Eric Ghysels

A study towards a unified approach to the joint estimation of objective and risk neutral measures for the purpose of options valuation

The purpose of this paper is to bridge two strands of the literature, one pertaining to the objective or physical measure used to model an underlying asset and the other pertaining to the risk-neutral measure used to price derivatives. We propose a generic procedure using simultaneously the fundamental price and a set of option contracts. We use Hestons (1993, Review of Financial Studies 6, 327--343) model as an example, and appraise univariate and multivariate estimation of the model in terms of pricing and hedging performance. Our results, based on the SP Efficient method of moments; State price densities; Stochastic volatility models; Filtering

MIDAS Regressions: Further Results and New Directions

We explore mixed data sampling (henceforth MIDAS) regression models. The regressions involve time series data sampled at different frequencies. Volatility and related processes are our prime focus, though the regression method has wider applications in macroeconomics and finance, among other areas. The regressions combine recent developments regarding estimation of volatility and a not-so-recent literature on distributed lag models. We study various lag structures to parameterize parsimoniously the regressions and relate them to existing models. We also propose several new extensions of the MIDAS framework. The paper concludes with an empirical section where we provide further evidence and new results on the risk–return trade-off. We also report empirical evidence on microstructure noise and volatility forecasting.

On Stable Factor Structures in the Pricing of Risk: Do Time‐Varying Betas Help or Hurt?

There is now considerable evidence suggesting that estimated betas of unconditional capital asset pricing models (CAPMs) exhibit statistically significant time variation. Therefore, many have advocated the use of conditional CAPMs. If we succeed in capturing the dynamics of beta risk, we are sure to outperform constant beta models. However, if the beta risk is inherently misspecified, there is a real possibility that we commit serious pricing errors, potentially larger than with a constant traditional beta model. In this paper we show that this is indeed the case, namely that pricing errors with constant traditional beta models are smaller than with conditional CAPMs. Copyright The American Finance Association 1998.

Periodic Autoregressive Conditional Heteroskedasticity

Most high-frequency asset returns exhibit seasonal volatility patterns. This article proposes a new class of models featuring periodicity in conditional heteroscedasticity explicitly designed to capture the repetitive seasonal time variation in the second-order moments. This new class of periodic autoregressive conditional heteroscedasticity, or P-ARCH, models is directly related to the class of periodic autoregressive moving average (ARMA) models for the mean. The implicit relation between periodic generalized ARCH (P-GARCH) structures and time-invariant seasonal weak GARCH processes documents how neglected autoregressive conditional heteroscedastic periodicity may give rise to a loss in forecast efficiency. The importance and magnitude of this informational loss are quantified for a variety of loss functions through the use of Monte Carlo simulation methods. Two empirical examples with daily bilateral Deutschemark/British pound and intraday Deutschemark/U.S. dollar spot exchange rates highlight the prac...

Testing for unit roots in seasonal time series Some theoretical extensions and a Monte Carlo investigation

Abstract Part of the increasing interest in the treatment of seasonality in economic time series has focused on detecting the presence of unit roots at some of the seasonal frequencies as well as at the zero frequency. In this paper we introduce new test statistics, analyze both theoretically and via simulation the properties of Dickey-Fuller-type tests in seasonal time series which have roots at frequencies other than the zero frequency. We also investigate the properties of the standard testing procedures for unit roots in seasonal time series via Monte Carlo simulations. We show that the Dickey-Fuller tests can still be used to test for a unit root at the zero frequency to the extent that appropriate autoregressive correction terms are augmented to the model. Our Monte Carlo simulations reveal that tests for unit roots at seasonal frequencies have severe size distortions in many cases commonly encountered in practice. While we find the procedure proposed by Hylleberg, Engle, Granger, and Yoo (1990) the most useful among the alternative procedures, we caution users of many remaining serious obstacles when testing for unit roots in seasonal time series.

Stock Market Volatility and Macroeconomic Fundamentals

We revisit the relation between stock market volatility and macroeconomic activity using a new class of component models that distinguish short-run from long-run movements. We formulate models with the long-term component driven by inflation and industrial production growth that are in terms of pseudo out-of-sample prediction for horizons of one quarter at par or outperform more traditional time series volatility models at longer horizons. Hence, imputing economic fundamentals into volatility models pays off in terms of long-horizon forecasting. We also find that macroeconomic fundamentals play a significant role even at short horizons.

Rolling-sample volatility estimators: Some new theoretical, simulation, and empirical results

We propose extensions of the continuous record asymptotic analysis for rolling sample variance estimators developed for estimating the quadratic variation of asset returns, referred to as integrated or realized volatility. We treat integrated volatility as a continuous time stochastic process sampled at high frequencies and suggest rolling sample estimators which share many features with spot volatility estimators. We discuss asymptotically efficient window lengths and weighting schemes for estimators of the quadratic variation and establish links between various spot and integrated volatility estimators. Theoretical results are complemented with extensive Monte Carlo simulations and an empirical investigation.

The effect of seasonal adjustment filters on tests for a unit root

Abstract We consider the effect of seasonal adjustment filters in univariate dynamic models. We concentrate our analysis on the behavior of the least-squares estimator of the sum of the autoregressive coefficients in a regression. We show the existence of a limiting upward bias with the X-11 filter when the process does not contain a unit root. We quantify the extent of this bias for a range of models and filtering procedures. The asymptotic bias has interesting implications with respect to the power of tests for a unit root. In order to assess the importance of this effect we present an extensive simulation study of both the size and power of the usual Dickey-Fuller (1979) and Phillips-Perron (1988) statistics. We show that, in many cases, there is considerable reduction in power compared to the benchmark cases where the data is unfiltered. Finally some practical implications of our study are addressed with respect to tests for unit roots with seasonally adjusted data.

5 Stochastic volatility

Publisher Summary The class of stochastic volatility (SV) models has its roots in both, mathematical finance and financial econometrics. In fact, several variations of SV models originated from research looking at very different issues. Volatility plays a central role in the pricing of derivative securities. The Black-Scholes model for the pricing of an European option is by far the most widely used formula even when the underlying assumptions are known to be violated. The Black-Scholes model predicts a flat term structure of volatilities. In reality, the term structure of at-the-money implied volatilities is typically upward sloping when short term volatilities are low and the reverse when they are high. The Black-Scholes model is taken as a reference point from which several notions of volatility are presented. Several stylized facts regarding volatility and option prices are also presented. Both sections set the scene for a formal framework defining stochastic volatility. The chapter introduces the statistical models of stochastic volatility.

Stochastic Volatility Duration Models

We propose a class of two factor dynamic models for duration data and related risk analysis in finance and insurance. Empirical findings suggest that the conditional mean and (under) overdispersion of times elapsed between stock trades feature various patterns of temporal dependence. Therefore durations seem to be driven jointly by movements of two underlying factors. The paper presents a new model, called the stochastic volatility duration (SVD) model for processes that involve time varying uncertainty and time related risk. SVD-based estimation of market activity allows for the presence or absence of temporal interactions between the factors, depending on the market organization and the traded stock. The paper presents the distributional properties of SVD, and compares its performance to the performance of ACD models in an empirical study of intertrade durations of the Alcatel stock. Several new diagnostic tools for risk analysis are proposed, such as the conditional overdispersion and Time at Risk.