Bas J. M. Werker

Testing for Mean‐Variance Spanning with Short Sales Constraints and Transaction Costs: The Case of Emerging Markets

We propose regression-based tests for mean-variance spanning in the case where investors face market frictions such as short sales constraints and transaction costs. We test whether U.S. investors can extend their efficient set by investing in emerging markets when accounting for such frictions. For the period after the major liberalizations in the emerging markets, we find strong evidence for diversification benefits when market frictions are excluded, but this evidence disappears when investors face short sales constraints or small transaction costs. Although simulations suggest that there is a possible small-sample bias, this bias appears to be too small to affect our conclusions. Copyright The American Finance Association 2001.

Closing the GARCH gap: Continuous time GARCH modeling

Abstract It is the purpose of this paper to build a bridge between continuous time models, which are central in the modern finance literature, and (weak) GARCH processes in discrete time, which often provide parsimonious descriptions of the observed data. The properties of continuous time processes which exhibit GARCH-type behavior at all discrete frequencies will be discussed. Several examples of such processes illustrate the general theory. The class of continuous time GARCH models can be divided into two subclasses. In the first group (GARCH diffusions) the sample paths are smooth and in the other group (GARCH jump-diffusions) the sample paths are erratic. A simple, complete characterization of both types is given in terms of the kurtosis of the observed discrete time data. These two groups of GARCH processes can be described by three and four coefficients, respectively. Explicit formulas of all implied discrete time weak GARCH parameters are available. Moreover, knowledge of the discrete time GARCH parameters at only one frequency completely determines the continuous time coefficients of the GARCH process. So, in estimating a continuous time GARCH process it suffices to estimate the discrete time GARCH parameters for the available data frequency. The analysis carries over to models with an autoregressive component.

Adaptive estimation in time series models

In a framework particularly suited for many time-series models we obtain a LAN result under quite natural and economical conditions. This enables us to construct adaptive estimators for (part of) the Euclidean parameter in these semiparametric models. Special attention is directed to group models in time series with the important subclass of models with time varying location and scale. Our set-up is confronted with the existing literature and, as examples, we reconsider linear regression and ARMA, TAR and ARCH models.

Semiparametric Duration Models

In this article we consider semiparametric duration models and efficient estimation of the parameters in a non-iid environment. In contrast to classical time series models where innovations are assumed to be iid we show that in, for example, the often-used autoregressive conditional duration (ACD) model, the assumption of independent innovations is too restrictive to describe financial durations accurately. Therefore, we consider semiparametric extensions of the standard specification that allow for arbitrary kinds of dependencies between the innovations. The exact nonparametric specification of these dependencies determines the flexibility of the semiparametric model. We calculate semiparametric efficiency bounds for the ACD parameters, discuss the construction of efficient estimators, and study the efficiency loss of the exponential pseudolikelihood procedure. This efficiency loss proves to be sizeable in applications. For durations observed on the Paris Bourse for the Alcatel stock in July and August 1996, the proposed semiparametric procedures clearly outperform pseudolikelihood procedures. We analyze these efficiency gains using a simulation study confirming that, at least at the Paris Bourse, dependencies among rescaled durations can be exploited.

Conditions for the asymptotic semiparametric efficiency of an omnibus estimator of dependence parameters in copula models

Oakes (1994) described in broad terms an omnibus semiparametric procedure for estimating the dependence parameter in a copula model when marginal distributions are treated as (infinite-dimensional) nuisance parameters. The resulting estimator was subsequently shown to be consistent and normally distributed asymptotically (Genest et al. 1995, Shih and Louis 1995). Conditions under which it is also semiparametrically efficient in large samples are given. While these requirements are met for the normal copula model (Klaassen and Wellner 1997), it is argued that this is an exception rather than the norm.

Estimation and Testing in Models Containing Both Jumps and Conditional Heteroscedasticity

In this article we develop a test for the hypothesis that a series (observed in discrete time) is generated by a diffusion process. This test is based on an overidentifying relation between variance and kurtosis parameters that holds for generalized autoregressive conditional heteroscedastic diffusions. The proposed test is not specific to a particular data frequency and clearly indicates the presence of jumps in dollar exchange rates. To assess the size and intensity of the jumps, we estimate a model containing both jumps and conditional heteroscedasticity.

Currency hedging for international stock portfolios: The usefulness of mean¿variance analysis

Abstract We test whether hedging currency risk improves the performance of international stock portfolios.We show that an auxiliary regression provides a wealth of information about the optimal portfolio holdings for non-mean–variance investors, analogous to the information provided by the Jensen regression about optimal portfolio holdings for the mean–variance case. We find that static hedging with currency forwards does not lead to significant improvements in portfolio performance for a US-Dollar based stock portfolio from the G5 countries, whereas dynamic hedges that are conditional on the interest rate spread do. These conclusions hold for both mean–variance and power utility investors and show up both in-sample and out-of-sample. However, the optimal forward positions can differ significantly for both types of investors.

A jump diffusion model for exchange rates in a target zone

We propose a simple jump‐diffusion model for an exchange rate target zone. The model captures most stylized facts from the existing target zone models while remaining analytically tractable. The model is based on a modified two‐limit version of the COX, INGERSOLL and ROSS (1985) model. In the model the exchange rate is kept within the band because the variance decreases as the exchange rate approaches the upper or lower limits of the band. We also consider an extension of the model with parity adjustments, which are modeled as Poisson jumps. Estimation of the model is by GMM based on conditional moments. We derive prices of currency options in our model, assuming that realignment jump risk is idiosyncratic. Throughout, we apply the theory to EMS exchange rate data. We show that, after the EMS crisis of 1993, currencies remain in an implicit target zone which is narrower than the officially announced target zones.

Semiparametric lower bounds for tail index estimation

We consider estimation of the tail index parameter from i.i.d. observations in Pareto and Weibull type models, using a local and asymptotic approach. The slowly varying function describing the non-tail behavior of the distribution is considered as an infinite dimensional nuisance parameter. Without further regularity conditions, we derive a local asymptotic normality (LAN) result for suitably chosen parametric submodels of the full semiparametric model. From this result, we immediately obtain the optimal rate of convergence of tail index parameter estimators for more specific models previously studied. On top of the optimal rate of convergence, our LAN result also gives the minimal limiting variance of estimators (regular for our parametric model) through the convolution theorem. We show that the classical Hill estimator is regular for the submodels introduced with limiting variance equal to the induced convolution theorem bound. We also discuss the Weibull model in this respect.

The Impact of Overnight Periods on Option Pricing

This paper investigates the effect of closed overnight exchanges on option prices.During the trading day asset prices follow the literature s standard affine model which allows asset prices to exhibit stochastic volatility and random jumps.Independently, the overnight asset price process is modelled by a single jump.We find that the overnight component reduces the variation in the random jump process significantly.However, neither the random jumps nor the overnight jumps alone are able to empirically describe all features of asset prices.We conclude that both random jumps during the day and overnight jumps are important in explaining option prices, where the latter account for about one quarter of total jump risk.