysian Ringgit and Singapore Dollar

Abstract In this paper we examine the conditional volatility of the exchange rates of two Asia-Pacific currencies. These are the Malaysian ringgit-US dollar and the Singapore dollar-US dollar exchange rates. Both currencies are under relatively intervention-free managed-float systems. We employ the new class of APARCH model of Ding et al. (1993) to capture the possibly asymmetric effects of exchange shocks on future volatilities. In addition, we take account of the nonnormality in the residuals by using f-distributed errors . Similar to the findings for the major currencies under flexible exchange rate systems, the exchange rates of the two Asia-Pacific currencies demonstrate conditional heteroscedasticity and are adequately described by the APARCH model. We also find that a depreciation shock in the Malaysian ringgit against the US dollar has a greater effect on future volatilities than an appreciation shock of the same magnitude. However, such asymmetric effects are not significant in the Singapore market.