Showing papers by "Francis X. Diebold published in 2001"

Modeling and Forecasting Realized Volatility

Abstract: This paper provides a general framework for integration of high-frequency intraday data into the measurement, modeling and forecasting of daily and lower frequency volatility and return distributions. Most procedures for modeling and forecasting financial asset return volatilities, correlations, and distributions rely on restrictive and complicated parametric multivariate ARCH or stochastic volatility models, which often perform poorly at intraday frequencies. Use of realized volatility constructed from high-frequency intraday returns, in contrast, permits the use of traditional time series procedures for modeling and forecasting. Building on the theory of continuous-time arbitrage-free price processes and the theory of quadratic variation, we formally develop the links between the conditional covariance matrix and the concept of realized volatility. Next, using continuously recorded observations for the Deutschemark/Dollar and Yen /Dollar spot exchange rates covering more than a decade, we find that forecasts from a simple long-memory Gaussian vector autoregression for the logarithmic daily realized volatitilies perform admirably compared to popular daily ARCH and related models. Moreover, the vector autoregressive volatility forecast, coupled with a parametric lognormal-normal mixture distribution implied by the theoretically and empirically grounded assumption of normally distributed standardized returns, gives rise to well-calibrated density forecasts of future returns, and correspondingly accurate quintile estimates. Our results hold promise for practical modeling and forecasting of the large covariance matrices relevant in asset pricing, asset allocation and financial risk management applications.

The Distribution of Realized Exchange Rate Volatility

Abstract: Using high-frequency data on deutschemark and yen returns against the dollar, we construct model-free estimates of daily exchange rate volatility and correlation that cover an entire decade. Our estimates, termed realized volatilities and correlations, are not only model-free, but also approximately free of measurement error under general conditions, which we discuss in detail. Hence, for practical purposes, we may treat the exchange rate volatilities and correlations as observed rather than latent. We do so, and we characterize their joint distribution, both unconditionally and conditionally. Noteworthy results include a simple normality-inducing volatility transformation, high contemporaneous correlation across volatilities, high correlation between correlation and volatilities, pronounced and persistent dynamics in volatilities and correlations, evidence of long-memory dynamics in volatilities and correlations, and remarkably precise scaling laws under temporal aggregation.

Modeling and Forecasting Realized Volatility

Abstract: This paper provides a general framework for integration of high-frequency intraday data into the measurement, modeling, and forecasting of daily and lower frequency volatility and return distributions. Most procedures for modeling and forecasting financial asset return volatilities, correlations, and distributions rely on restrictive and complicated parametric multivariate ARCH or stochastic volatility models, which often perform poorly at intraday frequencies. Use of realized volatility constructed from high-frequency intraday returns, in contrast, permits the use of traditional time series procedures for modeling and forecasting. Building on the theory of continuous-time arbitrage-free price processes and the theory of quadratic variation, we formally develop the links between the conditional covariance matrix and the concept of realized volatility. Next, using continuously recorded observations for the Deutschemark / Dollar and Yen / Dollar spot exchange rates covering more than a decade, we find that forecasts from a simple long-memory Gaussian vector autoregression for the logarithmic daily realized volatilities perform admirably compared to popular daily ARCH and related models. Moreover, the vector autoregressive volatility forecast, coupled with a parametric lognormal-normal mixture distribution implied by the theoretically and empirically grounded assumption of normally distributed standardized returns, gives rise to well-calibrated density forecasts of future returns, and correspondingly accurate quantile estimates. Our results hold promise for practical modeling and forecasting of the large covariance matrices relevant in asset pricing, asset allocation and financial risk management applications.

Range-Based Estimation of Stochastic Volatility Models

Abstract: We propose using the price range in the estimation of stochastic volatility models. We show theoretically, numerically, and empirically that the range is not only a highly efficient volatility proxy, but also that it is approximately Gaussian and robust to microstructure noise. The good properties of the range imply that range-based Gaussian quasi-maximum likelihood estimation produces simple and highly efficient estimates of stochastic volatility models and extractions of latent volatility series. We use our method to examine the dynamics of daily exchange rate volatility and discover that traditional one-factor models are inadequate for describing simultaneously the high- and low-frequency dynamics of volatility. Instead, the evidence points strongly toward tw-factor models with one highly persistent factor and one quickly mean-reverting factor.

