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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.

We provide a framework for integration of high-frequency intraday data into the measurement, modeling, and forecasting of daily and lower frequency return volatilities and return distributions. Building on the theory of continuous-time arbitrage-free price processes and the theory of quadratic variation, we develop formal links between realized volatility and the conditional covariance matrix. Next, using continuously recorded observations for the Deutschemark/Dollar and Yen/Dollar spot exchange rates, we find that forecasts from a simple long-memory Gaussian vector autoregression for the logarithmic daily realized volatilities perform admirably. Moreover, the vector autoregressive volatility forecast, coupled with a parametric lognormal-normal mixture distribution produces well-calibrated density forecasts of future returns, and correspondingly accurate quantile predictions. 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.

It is well known that high-frequency asset returns are fat-tailed relative to the Gaussian distribution, and that the fat tails are typically reduced but not eliminated when returns are standardized by volatilities estimated from popular ARCH and stochastic volatility models. Two major dollar exchange rates are considered, and it is shown that returns standardized instead by the realized volatilities of Andersen, Bollerslev, Diebold and Labys (2000a) are very nearly Gaussian. Both univariate and multivariate analyses were performed, and the differing effects of the different standardizations are traced to differences in information sets.

Competitive international financial exchanges can distinguish themselves by offering different types of trading features, such as the ability to partially hide an order's quantity. Although order hiding is generally assumed to be an advantageous mechanism, it has undergone very little empirical analysis, due in part to a lack of appropriate data. The Paris Bourse does provide limit order trading records on a second-by-second basis, but its data set omits such critical elements as the time of order cancellation and the electronic order book's composition. In this dissertation, I develop a method to reconstruct the internal states of the Bourse, then explore the role and impact of hidden orders from both empirical and theoretical perspectives. In Chapter One, I discuss the reconstruction itself: the Bourse's electronic trading system is reverse-engineered and a working model is constructed. By running historical streams of orders through this model, it is possible to simulate the internal state of the system over time, replicating the markets hidden microstructural dynamics. In Chapter Two, I conduct an empirical analysis of a year's worth of reconstructed second-by-second data for representative French stocks, testing a series of hypotheses relevant to order hiding. I find that order hiding decreases the immediate impact that a limit order has on the market while reducing the amount of undercutting; however, order hiding also increases the probability that the order will not execute in full. Because it slows down the interaction of orders with the market, order hiding can be a useful tool for limit order traders wishing to mitigate adverse selection risk. In Chapter Three, I construct a theoretic model of a limit order market in which traders use order hiding as a strategic mechanism in the struggle for liquidity. Their interaction can be represented as a dynamic game of incomplete information, or signaling game, in which traders try to deduce the true depths contained in the book, information which has a critical effect on their probabilities of execution. I show that the equilibrium of this game is consistent with observed facts.

We provide a general framework for integration of high-frequency intraday data into the measurement, modeling and forecasting of daily and lower frequency return volatilities and return distributions. Most procedures for modeling and forecasting financial asset return volatilities, correlations, and distributions rely on potentially restrictive and complicated parametric multivariate ARCH or stochastic volatility models. Use of realized volatility constructed from high-frequency intraday returns, in contrast, permits the use of traditional time-series methods for modeling and forecasting. Building on the theory of continuous-time arbitrage-free price processes and the theory of quadratic variation, we develop formal links between realized volatility and the conditional covariance matrix. 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 a variety of popular daily ARCH and more complicated high-frequency 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, produces well-calibrated density forecasts of future returns, and correspondingly accurate quantile predictions. 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.

Working Paper No. 8160 This paper provides a general framework for integration of high-frequency intraday data into the measurement 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 covariancematrix 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.

Using high-frequency data on deutschmark 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.

Working Paper No. 7488 It is well known that high-frequency asset returns are fat-tailed relative to the Gaussian distribution tails are typically reduced but not eliminated when returns are standardized by volatilities estimated from popular models such as GARCH. We consider two major dollar exchange rates, and we show that returns standardized instead by the realized volatilities of Andersen, Bollerslev, Diebold and Labys (1999) are very nearly Gaussian. We perform both univariate and multivariate analyses, we trace the different effects of the different standardizations to differences in information sets, and we draw implications for the presence of jumps in exchange rate diffusions.

Using high-frequency data on Deutschemark and Yen returns against the dollar, we construct model-free estimates of daily exchange rate volatility and correlation, covering an entire decade. In addition to being model-free, our estimates are also approximately free of measurement error under general conditions, which we delineate. Hence, for all practical purposes, we can 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 highly persistent temporal variation in both volatilities and correlation, clear evidence of long-memory dynamics in both volatilities and correlation, and remarkably precise scaling laws under temporal aggregation.

We review and synthesize our recent work on realized volatility in financial markets. This includes (1) constructing and interpreting realized volatilities for a variety of asset returns (\"understanding\"), (2) determining underlying sampling frequencies high enough to produce precise estimates yet low enough to mitigate microstructure bias (\"optimizing\"), (3) putting realized volatilities to work in various contexts, such as the production of standardized returns series with desirable properties (\"using\"), and (4) using predictions of realized volatility for improved financial risk management (\"forecasting\").