Michel M. Dacorogna

Volatilities of different time resolutions — Analyzing the dynamics of market components

The heterogeneous market states that the diversity of actors causes different behaviors of volatilities of different time resolutions. A lagged correlation study reveals that statistical volatility defined over a coarse time grid significantly predicts volatility defined over a fine grid. This empirical fact is not explained by conventional theories and models.

Statistical study of foreign exchange rates, empirical evidence of a price change scaling law, and intraday analysis☆

Abstract In this paper we present a statistical analysis of four foreign exchange spot rates against the U.S. Dollar with several million intra-day prices over 3 years. The analysis also includes gold prices and samples of daily foreign exchange prices over 15 years. The mean absolute changes of logarithmic prices are found to follow a scaling law against the time interval on which they are measured. This empirical law holds although the distributions of the price changes strongly differ for different interval sizes. Systematic variations of the volatility are found even during business hours by an intra-day analysis of price changes. Seasonal heteroskedasticity is observed with a period of one day as well as one week as the result of an analogous intra-week analysis; taking this into account is necessary for any future study of intra-day price change distributions and their generating process. The same type of analysis is also made for the bid-ask spreads.

From the bird's eye to the microscope: A survey of new stylized facts of the intra-daily foreign exchange markets

Abstract.This paper presents stylized facts concerning the spot intra-daily foreign exchange markets. It first describes intra-daily data and proposes a set of definitions for the variables of interest. Empirical regularities of the foreign exchange intra-daily data are then grouped under three major topics: the distribution of price changes, the process of price formation and the heterogeneous structure of the market. The stylized facts surveyed in this paper shed new light on the market structure that appears composed of heterogeneous agents. It also poses several challenges such as the definition of price and of the time-scale, the concepts of risk and efficiency, the modeling of the markets and the learning process.

Scaling behaviors in differently developed markets

Scaling properties of four different stock market indices are studied in terms of a generalized Hurst exponent approach. We find that the deviations from pure Brownian motion behavior are associated with the degrees of development of the markets and we observe strong differentiations in the scaling properties of markets at different development stage.

Modelling Short-Term Volatility with GARCH and HARCH Models

In this paper we present both a new formulation of the HARCH process and a study of the forecasting accuracy of ARCH-type models for predicting short-term volatility. Using high frequency data, the market volatility is expressed in terms of partial volatilities which are formally exponential moving averages of squared returns measured at different frequencies. This new formulation is shown to produce more accurate fits to the data and, at the same time, to be easier to compute than the earlier version of the HARCH process. This is obtained without losing the nice property of the HARCH process to identify different market components. In a second part, some performance measures of forecasting accuracy are discussed and the ARCH-type models are shown to be good predictors of the short-term hourly historical volatility with the new formulation of the HARCH process being the best predictor.

Defining efficiency in heterogeneous markets

Michel Dacorogna, Ulrich Müller, Richard Olsen and Olivier Pictet offer a new definition of efficient markets that takes into account heterogeneity and varying time scales.

Extremal forex returns in extremely large data sets

Exciting information for risk and investment analysis is obtained from an exceptionally large and automatically filtered high frequency data set containing all the forex quote prices on Reuters during a ten-year period. It is shown how the high frequency data improve the efficiency of the tail risk cum loss estimates. We demonstrate theoretically and empirically that the heavy tail feature of foreign exchange rate returns implies that position limits for traders calculated under the industry standard normal model are either not prudent enough, or are overly conservative depending on the time horizon.

Effective Return, Risk Aversion and Drawdowns

We derive two risk adjusted performance measures for investors with risk averse preferences. Maximizing these measures is equivalent to maximizing the expected utility of an investor. The first measure, X(eff), is derivedassuming a constant risk aversion while the second measure, R(eff),is based on a stronger risk aversion to clustering of losses than of gains. The clustering of returns is captured through a multi-horizon framework. The empirical properties of X(eff), R(eff) are studied within the context of real-time trading models for foreign exchange rates and their properties are compared to those of more traditional measures like the annualized return, the Sharpe Ratio and the maximum drawdown. Our measures are shown to be more robust against clustering of losses and has the ability to fully characterize the dynamic behavior of investment strategies.

Foreign exchange trading models and market behavior

Abstract The contributions of this paper are twofold. First, the performance of a widely used commercial real-time trading model is compared with a simple exponential moving average model. Second, the trading models are used as diagnostic tools to evaluate the statistical properties of foreign exchange rates. The results presented in this paper have a general message to the standard paradigm in econometrics. It is not sufficient to develop sophisticated statistical processes and choose an arbitrary data frequency (e.g. one week, one month, annual, etc.) claiming afterwards that this particular process does a “good job” of capturing the dynamics of the data generating process. In financial markets, the data generating process is a complex network of layers where each layer corresponds to a particular frequency. A successful characterization of such data generating processes should be estimated with models whose parameters are functions of intra and inter frequency dynamics. In other fields, such as in signal processing, paradigms of this sort are already in place. Our understanding of financial markets would be increased with the incorporation of such paradigms into financial econometrics. Our trading models, within this perspective, help to observe this subtle structure as a diagnostic tool.

Changing time scale for short‐term forecasting in financial markets

A forecasting model based on high-frequency market makers quotes of financial instruments is presented. The statistical behaviour of these time series leads to discussion of the appropriate time scale for forecasting. We introduce variable time scales in a general way and define the new concept of intrinsic time. The latter reflects better the actual trading activity. Changing time scale means forecasting in two steps, first an intrinsic time forecast against physical time, then a price forecast against intrinsic time. The forecasting model consists, for both steps, of a linear combination of non-linear price-based indicators. The indicator weights are continuously re-optimized through a modified linear regression on a moving sample of past prices. The out-of-sample performance of this algorithm is reported on a set of important FX rates and interest rates over many years. It is remarkably consistent. Results for short horizons as well as techniques to measure this performance are discussed.