Assessing Value at Risk with CARE, the Conditional AutoRegressive Expectile Models
نویسندگان
چکیده
In this paper we propose a downside risk measure, the expectile-based Value at Risk (EVaR), which is more sensitive to the magnitude of extreme losses than the conventional quantile-based VaR (QVaR). The index θ of an EVaR is the relative cost of the expected margin shortfall and hence reflects the level of prudentiality. It is also shown that a given expectile corresponds to the quantiles with distinct tail probabilities under different distributions. Thus, an EVaR may be interpreted as a flexible QVaR, in the sense that its tail probability is determined by the underlying distribution. We further consider conditional EVaR and propose various Conditional AutoRegressive Expectile models that can accommodate some stylized facts in financial time series. For model estimation, we employ the method of asymmetric least squares proposed by Newey and Powell (1987, Econometrica) and extend their asymptotic results to allow for stationary and weakly dependent data. We also derive an encompassing test for non-nested expectile models. As an illustration, we apply the proposed modeling approach to evaluate the EVaR of stock market indices. JEL classification: C22, C51
منابع مشابه
Nonparametric Expectile Regression for Conditional Autoregressive Expected Shortfall Estimation
In this chapter, we estimate the Expected Shortfall (ES) in conditional autoregressive expectile models by using a nonparametric multiple expectile regression via gradient tree boosting. This approach has the advantages generated by the flexibility of not having to rely on data assumptions and avoids the drawbacks and fragilities of a restrictive estimator such as Historical Simulation. We cons...
متن کاملPresenting a model for Multiple-step-ahead-Forecasting of volatility and Conditional Value at Risk in fossil energy markets
Fossil energy markets have always been known as strategic and important markets. They have a significant impact on the macro economy and financial markets of the world. The nature of these markets are accompanied by sudden shocks and volatility in the prices. Therefore, they must be controlled and forecasted by using appropriate tools. This paper adopts the Generalized Auto Regressive Condition...
متن کاملRobust portfolio selection with polyhedral ambiguous inputs
Ambiguity in the inputs of the models is typical especially in portfolio selection problem where the true distribution of random variables is usually unknown. Here we use robust optimization approach to address the ambiguity in conditional-value-at-risk minimization model. We obtain explicit models of the robust conditional-value-at-risk minimization for polyhedral and correlated polyhedral am...
متن کاملBUSINESS ANALYTICS WORKING PAPER SERIES Bayesian Semi-parametric Expected Shortfall Forecasting in Financial Markets
Bayesian semi-parametric estimation has proven effective for quantile estimation in general and specifically in financial Value at Risk forecasting. Expected short-fall is a competing tail risk measure, involving a conditional expectation beyond a quantile, that has recently been semi-parametrically estimated via asymmetric least squares and so-called expectiles. An asymmetric Gaussian density ...
متن کاملFinancial Risk Modeling with Markova Chain
Investors use different approaches to select optimal portfolio. so, Optimal investment choices according to return can be interpreted in different models. The traditional approach to allocate portfolio selection called a mean - variance explains. Another approach is Markov chain. Markov chain is a random process without memory. This means that the conditional probability distribution of the nex...
متن کامل