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This paper analyzes the behavior of one-minute high-frequency time-series data of exchange rates for five currencies (Japanese Yen, Australian Dollar, Canadian Dollar, Euro, and Pound Sterling) against the US Dollar when the Chinese Yuan was revalued on July 21st, 2005. The data show the following distinctive features: (1) There is a large jump in the exchange rates time series at the time of the Yuan revaluation. (2) Large volatility in the returns of exchange rates is observed for a while after the jump. (3) There are many other jumps, possibly correlated, in each exchange rate time series. To capture these features we fit the following models to the data: (i) a univariate GARCH-Jump model with a large jump that is influential on volatility, and (ii) a bivariate GARCH-Jump model with correlated Poisson jumps. For comparison, we also estimate these GARCH models without the associated jumps. The model performance is evaluated based on Value-at-Risk (VaR).

The price and return time series are two distinct features of any financial asset. Hence, examining the evolution of multiscale characteristics of price and returns sequential data in time domain would be helpful in gaining a better understanding of the dynamical evolution mechanism of the financial asset as a complex system. In fact, this is important to understand their respective dynamics and to design their appropriate predictive models. The main purpose of the current work is to investigate the multiscale fractals of price and return high frequency data in Turkish stock market. In this regard, the wavelet leaders computational method is applied to each high frequency data to reveal its multi-fractal behavior. In particular, the method is applied to a large set of Turkish stocks and statistical results are performed to check for (i) presence of multi-fractals in price and return series and (ii) differences between prices and returns in terms of multi-fractals. Our statistical results show strong evidence that high frequency price and return data exhibit multi-fractal dynamics. In addition, they show evidence of distinct fractal characteristics on different scales between price and return series. Furthermore, our statistical results show evidence of differences in local fluctuation characteristics of price and return time series. Therefore, differences in local characteristics are useful to build specific predictive models for each type of data for better modeling and prediction to generate profits. Besides, we found evidence that both long-range correlations and fat-tail distributions contribute to the multifractality in Turkish stocks. This finding can be attributed to the major role played by international investors in increasing the volatility of Turkish stocks.

Epps [17] reported empirical evidence that stock correlations decrease when sampling frequency increases. This phenomenon, named Epps effect, has been observed in several markets. In this paper, the dynamics underlying the Epps effect are investigated. Using Monte Carlo simulations and the analysis of high frequency foreign exchange rate and stock price data, it is shown that the Epps effect can largely be explained by two factors: the non-synchronicity of price observations and the existing lead-lag relationship between asset prices. In order to compute co-volatilities, an original method based upon the Fourier analysis is adopted. This method performs well in estimating correlations precisely, as illustrated by simulated experiments. Being naturally embedded in the frequency domain, this estimator is well suited to the study of the Epps effect.

In this paper we propose a continuous time model capable of describing the dynamics of futures equity index returns at different time frequencies. Unlike several related works in the literature, we avoid specifying a model a priori and we attempt, instead, to infer it from the analysis of a data set of 5-minute returns on the S&P500 futures contract. We start with a very general specification. First we model the seasonal pattern in intraday volatility. Once we correct for this component, we aggregate intraday data into a daily volatility measure to reduce the amount of noise and its distorting impact on the results. We then employ this measure to infer the structure of the stochastic volatility model and of the leverage component, as well as to obtain insights on the shape of the distribution of conditional returns. Our model is then refined at a high frequency level by means of a simple nonlinear filtering technique, which provides an intraday update of volatility and return density estimates on the basis of observed 5-minute returns. The results from a Monte Carlo experiment indicate that a sample of returns simulated according to our model successfully replicates the main features observed in market returns.

Traditionally, central banks have used direct intervention in currency markets when the exchange rate has moved away from equilibrium or when the volatility has been excessive and the literature on the effects of indirect intervention is sparse. We examine whether indirect intervention has any impact on the exchange rate levels by examining the central bank verbal communications in Australia and Canada. We find evidence that the Bank of Canada’s (BOC’s) speeches reduce the mean exchange rate returns but not the Reserve Bank of Australia’s (RBA’s) speeches. Our results show that the socio-economic similarities between countries do not guarantee a similar impact of indirect intervention.

Due to increasing speculation, crude oil futures are now becoming one of the highest traded commodities. This paper studies the relationship between trading volume and serial correlation in crude oil futures returns using high frequency data. We find that volume can positively predict the serial correlation in the short run (within an hour) but negatively predict the serial correlation in the midterm. The trading volume is not able to consistently predict serial correlation in the long run (more than a day). The results from our empirical studies are robust to a variety of controls and our study gives a new insight in the relation between volume and serial correlation of crude oil futures returns.

Recent progress of graphics processing unit (GPU) computing with applications in science and technology has demonstrated tremendous impact over the last decade. However, financial applications by GPU computing are less discussed and may cause an obstacle toward the development of financial technology, an emerging and disruptive field focusing on the efficiency improvement of our current financial system. This chapter aims to raise the attention of GPU computing in finance by first empirically investigating the performance of three basic computational methods including solving a linear system, Fast Fourier transform, and Monte Carlo simulation. Then a fast calibration of the wing model to implied volatilities is explored with a set of traded futures and option data in high frequency. At least 60% executing time reduction on this calibration is obtained under the Matlab computational environment. This finding enables the disclosure of an instant market change so that a real-time surveillance for financial markets can be established for either trading or risk management purposes.

Estimating volatility from recent high frequency data, we revisit the question of the smoothness of the volatility process. Our main result is that log-volatility behaves essentially as a fractional Brownian motion with Hurst exponent H of order 0.1, at any reasonable time scale. This leads us to adopt the fractional stochastic volatility (FSV) model of Comte and Renault [21]. We call our model Rough FSV (RFSV) to underline that, in contrast to FSV, H < 1/2. We demonstrate that our RFSV model is remarkably consistent with financial time series data; one application is that it enables us to obtain improved forecasts of realized volatility. Furthermore, we find that although volatility is not a long memory process in the RFSV model, classical statistical procedures aiming at detecting volatility persistence tend to conclude the presence of long memory in data generated from it. This sheds light on why long memory of volatility has been widely accepted as a stylized fact.

A model is useless if it cannot be taken to data, so it makes sense to begin modeling by looking at the data. Simple exploratory techniques can quickly reveal stylized facts of the data, and may suggest modeling hypotheses, but it is important to be cautious before jumping to conclusions, and to keep an open mind about other possibilities. This chapter considers some examples related to asset returns.