## C2 - Risk measures

A fundamental concept in finance is risk and different types of risk measures are developed, including Value at Risk (VaR), Expected Shortfall(ES), tail index, entropic risk measure and expectile. Researchers also propose the concept of systemic risk and its measure such as CoVaR. It is very important to calibrate these properly using historical data, as they are the fundamental for derivative pricing and portfolio management. Existing measures like VaR or Expected shortfall (ES) are defined in a static setting with only one period considered. However, as time goes by, new information is continuously released and adjustments should be made instantaneously. Hence extension to a dynamic framework is needed.

**Haiqiang Chen: **His main interests are Financial Econometrics, Time Series Econometrics and Financial Economics. His current research includes the estimation and inference for nonlinear nonstionary time series models, quantitative prediction models and high frequency data.

**Zongwu Cai: **His main interests are Econometrics, Quantitative Finance, Nonlinear Time Series. His research includes work in Theoretical and applied econometrics, quantitative finance and risk management, nonparametric curve estimation problems, nonlinear and nonstationary time series, panel data analysis.

**Wolfgang Karl Härdle: **His main interests are non- and semiparametrics statistics and econometrics. His research includes work in nonparametric modelling, local adaptive models, reduction techniques, stationary models, quantile regression.

**Markus Reiß**: His main research interests lie in mathematical statistics and stochastic analysis. His research includes work on nonparametric statistics, statistics for stochastic processes, statistical inverse problems, stochastic differential equations and applications in finance.

**Weining Wang: **Her research interest are on financial econometrics and statistics. In particular, her research includes topics like non and semiparametric statistics, network models, high dimensional time series analysis, spatial temporal copula models, etc.

**Yinggang Zhou**: His main interests are Empirical Asset Pricing, International Finance, and Financial econometrics. His current research includes the estimation and inference of network structure and dynamics among financial markets and institutions, applications of various time series models in Finance.

**Exemplary PhD-Theses**

- Developing dynamic coherent risk measures with high frequency data

(Markus Reiß)

The existing measures of risk like Value at Risk(VaR) or Expected shortfall (ES) are usually defined in a static setting with only one period considered. However, in practical investment, as time goes by, new information is continuously released and changes should be made on investment positions instantaneously. Hence, a key issue is how we should extend the classic risk measures to such dynamic framework in a coherent way.

- Systemic risk measures in high frequency framework and their applications

The concept of systemic risk has attracted much attention for both academic researchers and regulators, as a result of the heated debate on the issue of "too big to fail" during the global financial crisis. Theoretically, systemic risk measures the possibility of spreading distress across the whole system when a tail event for a specific institution happens. However, how to measure such a systemic risk using observed data is still very challenging. In the literature, a popular measure is CoVaR, defined as the impact to the system’s VaR when one particular institution is under financial stress as measured by its own individual VaR, see Adrian and Brunnermeier (2016). However, CoVar relies on the risk measure of VaR, and thus it inherits all limitations of VaR. For example, VaR does not account for "tail risk". Though it tells us the most we can lose if a tail event does not occur, it does not tell how much the loss could be if a tail event does occur. Moreover, VaR lacks of subadditivity, see Artzner et al. (1997, 1999) and Acerbi and Tasche (2002) and convexity, see Basak and Shapiro (2001). It will be very difficult if we want to calculate VaR for large portfolios as well. Hence, we may prefer to develop new systemic risk measures based on other measures, such as Expected shortfall or Expectiles. Moreover, applications in different financial industries could also be considered.

- Generalized spectral backtesting for tail-related risk measure models

Value-at-Risk (VaR) has been used as a main risk measure in financial market and banking regulation for a long term. However, the Basel Committee on Banking Supervision (BIS) recently recommended Expected Shortfall (ES) as the market risk measure for banking regulatory purposes, replacing Value-at-Risk (VaR), motivated by the appealing theoretical properties of ES and the poor properties of VaR in many crisis situations. In the literature, relatively little work has been done to evaluate the performance of these models. We propose generalized spectral based back-tests for evaluating both VaR and Expected Shortfall(ES) models. We establish the asymptotic properties of the tests, and investigate their finite sample performance through Monte Carlo simulations. An empirical application to some stock indexes is also provided.

- Developing risk measures for crypto currencies markets

The crypto currency market has captured the public’s attention since Bitcoin, the first cryptocurrency, was successful launched in 2009. Today there are hundreds of cryptocurrencies, such as Litecoin, Namecoin and PPCoin, traded simultaneously in the market. Different from traditional currency or security markets, the cryptocurrency market is frequently changing, as new cryptocurrencies are created continuously and some of the exiting cryptocurrencies may lose liquidity in some periods. For such a fast changing market, how to design risk measures is still unclear. This project will modify the traditional risk measures for crypto currencies market. By doing so, one can manage their risk and design optimal investment portfolios.

**References**

- Acerbi C, Tasche D (2002) On the Coherence of Expected Shortfall. Journal of Banking and Finance, 26 (7) 1487-1503 doi:10.1016/S0378-4266(02)00283-2
- Adrian T, Brunnermeier M K (2016) CoVaR American Economic Review. 106(7): 1705-1741
- Artzner P, Delbaen F, Eber J M, Heath D (1997) Thinking Coherently. Risk, 10 (11), 68–71.
- Artzner P, Delbaen F, Eber J M, Heath D (1999) Coherent Measures of Risk. Mathematical Finance, 9 (3), 203–228.
- Basak S, Shapiro A (2001) Value-at-risk based risk management: optimal policies and asset prices. Review of Financial Studies 14, 371-405.