The realized-GARCH framework is extended to incorporate the two-sided Weibull distribution, for the purpose of volatility and tail risk forecasting in a financial time series. Further, the realized range, as a competitor for realized variance or daily returns, is employed as the realized measure in the realized-GARCH framework. Sub-sampling and scaling methods are applied to both the realized range and realized variance, to help deal with inherent micro-structure noise and inefficiency. A Bayesian Markov Chain Monte Carlo (MCMC) method is adapted and employed for estimation and forecasting, while various MCMC efficiency and convergence measures are employed to assess the validity of the method. In addition, the properties of the MCMC estimator are assessed and compared with maximum likelihood, via a simulation study. Compared to a range of well-known parametric GARCH and realized-GARCH models, tail risk forecasting results across seven market indices, as well as two individual assets, clearly favour the proposed realized-GARCH model incorporating the two-sided Weibull distribution; especially those employing the sub-sampled realized variance and sub-sampled realized range. 相似文献
We introduce new Markov-switching (MS) dynamic conditional score (DCS) exponential generalized autoregressive conditional heteroscedasticity (EGARCH) models, to be used by practitioners for forecasting value-at-risk (VaR) and expected shortfall (ES) in systematic risk analysis. We use daily log-return data from the Standard & Poor’s 500 (S&P 500) index for the period 1950–2016. The analysis of the S&P 500 is useful, for example, for investors of (i) well-diversified US equity portfolios; (ii) S&P 500 futures and options traded at Chicago Mercantile Exchange Globex; (iii) exchange traded funds (ETFs) related to the S&P 500. The new MS DCS-EGARCH models are alternatives to of the recent MS Beta-t-EGARCH model that uses the symmetric Student’s t distribution for the error term. For the new models, we use more flexible asymmetric probability distributions for the error term: Skew-Gen-t (skewed generalized t), EGB2 (exponential generalized beta of the second kind) and NIG (normal-inverse Gaussian) distributions. For all MS DCS-EGARCH models, we identify high- and low-volatility periods for the S&P 500. We find that the statistical performance of the new MS DCS-EGARCH models is superior to that of the MS Beta-t-EGARCH model. As a practical application, we perform systematic risk analysis by forecasting VaR and ES.
Abbreviation Single regime (SR); Markov-switching (MS); dynamic conditional score (DCS); exponential generalized autoregressive conditional heteroscedasticity (EGARCH); value-at-risk (VaR); expected shortfall (ES); Standard & Poor's 500 (S&P 500); exchange traded funds (ETFs); Skew-Gen-t (skewed generalized t); EGB2 (exponential generalized beta of the second kind); NIG (normal-inverse Gaussian); log-likelihood (LL); standard deviation (SD); partial autocorrelation function (PACF); likelihood-ratio (LR); ordinary least squares (OLS); heteroscedasticity and autocorrelation consistent (HAC); Akaike information criterion (AIC); Bayesian information criterion (BIC); Hannan-Quinn criterion (HQC). 相似文献
The risk of outliving your money (or shortfall) with low risk, low return investments is very often more serious than the risk of losing money on high risk investments, until quite late in life. A stochastic process model incorporating mortality tables for men and women of retirement age, random rates of return and fixed initial wealth and desired level of consumption provides the analytical tool. A simulation using Canadian mortality tables and rates of return shows that almost all retirees should invest some of their wealth in equity, and for many the optimal allocation is 70–100% equity. The risk of shortfall is surprisingly high for a reasonable range of values of the variables, especially for an allocation of 100% in treasury bills. Women face much greater risk of shortfall than men. The analytical model also permits calculation of the distribution of the bequest and hence allows an individual to trade off changes in shortfall risk against changes in the expected bequest to the heirs. 相似文献
This article studies the optimal portfolio selection of expected utility‐maximizing investors who must also manage their market‐risk exposures. The risk is measured by a so‐called weighted value‐at‐risk (WVaR) risk measure, which is a generalization of both value‐at‐risk (VaR) and expected shortfall (ES). The feasibility, well‐posedness, and existence of the optimal solution are examined. We obtain the optimal solution (when it exists) and show how risk measures change asset allocation patterns. In particular, we characterize three classes of risk measures: the first class will lead to models that do not admit an optimal solution, the second class can give rise to endogenous portfolio insurance, and the third class, which includes VaR and ES, two popular regulatory risk measures, will allow economic agents to engage in “regulatory capital arbitrage,” incurring larger losses when losses occur. 相似文献
In various fields of applications such as capital allocation, sensitivity analysis, and systemic risk evaluation, one often needs to compute or estimate the expectation of a random variable, given that another random variable is equal to its quantile at some prespecified probability level. A primary example of such an application is the Euler capital allocation formula for the quantile (often called the value‐at‐risk), which is of crucial importance in financial risk management. It is well known that classic nonparametric estimation for the above quantile allocation problem has a slower rate of convergence than the standard rate. In this paper, we propose an alternative approach to the quantile allocation problem via adjusting the probability level in connection with an expected shortfall. The asymptotic distribution of the proposed nonparametric estimator of the new capital allocation is derived for dependent data under the setup of a mixing sequence. In order to assess the performance of the proposed nonparametric estimator, AR‐GARCH models are proposed to fit each risk variable, and further, a bootstrap method based on residuals is employed to quantify the estimation uncertainty. A simulation study is conducted to examine the finite sample performance of the proposed inference. Finally, the proposed methodology of quantile capital allocation is illustrated for a financial data set. 相似文献
A new semi-parametric expected shortfall (ES) estimation and forecasting framework is proposed. The proposed approach is based on a two-step estimation procedure. The first step involves the estimation of value at risk (VaR) at different quantile levels through a set of quantile time series regressions. Then, the ES is computed as a weighted average of the estimated quantiles. The quantile weighting structure is parsimoniously parameterized by means of a beta weight function whose coefficients are optimized by minimizing a joint VaR and ES loss function of the Fissler–Ziegel class. The properties of the proposed approach are first evaluated with an extensive simulation study using two data generating processes. Two forecasting studies with different out-of-sample sizes are then conducted, one of which focuses on the 2008 Global Financial Crisis period. The proposed models are applied to seven stock market indices, and their forecasting performances are compared to those of a range of parametric, non-parametric, and semi-parametric models, including GARCH, conditional autoregressive expectile (CARE), joint VaR and ES quantile regression models, and a simple average of quantiles. The results of the forecasting experiments provide clear evidence in support of the proposed models. 相似文献
This paper examines the systemic risk of financial firms in Turkey. Using Component Expected Shortfall, we provide estimates of systemic risk in Turkey using daily data from 2005 to 2018 and a comprehensive data set encompassing 54 financial firms. Empirical results show that the preponderance of systemic risk in the sample in Turkey is due to large commercial banks. Top ten systemically important financial institutions dominate systemic risk measures in Turkey and account for more than 90 % of total risk over the sample. Consequently, the risk in the Turkish financial system is concentrated in specific financial institutions and makes close monitoring of the top firms essential. Historical incidence of systemic risk in the sample shows elevated levels of systemic risk correspond to well-known external events. Finally, a bivariate VAR model shows that systemic risk is correlated with measures of global financial risks and has significant negative effects on the real economy particularly on industrial production. This is important from a financial stability point of view in that close monitoring of the systemic risk is important in maintaining a healthy financial system and a well- functioning market economy. 相似文献