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

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

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

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

Complex-valued wavelet lifting and applications

Signals with irregular sampling structures arise naturally in many fields. In applications such as spectral decomposition and nonparametric regression, classical methods often assume a regular sampling pattern, thus cannot be applied without prior data processing. This work proposes new complex-valued analysis techniques based on the wavelet lifting scheme that removes ‘one coefficient at a time’. Our proposed lifting transform can be applied directly to irregularly sampled data and is able to adapt to the signal(s)’ characteristics. As our new lifting scheme produces complex-valued wavelet coefficients, it provides an alternative to the Fourier transform for irregular designs, allowing phase or directional information to be represented. We discuss applications in bivariate time series analysis, where the complex-valued lifting construction allows for coherence and phase quantification. We also demonstrate the potential of this flexible methodology over real-valued analysis in the nonparametric regression context