We use tail expectiles to estimate alternative measures to the Value at Risk (VaR), Expected Shortfall (ES) and Marginal Expected Shortfall (MES), three instruments of risk protection of utmost importance in actuarial science and statistical finance. The concept of expectiles is a least squares analogue of quantiles. Both expectiles and quantiles were embedded in the more general class of M-quantiles as the minimizers of an asymmetric convex loss function. It has been proved very recently that the only M-quantiles that are coherent risk measures are the expectiles. Moreover, expectiles define the only coherent risk measure that is also elicit able. The elicit ability corresponds to the existence of a natural backtesting methodology. The estimation of expectiles did not, however, receive yet any attention from the perspective of extreme values. The first estimation method that we propose enables the usage of advanced high quantile and tail index estimators. The second method joins together the least asymmetrically weighted squares estimation with the tail restrictions of extreme-value theory. A main tool is to first estimate the large expectile-based VaR, ES and MES when they are covered by the range of the data, and then extrapolate these estimates to the very far tails. We establish the limit distributions of the proposed estimators when they are located in the range of the data or near and even beyond the maximum observed loss. We show through a detailed simulation study the good performance of the procedures, and also present concrete applications to medical insurance data and three large US investment banks.

Estimation of Tail Risk based on Extreme Expectiles

In this study we examine the time-varying causal effect of the novel COVID-19 pandemic in the major oil-importing and oil-exporting countries on the oil price changes, stock market volatilities and the economic uncertainty using the wavelet coherence and network analysis. During the period of the pandemic, we explore such relationship by resorting to the wavelet coherence and gaussian graphical model (GGM) frameworks. Wavelet analysis enables us to measure the dynamics of the causal effect of the novel covid-19 pandemic in the time-frequency space. Regarding the findings displayed herein, we first found that the COVID-19 pandemic has a severe influence on oil prices, stock market indices, and the economic uncertainty. Second the intensity of the causality effect is stronger in the longer horizon than in the short ones, suggesting that the causality exercise continues. Our findings also provide evidence that the COVID-19 pandemic and oil price changes in oil-importing countries mirror those in oil-exporting countries and vice versa. Further, the COVID-19 pandemic has a profound immediate time-frequency effect on the US, Japanese, South Korean, Indian, and Canadian economic uncertainties. A better understanding of oil and stock market prices in the oil-importing and oil-exporting countries is vital for investors and policymakers, specially since the novel unprecedented COVID-19 crisis has been recognized among the most serious ever happened. Thus, the findings suggest that the authorities should strongly take efficient actions to minimize risk. 

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Dynamic causality interplay from COVID-19 pandemic to oil price, stock market, and economic policy uncertainty: evidence from oil-importing and oil-exporting countries

To test the nonlinearity and non-stationarity of measured dynamic signals from a bridge structure with high-level noise and dense modal characteristics, a method that combines the adaptive signal decomposition with the recurrence analysis is proposed to solve the difficulty of testing nonlinearity and non-stationarity of bridge structure signals. A novel white noise assistance and cluster analysis are introduced to the ensemble empirical mode decomposition to alleviate mode-mixing issues and generate single-mode intrinsic mode functions. Combining the hypothesis-testing scheme of nonstationary and nonlinear synchronization and surrogate techniques, a data-driven recurrence quantification analysis method is proposed and a novel recurrence quantification measure pairs are set up. To demonstrate the efficacy of the proposed methodology, complex signals, which are collected from a carefully instrumented model of a cable-stayed bridge, are utilized as the basis for comparing with traditional nonlinear and non-stationary test methods. Results show that the proposed multiscale recurrence method is feasible and effective for applications to a nonlinear and non-stationary test for real complex civil structures.

Nonlinear and Non-Stationary Detection for Measured Dynamic Signal from Bridge Structure Based on Adaptive Decomposition and Multiscale Recurrence Analysis

In this article, we formulate a time-scale decomposition of an international version of the CAPM that accounts for both market and exchange-rate risk. In addition, we derive an analytical formula for time-scale value at risk and marginal value at risk (VaR) of a portfolio. We apply our methodology to stock indices of seven emerging economies belonging to Latin America and Asia, for the sample period 1990-2004. Our main conclusions are the following. First, the estimation results hinge upon the choice of the world market portfolio. In particular, the stock markets of the sampled countries appear to be more integrated with other emerging countries than with developed ones. Second, value at risk depends on the investor's time horizon. In the short run, potential losses are greater than in the long run. Third, additional exposure to some specific stock indices will increase value at risk to a greater extent, depending on the investment horizon. Our results go in line with recent research in asset pricing that stresses the importance of heterogeneous investors.

The International CAPM and a wavelet-based decomposition of Value at Risk

It is well documented that the biopharmaceutical sector has exhibited weak financial returns, contributing to underinvestment. Innovations in the industry carry high risks; however, an analysis of systematic risk and return compared to other asset classes is missing. This paper investigates the time–frequency interconnectedness between stocks in the biotech sector and ten asset classes using daily cross-country data from 1995 to 2019. We capture investors' heterogeneous investment horizons by decomposing time series according to frequencies. Using a maximal overlap discrete wavelet transform (MODWT) and a dynamic conditional correlation (DCC)-Student-t copula, diversification potentials are revealed, helping investors to reap the benefits of investing in biotech. Our findings indicate that the underlying assets exhibit nonlinear asymmetric behavior that strengthens during periods of turmoil.

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Systematic risk in the biopharmaceutical sector: a multiscale approach

Capital requirements for financial institutions are based on the accurate quantification of the inherent risk. To this end, time is the important parameter for all the well-established risk measures, whereas risk managers make no explicit distinction between the information captured by patterns of different frequency content. Accordingly, the original full-time-resolution series of returns is considered, regardless of the selected trading horizon. To address this issue, we propose a novel risk quantification method exploiting the time-evolving energy distribution of returns, which is expressed by the sum of squared magnitudes of a set of transform coefficients. Specifically, a wavelet-based time-scale decomposition is applied first on the returns series to extract the energy contribution of the wavelet coefficients at multiple frequencies. Then, the statistics of an optimal subset of frequencies are linearly combined to estimate the overall risk at a given trading horizon. Most importantly, our proposed energy-based method can be coupled with the commonly used quantile-based risk measures to enhance their performance. The experimental results reveal an increased robustness of our method at efficiently controlling under- or over-estimated risk values, especially for long-run horizons.

An energy-based measure for long-run horizon risk quantification

The success of a trading strategy can be significantly enhanced by tracking accurately the implied volatility changes, which refers to the amount of uncertainty or risk about the degree of changes in a market index. This fosters the need for accurate estimation of the time-synchronization profile between a given market index and its associated volatility index. In this chapter, we advance existing solutions, which are based widely on the typical correlation, for identifying this temporal interdependence. To this end, cross-recurrence plot (CRP) analysis is exploited for extracting the underlying dynamics of a given market and volatility indexes pair, along with their time-synchronization profile. However, CRPs of degraded quality, for instance due to missing information, may yield a completely erroneous estimation of this profile. To overcome this drawback, a restoration stage based on the concept of matrix completion is applied on a corrupted CRP prior to the estimation of the time-synchronization relationship. A performance evaluation on the S&P 500 index and its associated VIX volatility index reveals the superior capability of our proposed approach in restoring accurately their CRP and subsequently estimating a temporal relation between the two indexes even when \(80\,\%\) of CRP values are missing.

George Tzagkarakis

Papers

An energy-based measure for long-run horizon risk quantification

Restoring Corrupted Cross-Recurrence Plots Using Matrix Completion: Application on the Time-Synchronization Between Market and Volatility Indexes