EMPIRICAL PERFORMANCE OF GARCH MODELS WITH HEAVY‐TAILED INNOVATIONS

We introduce a new type of heavy‐tailed distribution, the normal reciprocal inverse Gaussian distribution (NRIG), to the GARCH and Glosten‐Jagannathan‐Runkle (1993) GARCH models, and compare its empirical performance with two other popular types of heavy‐tailed distribution, the Student's t distribution and the normal inverse Gaussian distribution (NIG), using a variety of asset return series. Our results illustrate that there is no overwhelmingly dominant distribution in fitting the data under the GARCH framework, although the NRIG distribution performs slightly better than the other two types of distribution. For market indexes series, it is important to introduce both GJR‐terms and the NRIG distribution to improve the models’ performance, but it is ambiguous for individual stock prices series. Our results also show the GJR‐GARCH NRIG model has practical advantages in quantitative risk management. Finally, the convergence of numerical solutions in maximum‐likelihood estimation of GARCH and GJR‐GARCH models with the three types of heavy‐tailed distribution is investigated.     

An analysis of option pricing under systematic consumption risk using GARCH

An issue in the pricing of contingent claims is whether to account for consumption risk. This is relevant for contingent claims on stock indices, such as the FTSE 100 share price index, as investor’s desire for smooth consumption is often used to explain risk premiums on stock market portfolios, but is not used to explain risk premiums on contingent claims themselves. This paper addresses this fundamental question by allowing for consumption in an economy to be correlated with returns. Daily data on the FTSE 100 share price index are used to compare three option pricing models: the Black–Scholes option pricing model, a GARCH (1, 1) model priced under a risk-neutral framework, and a GARCH (1, 1) model priced under systematic consumption risk. The findings are that accounting for systematic consumption risk only provides improved accuracy for in-the-money call options. When the correlation between consumption and returns increases, the model that accounts for consumption risk will produce lower call option prices than observed prices for in-the-money call options. These results combined imply that the potential consumption-related premium in the market for contingent claims is constant in the case of FTSE 100 index options.     

Information Flows across Markets: Evidence from China–Backed Stocks Dual–Listed in Hong Kong and New York

Using a bivariate generalized autoregressive conditional heteroskedasticity (GARCH) model, we examine patterns of information flows for China–backed stocks that are cross–listed on exchanges in Hong Kong and New York. Results analyzing the dual–listed stocks indicate significant mutual feedback of information between domestic (Hong Kong) and offshore (New York) markets in terms of pricing and volatility. Stocks listed on the domestic market appear to play a more significant role of information transmission in the pricing process, whereas stocks listed on the offshore market play a bigger role in volatility spillover.     

The impacts of Hong Kong’s Currency Board reforms on the interbank market

Among the economies with a Currency Board System (CBS), Hong Kong (HK) is probably the one with the largest and most developed financial sector, as well as the highest capital mobility. Hence, studying HK’s CBS is not only crucial to HK, but also important for the understanding of the modern CBS. This paper outlines the major monetary reforms in HK since the late 1980s. The impacts of these reforms and the 1997–1998 Asian Financial Crisis are then examined empirically. We focus on the differentials between the US and HK interbank interest rates. We assume the conditional-mean equation follows an autoregressive process and the conditional-variance equation follows a generalized autoregressive conditional heteroscedasticity process. This model captures the time-varying level and volatility of the differential. In light of the empirical results we provide an assessment of the reforms in HK.     

Backtesting Value-at-Risk: A Duration-Based Approach

Financial risk model evaluation or backtesting is a key partof the internal model's approach to market risk management aslaid out by the Basle Committee on Banking Supervision. However,existing backtesting methods have relatively low power in realisticsmall sample settings. Our contribution is the exploration ofnew tools for backtesting based on the duration of days betweenthe violations of the Value-at-Risk. Our Monte Carlo resultsshow that in realistic situations, the new duration-based testshave considerably better power properties than the previouslysuggested tests.     

Modelling soccer matches using bivariate discrete distributions with general dependence structure

In this paper copulas are used to generate bivariate discrete distributions. These distributions are fitted to soccer data from the English Premier League. An interesting aspect of these data is that the primary variable of interest, the discrete pair shots-for and shots-against, exhibits negative dependence; thus, in particular, we apply bivariate Poisson-related distributions that allow such dependence. The paper focuses on Archimedian copulas, for which the dependence structure is fully determined by a one-dimensional projection that is invariant under marginal transformations. Diagnostic plots for copula fit based on this projection are adapted to deal with discrete variables. Covariates relating to within-match contributions such as numbers of passes and tackles are introduced to explain variability in shot outcomes. The results of this analysis would appear to support the notion that playing the 'beautiful game' is an effective strategy—more passes and crosses contribute to more effective play and more shots on the goal.     

The relevance of currency risk in the EMU

We investigate how the elimination of intra-European exchange risk may affect international financial markets using a conditional version of the International CAPM. We estimate the EMU and non-EMU components of aggregate currency risk and document significant exposures to both. The premium for EMU risk is positive and associated with exposure to the French, Italian and Spanish currencies. The premium for non-EMU risk is consistently negative and accounts for most of the aggregate currency premiums. In the 1990s, exposures to EMU risk declined significantly while exposures to non-EMU risk increased. Hence the adoption of the Euro is unlikely to have a large impact on aggregate currency risk premiums.     

A new bivariate distribution in natural exponential family

We propose a new bivariate distribution following a GLM form i.e., natural exponential family given the constantly correlated covariance matrix. The proposed distribution can represent an independent bivariate gamma distribution as a special case. In order to derive the distribution we utilize an integrating factor method to satisfy the integrability condition of the quasi-score function. The derived distribution becomes a mixture of discrete and absolute continuous distributions. The proposal of our new bivariate distribution will make it possible to develop some bivariate generalized linear models. Further the discrete correlated bivariate distribution will also arise from an independent bivariate Poisson mass function by compounding our proposed distribution (Iwasaki and Tsubaki, 2002).Received March 2003