Mathematical Finance
Department of Mathematics and Statistics
Texas Tech University
Please attend this seminar given jointly with Analysis at this url on Monday the 8th at 2 PM. The passcode is 087956
Systemic risk is the risk that the distress of one or more institutions triggers a collapse of the entire financial system. We extend CoVaR (value-at-risk conditioned on an institution) and CoCVaR (conditional value-at-risk conditioned on an institution) systemic risk contribution measures and propose a new CoCDaR (conditional drawdown-at-risk conditioned on an institution) measure based on drawdowns. This new measure accounts for consecutive negative returns of a security, while CoVaR and CoCVaR combine together negative returns from different time periods. For instance, ten 2% consecutive losses resulting in 20% drawdown will be noticed by CoCDaR, while CoVaR and CoCVaR are not sensitive to relatively small one period losses. The proposed measure provides insights for systemic risks under extreme stresses related to drawdowns. CoCDaR and its multivariate version, mCoCDaR, estimate an impact on big cumulative losses of the entire financial system caused by an individual firm’s distress. It can be used for ranking individual systemic risk contributions of financial institutions (banks). CoCDaR and mCoCDaR are computed with CVaR regression of drawdowns. Moreover, mCoCDaR can be used to estimate drawdowns of a security as a function of some other factors. For instance, we show how to perform fund drawdown style classification depending on drawdowns of indices. Case study results, data, and codes are posted on the web.
Please attend the Mathematical Finance seminar this Friday, March 19th via this zoom link at 2 PM, passcode 455846.This talk examines and reports the results of few papers on portfolio diversification. In particular, we first provide a general valuation of the diversification attitude of investors and then we discuss how to quantify portfolio risk diversification. Therefore, we first analyze the diversification problem from the perspective of risk-averse investors, risk-seeking investors, and non-satiable investors' attitude towards diversification when the choices available to investors depend on several parameters. Then, starting from some examples proposed in literature we discuss how to quantify portfolio risk diversification. In particular, we propose a definition of risk diversification measure and we examine the portfolio problem in a mean-risk diversification framework.
Please attend the Mathematical Finance seminar this Friday at noon, April 30th via this zoom link, passcode 146490.