Expected shortfall(ES) is a new method to measure market risk. In this paper, an example was presented to illustrate that the ES is coherent but value-at-risk(VaR) is not coherent. Three formulas for calculating the E...Expected shortfall(ES) is a new method to measure market risk. In this paper, an example was presented to illustrate that the ES is coherent but value-at-risk(VaR) is not coherent. Three formulas for calculating the ES based on historical simulation method, normal method and GARCH method were derived. Further, a numerical experiment on optimizing portfolio using ES was provided.展开更多
In this paper we consider the problem of estimating expected shortfall(ES)for discrete time stochastic volatility(SV)models.Specifically,we develop Monte Carlo methods to evaluate ES for a variety of commonly used SV ...In this paper we consider the problem of estimating expected shortfall(ES)for discrete time stochastic volatility(SV)models.Specifically,we develop Monte Carlo methods to evaluate ES for a variety of commonly used SV models.This includes both models where the innovations are independent of the volatility and where there is dependence.This dependence aims to capture the well-known leverage effect.The performance of our Monte Carlo methods is analyzed through simulations and empirical analyses of four major US indices.展开更多
文摘Expected shortfall(ES) is a new method to measure market risk. In this paper, an example was presented to illustrate that the ES is coherent but value-at-risk(VaR) is not coherent. Three formulas for calculating the ES based on historical simulation method, normal method and GARCH method were derived. Further, a numerical experiment on optimizing portfolio using ES was provided.
文摘In this paper we consider the problem of estimating expected shortfall(ES)for discrete time stochastic volatility(SV)models.Specifically,we develop Monte Carlo methods to evaluate ES for a variety of commonly used SV models.This includes both models where the innovations are independent of the volatility and where there is dependence.This dependence aims to capture the well-known leverage effect.The performance of our Monte Carlo methods is analyzed through simulations and empirical analyses of four major US indices.