Overnight borrowing, interest rates and extreme value theory

We examine the dynamics of extreme values of overnight borrowing rates in an inter-bank money market before a financial crisis during which overnight borrowing rates rocketed up to (simple annual) 4000 percent. It is shown that the generalized Pareto distribution fits well to the extreme values of the interest rate distribution. We also provide predictions of extreme overnight borrowing rates using pre-crisis data. The examination of tails (extreme values) provides answers to such issues as to what are the extreme movements to be expected in financial markets; is there a possibility for even larger movements and, are there theoretical processes that can model the type of fat-tails in the observed data? The answers to such questions are essential for proper management of financial exposures and laying ground for regulations. © 2005 Elsevier B.V. All rights reserved

Using genetic algorithms to select architecture of a feedforward artificial neural network

This paper proposes a model selection methodology for feedforward network models based on the genetic algorithms and makes a number of distinct but inter-related contributions to the model selection literature for the feedforward networks. First, we construct a genetic algorithm which can search for the global optimum of an arbitrary function as the output of a feedforward network model. Second, we allow the genetic algorithm to evolve the type of inputs, the number of hidden units and the connection structure between the inputs and the output layers. Third, we study how introduction of a local elitist procedure which we call the election operator affects the algorithm's performance. We conduct a Monte Carlo simulation to study the sensitiveness of the global approximation properties of the studied genetic algorithm. Finally, we apply the proposed methodology to the daily foreign exchange returns

Is the largest Lyapunov exponent preserved in embedded dynamics?

The method of reconstruction for an n-dimensional system from observations is to form vectors of m consecutive observations, which for m > 2n, is generically an embedding. This is Takens' result. Our analytical examples show that it is possible to obtain spurious Lyapunov exponents that are even larger than the largest Lyapunov exponent of the original system. Therefore, we present examples where the largest Lyapunov exponent may not be preserved under Takens' embedding theorem. (C) 2000 Elsevier Science B.V

Multiscaled Cross-Correlation Dynamics in Financial Time-Series

The cross correlation matrix between equities comprises multiple interactions between traders with varying strategies and time horizons. In this paper, we use the Maximum Overlap Discrete Wavelet Transform to calculate correlation matrices over different timescales and then explore the eigenvalue spectrum over sliding time windows. The dynamics of the eigenvalue spectrum at different times and scales provides insight into the interactions between the numerous constituents involved. Eigenvalue dynamics are examined for both medium and high-frequency equity returns, with the associated correlation structure shown to be dependent on both time and scale. Additionally, the Epps effect is established using this multivariate method and analyzed at longer scales than previously studied. A partition of the eigenvalue time-series demonstrates, at very short scales, the emergence of negative returns when the largest eigenvalue is greatest. Finally, a portfolio optimization shows the importance of timescale information in the context of risk management

Intraday dynamics of stock market returns and volatility

This paper provides new empirical evidence for intraday scaling behavior of stock market returns utilizing a 5 min stock market index (the Dow Jones Industrial Average) from the New York Stock Exchange. It is shown that the return series has a multifractal nature during the day. In addition, we show that after a financial "earthquake", aftershocks in the market follow a power law, analogous to Omori's law. Our findings indicate that the moments of the return distribution scale nonlinearly across time scales and accordingly, volatility scaling is nonlinear under such a data generating mechanism. © 2006 Elsevier B.V. All rights reserved

Exploring exchange rate returns at different time horizons

The performance of the well-known stochastic processes used for the empirical distribution of the exchange rate returns at different time scales was discussed. The parameters of the candidate processes at different time scales were estimated and proceed with simulating the empirical distributions of exchange rate returns from selected candidate processes. Results showed that the empirical distribution of returns behaves differently at different frequencies

Scaling properties of foreign exchange volatility

In this paper, we investigate the scaling properties of foreign exchange volatility. Our methodology is based on a wavelet multi-scaling approach which decomposes the variance of a time series and the covariance between two time series on a scale by scale basis through the application of a discrete wavelet transformation. It is shown that foreign exchange rate volatilities follow different scaling laws at different horizons. Particularly, there is a smaller degree of persistence in intra-day volatility as compared to volatility at one day and higher scales. Therefore, a common practice in the risk management industry to convert risk measures calculated at shorter horizons into longer horizons through a global scaling parameter may not be appropriate. This paper also demonstrates that correlation between the foreign exchange volatilities is the lowest at the intra-day scales but exhibits a gradual increase up to a daily scale. The correlation coefficient stabilizes at scales one day and higher. Therefore, the benefit of currency diversification is the greatest at the intra-day scales and diminishes gradually at higher scales (lower frequencies). The wavelet cross-correlation analysis also indicates that the association between two volatilities is stronger at lower frequencies

Multiscale systematic risk

In this paper we propose a new approach to estimating systematic risk (the beta of an asset). The proposed method is based on a wavelet multiscaling approach that decomposes a given time series on a scale-by-scale basis. The empirical results from different economies show that the relationship between the return of a portfolio and its beta becomes stronger as the wavelet scale increases. Therefore, the predictions of the CAPM model should be investigated considering the multiscale nature of risk and return. © 2004 Elsevier Ltd. All rights reserved

High volatility, thick tails and extreme value theory in value-at-risk estimation

In this paper, the performance of the extreme value theory in value-at-risk calculations is compared to the performances of other well-known modeling techniques, such as GARCH, variance-covariance (Var-Cov) method and historical simulation in a volatile stock market. The models studied can be classified into two groups. The first group consists of GARCH(1, 1) and GARCH(1, 1)- t models which yield highly volatile quantile forecasts. The other group, consisting of historical simulation, Var-Cov approach, adaptive generalized Pareto distribution (GPD) and nonadaptive GPD models, leads to more stable quantile forecasts. The quantile forecasts of GARCH(1, 1) models are excessively volatile relative to the GPD quantile forecasts. This makes the GPD model be a robust quantile forecasting tool which is practical to implement and regulate for VaR measurements. © 2003 Elsevier B.V. All rights reserved

Informed traders’ arrival in foreign exchange markets: Does geography matter?

This article critically investigates the possibility that private information offering systematic profit opportunities exists in the spot foreign exchange market. Using a unique dataset with trader-specific limit and market order histories for more than 10,000 traders, we detect transaction behavior consistent with the informed trading hypothesis, where traders consistently make money. We then work within the theoretical framework of a high-frequency version of a structural microstructure trade model, which directly measures the market maker’s beliefs. Both the estimates of the trade model parameters and our model-free analysis of the data suggest that the time-varying pattern of the probability of informed trading is rooted in the strategic arrival of informed traders on a particular day-of-week, hour-of-day, or geographic location (market). © 2015, Springer-Verlag Berlin Heidelberg