Modeling Liquidity Risk, with Implications for Traditional Market Risk Measurement and Management

Abstract: Market risk management has traditionally focussed on the distribution of portfolio value changes produced by changes in the midpoint of bid and ask prices. Hence market risk is traditionally assessed under the assumption of an idealized market with a negligible bid-ask spread. In reality, however, spreads can be both wide and variable; hence a superior approach would recognize that positions will not be liquidated at the mid-price, but rather at the mid-price less the uncertain bid-ask spread. Liquidity risk associated with the uncertainty of the spread, particularly for thinly traded or emerging market securities under adverse market conditions, is an important part of overall market risk and is therefore important to model. We do so, proposing a simple liquidity risk methodology that can be easily and seamlessly integrated into standard value-at-risk models. We show that ignoring the liquidity effect can produce underestimates of market risk in emerging markets by as much as thirty percent. Furthermore, we show that because the BIS is already implicitly monitoring liquidity risk, banks that fail to model liquidity risk explicitly and capitalize against it will likely experience surprisingly many violations of capital requirements, particularly if their portfolios are concentrated in emerging markets.

Five questions about business cycles

Abstract: This article considers five broad questions about the fundamental nature of business cycles and surveys relevant recent research. It is a slightly revised version of the introductory chapter to our book, Business Cycles: Durations, Dynamics, and Forecasting (Diebold and Rudebusch 1999). Both the book and this article attempt to place recent empirical business cycle research, and especially our own work, in a broader perspective. In particular, we focus on research that analyzes the durations or lengths of expansions and contractions, the co-movement and dynamics of cyclical variables, and the prediction of macroeconomic fluctuations.

Weather Forecasting for Weather Derivatives

Abstract: Weather derivatives are a fascinating new type of Arrow-Debreu security, making pre-specified payouts if pre-specified weather events occur, and the market for such derivatives has grown rapidly. Weather modeling and forecasting are crucial to both the demand and supply sides of the weather derivatives market. On the demand side, to assess the potential for hedging against weather surprises and to formulate the appropriate hedging strategies, one needs to determine how much "weather noise" exists for weather derivatives to eliminate, and that requires weather modeling and forecasting. On the supply side, standard approaches to arbitrage-free pricing are irrelevant in weather derivative contexts, and so the only way to price options reliably is again by modeling and forecasting the underlying weather variable. Curiously, however, little thought has been given to the crucial question of how best to approach weather modeling and forecasting in the context of weather derivative demand and supply. The vast majority of extant weather forecasting literature has a structural "atmospheric science" feel, and although such an approach may be best for forecasting six hours ahead, it is not obvious that it is best for the longer horizons relevant for weather derivatives, such as six days, six weeks, or six months. In particular, good forecasting does not necessarily require a structural model. In this paper, then, we take a seemingly-naive nonstructural time-series approach to modeling and forecasting daily average temperature in ten U.S. cities, and we inquire systematically as to whether it proves useful. The answer is, perhaps surprisingly, yes. Time series modeling reveals a wealth of information about both conditional mean dynamics and the conditional variance dynamics of average daily temperature, some of which seems not to have been noticed previously, and it provides similarly sharp insights into both the distributions of weather and the distributions of weather surprises, and the key differences between them. The success of time-series modeling in capturing conditional mean dynamics translates into successful point forecasting, a fact which, together with the success of time-series modeling in identifying and characterizing the distributions of weather surprises, translates as well into successful density forecasting.

High- and Low-Frequency Exchange Rate Volatility Dynamics: Range-Based Estimation of Stochastic Volatility Models

Abstract: We propose using the price range in the estimation of stochastic volatility models. We show theoretically, numerically, and empirically that the range is not only a highly efficient volatility proxy, but also that it is approximately Gaussian and robust to microstructure noise. The good properties of the range imply that range-based Gaussian quasi-maximum likelihood estimation produces simple and highly efficient estimates of stochastic volatility models and extractions of latent volatility series. We use our method to examine the dynamics of daily exchange rate volatility and discover that traditional one-factor models are inadequate for describing simultaneously the high- and low-frequency dynamics of volatility. Instead, the evidence points strongly toward two-factor models with one highly persistent factor and one quickly mean-reverting factor.

High- and Low-Frequency Exchange Rate Volatility Dynamics: Range-Based Estimation of Stochastic Volatility Models

Abstract: We propose using the price range in the estimation of stochastic volatility models. We show theoretically, numerically, and empirically that the range is not only a highly efficient volatility proxy, but also that it is approximately Gaussian and robust to microstructure noise. The good properties of the range imply that range-based Gaussian quasi-maximum likelihood estimation produces simple and highly efficient estimates of stochastic volatility models and extractions of latent volatility series. We use our method to examine the dynamics of daily exchange rate volatility and discover that traditional one-factor models are inadequate for describing simultaneously the high- and low-frequency dynamics of volatility. Instead, the evidence points strongly toward two-factor models with one highly persistent factor and one quickly mean-reverting factor.