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Understanding volatility in emerging capital markets is important for determining the cost of capital and for evaluating direct investment and asset allocation decisions. We provide an approach that allows the relative importance of world and local information to change through time in both the expected returns and conditional variance processes. Our time-series and cross-sectional models analyze the reasons that volatility is different across emerging markets, particularly with respect to the timing of capital market reforms. We find that capital market liberalizations often increase the correlation between local market returns and the world market but do not drive up local market volatility.

University. We are especially grateful for suggestions from Geert Bekaert, Bob Hodrick, and Ken Singleton. We also thank an anonymous referee whose comments and suggestions greatly improved the paper.

We propose using the price range in the estimation of stochastic volatility models. We show theoretically, numerically, and empirically that range-based volatility proxies are not only highly efficient, but also approximately Gaussian and robust to microstructure noise. Hence range-based Gaussian quasi-maximum likelihood estimation produces highly efficient estimates of stochastic volatility models and extractions of latent volatility. We use our method to examine the dynamics of daily exchange rate volatility and find the evidence points strongly toward two-factor models with one highly persistent factor and one quickly mean-reverting factor. VOLATILITY IS A CENTRAL CONCEPT in finance, whether in asset pricing, portfolio choice, or risk management. Not long ago, theoretical models routinely assumed constant volatility ~e.g., Merton ~1969!, Black and Scholes ~1973!!. Today, however, we widely acknowledge that volatility is both time varying and predictable ~e.g., Andersen and Bollerslev ~1997!!, andstochastic volatility models are commonplace. Discrete- and continuous-time stochastic volatility models are extensively used in theoretical finance, empirical finance, and financial econometrics, both in academe and industry ~e.g., Hull and

Using a new dataset consisting of six years of real-time exchange rate quotations, macroeconomic expectations, and macroeconomic realizations (announcements), we characterize the conditional means of U.S. dollar spot exchange rates versus German Mark, British Pound, Japanese Yen, Swiss Franc, and the Euro. In particular, we find that announcement surprises (that is, divergences between expectations and realizations, or "news") produce conditional mean jumps; hence high-frequency exchange rate dynamics are linked to fundamentals. The details of the linkage are intriguing and include announcement timing and sign effects. The sign effect refers to the fact that the market reacts to news in an asymmetric fashion: bad news has greater impact than good news, which we relate to recent theoretical work on information processing and price discovery. Key Words: Exchange Rates; Macroeconomic News Announcements; Jumps; Market Microstructure; High-Frequency Data; Expectations Data; Anticipations Data; Order Flow; Asset Return Volatility; Forecasting.

We present a new methodology for estimating time-varying...stence in conditional variance.

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By using intra-day returns to calculate a measure for the time-varying volatility, Andersen and Bollerslev (1998a) established that volatility models do provide good forecasts of the conditional variance. In this paper, we take the same approach and use intra-day estimated measures of volatility to compare volatility models. Our objective is to evaluate whether the evolution of volatility models has led to better forecasts of volatility when compared to the first “species ” of volatility models. We make an out-of-sample comparison of 330 different volatility models using daily exchange rate data (DM/$) and IBM stock prices. Our analysis does not point to a single winner amongst the different volatility models, as it is different models that are best at forecasting the volatility of the two types of assets. Interestingly, the best models do not provide a significantly better forecast than the GARCH(1,1) model. This result is established by the tests for superior predictive ability of White (2000) and Hansen (2001). If an ARCH(1) model is selected as the benchmark, it is clearly outperformed. We thank Tim Bollerslev for providing us with the exchange rate data set, and Sivan Ritz for suggesting numerous clarifications. All errors remain our responsibility. 1 Hansen, P. R. and A. Lunde: A COMPARISON OF VOLATILITY MODELS 1

This paper investigates to what extent globalization and regional integration lead to increasing equity market interdependence. I focus on the case of Western Europe, as this region has gone through a unique period of economic, financial, and monetary integration. More specifically, I quantify the magnitude and time-varying nature of volatility spillovers from the aggregate European (EU) and US market to 13 local European equity markets. To account for time-varying integration, I allow the shock sensitivities to change through time by means of a regime-switching model. I find that these regime switches are both statistically and economically important. While both the EU and US shock spillover intensity has increased over the 1980s and 1990s, the rise is more pronounced for EU spillovers. In most countries, shock spillover intensities increased most strongly in the second half of 1980s and the first half of the 1990s. Increased trade integration, equity market development, and low inflation are shown to have contributed to the increase in EU shock spillover intensity. Finally, I find some evidence for contagion from the US market to a number of local European equity markets during periods of high world market volatility.

In this survey we discuss models with level-dependent and stochastic volatility from the viewpoint of derivative asset analysis. Both classes of models are generalisations of the classical Black-Scholes model; they have been developed in an effort to build models that are flexible enough to cope with the known deficits of the classical BlackScholes model. We start by briefly recalling the standard theory for pricing and hedging derivatives in complete frictionless markets and the classical Black-Scholes model. After a review of the known empirical contradictions to the classical Black-Scholes model we consider models with level-dependent volatility. Most of this survey is devoted to derivative asset analysis in stochastic volatility models. We discuss several recent developments in the theory of derivative pricing under incompleteness in the context of stochastic volatility models and review analytical and numerical approaches to the actual computation of option values.