
on Risk Management 
By:  Marco Rocco (Banca d'Italia) 
Abstract:  Extreme value theory is concerned with the study of the asymptotical distribution of extreme events, that is to say events which are rare in frequency and huge with respect to the majority of observations. Statistical methods derived from this theory have been increasingly employed in finance, especially in the context of risk measurement. The aim of the present study is twofold. The first part delivers a critical review of the theoretical underpinnings of extreme value theory. The second part provides a survey of some major applications of extreme value theory to finance, namely its use to test different distributional assumptions for the data, ValueatRisk and Expected Shortfall calculations, asset allocation under safetyfirst type constraints and the study of contagion and dependence across markets under stress conditions. 
Keywords:  extreme value theory, risk management, fattailed distributions, ValueatRisk, systemic risk, asset allocation 
JEL:  C10 C16 G10 G20 G21 
Date:  2011–07 
URL:  http://d.repec.org/n?u=RePEc:bdi:opques:qef_99_11&r=rmg 
By:  Toshiaki Watanabe 
Abstract:  This article applies the realized GARCH model, which incorporates the GARCH model with realized volatility (RV), to quantile forecasts of financial returns such as ValueatRisk and expected shortfall. This model has certain advantages in the application to quantile forecasts because it can adjust the bias of RV casued by microstructure noise and nontrading hours and enables us to estimate the parameters in the return distribution jointly with the other parameters. Student's t and skewed strudent's tdistributions as well as normal distribution are used for the return distribution. The EGARCH model is used for comparison. Main results for the S&P 500 stock index are: (1) the realized GARCH model with the skewed student's tdistribution performs better than that with the normal and student's tdistributions and the EGARCH model using the daily returns only, and (2) the performance does not improve if the realized kernel, which takes account of microstructure noise, is used instead of the plain realized volatility, implying that the realized GARCH model can adjust the bias of RV caused by microstructure noise. 
Keywords:  Expected shortfall, GARCH, Realized volatility, Skewed student's tdistribution, ValueatRisk 
JEL:  C52 C53 
Date:  2011–07 
URL:  http://d.repec.org/n?u=RePEc:hst:ghsdps:gd11195&r=rmg 
By:  Moy, Caroline; Roberts, Leigh 
Abstract:  A direct approach is taken to modelling New Zealand electricity prices, in which extreme value theory is used to augment a basic time series model. Despite its simplicity, the resulting model is suitable for answering fundamental questions of interest to risk managers, who might not find it worthwhile to apply a more sophisticated and complex approach to statistical modelling. 
Keywords:  electricity prices, extreme value theory, New Zealand, statistical modelling, 
Date:  2011–06–13 
URL:  http://d.repec.org/n?u=RePEc:vuw:vuwecf:1666&r=rmg 
By:  Neus, Werner; Stadler, Manfred 
Abstract:  In his basic model of debt renegotiation, BESTER [1994] argues that collateral is more effective if high risk projects are financed. This result, however, crucially depends on the definition of risk. Using the secondorder stochastic dominance criterion introduced by ROTHSCHILD AND STIGLITZ [1970], we show that it is not a project's high risk, induced by a high probability of default, that makes collateral more effective. Instead it turns out that, given the expected return, the probability of default has no impact on the collateral's effectiveness. Moreover, a higher risk of the project caused by a higher loss given default makes the use of collateral even less effective.  
Keywords:  Debt renegotiation,Collateral,Risk,Stochastic dominance 
JEL:  D81 D82 G21 G32 
Date:  2011 
URL:  http://d.repec.org/n?u=RePEc:zbw:tuewef:16&r=rmg 