Richard B. Olsen

A geographical model for the daily and weekly seasonal volatility in the foreign exchange market

Abstract The daily and weekly seasonality of foreign exchange volatility is modelled by introducing an activity variable. This activity is explained by a simple model of the changing and sometimes overlapping market presence of geographical components (East Asia, Europe, and America). Integrating this activity over time results in the new time scale, characterized by non-seasonal volatility. This scale, applied to dense datastreams of absolute price changes, suceeds in removing most of the seasonal heteroscedasticity in an autocorrelation study. Unexpectedly, the positive autocorrelation is found to decline hyperbolically rather than exponentially as a function of the lag.

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.

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.

Patterns in high-frequency FX data: discovery of 12 empirical scaling laws

We have discovered 12 independent new empirical scaling laws in foreign exchange data series that hold for close to three orders of magnitude and across 13 currency exchange rates. Our statistical analysis crucially depends on an event-based approach that measures the relationship between different types of events. The scaling laws give an accurate estimation of the length of the price-curve coastline, which turns out to be surprisingly long. The new laws substantially extend the catalogue of stylized facts and sharply constrain the space of possible theoretical explanations of the market mechanisms.

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.

The Intraday Multivariate Structure of the Eurofutures Markets

We investigate the multivariate intraday structure in interest rates, focusing on implied forward rates from Eurofutures contracts. Since futures markets are the most liquid for interest rate instruments and they yield high-quality intraday data, it is somehow surprising that their intraday behavior has not been thoroughly studied in the literature. We find interesting similarities with the foreign exchange market in terms of scaling law, intraday patterns, all of which point to the heterogeneity of market participants. Other properties like asymmetric causal information flow between fine and coarse volatilities for the same time series are present in our data. There are also lead/lag correlation across maturities and currencies, but they that tend to disappear as markets mature. A principal component analysis of the short end of the yield curve allows us to determine the most important components and to reduce the number of time series needed to describe the term structure. We find the decomposition rather stable over time. The first component which describes the curve level presents a HARCH effect while the remaining ones do not, having instead significant negative autocorrelations for the time series themselves. A HARCH model is applied to the first component and the impact of different market agents is discussed.

The scale of market quakes

We define a methodology to quantify market activity on a 24 hour basis by defining a scale, the so-called scale of market quakes (SMQ). The SMQ is designed within a framework where we analyse the dynamics of excess price moves from one directional change of price to the next. We use the SMQ to quantify the FX market and evaluate the performance of the proposed methodology at major news announcements. The evolution of SMQ magnitudes from 2003 to 2009 is analysed across major currency pairs.We define a methodology to quantify market activity on a 24 hour basis by defining a scale, the so-called scale of market quakes (SMQ). The SMQ is designed within a framework where we analyse the dynamics of excess price moves from one directional change of price to the next. We use the SMQ to quantify the FX market and evaluate the performance of the proposed methodology at major news announcements. The evolution of SMQ magnitudes from 2003 to 2009 is analysed across major currency pairs.