Realized Volatility or Price Range: Evidence from a discrete simulation of the continuous time diffusion process

The study provides evidence in favour of the price range as a proxy estimator of volatility in financial time series, in the cases that either intra-day datasets are unavailable or they are available at a low sampling frequency. A stochastic differential equation with time varying volatility of the instantaneous log-returns process is simulated, in order to mimic the continuous time diffusion analogue of the discrete time volatility process. The simulations provide evidence that the price range measures are superior to the realized volatility constructed at low sampling frequency. The high-low price range volatility estimator is more accurate than the realized volatility estimator based on five, or less, equidistance points in time. The open-high-low-close price range is more accurate than the realized volatility estimator based on eight, or less, intra-period log-returns

Realized Volatility or Price Range: Evidence from a discrete simulation of the continuous time diffusion process

The study provides evidence in favour of the price range as a proxy estimator of volatility in financial time series, in the cases that either intra-day datasets are unavailable or they are available at a low sampling frequency. A stochastic differential equation with time varying volatility of the instantaneous log-returns process is simulated, in order to mimic the continuous time diffusion analogue of the discrete time volatility process. The simulations provide evidence that the price range measures are superior to the realized volatility constructed at low sampling frequency. The high-low price range volatility estimator is more accurate than the realized volatility estimator based on five, or less, equidistance points in time. The open-high-low-close price range is more accurate than the realized volatility estimator based on eight, or less, intra-period log-returns

Realized Volatility or Price Range: Evidence from a discrete simulation of the continuous time diffusion process

The study provides evidence in favour of the price range as a proxy estimator of volatility in financial time series, in the cases that either intra-day datasets are unavailable or they are available at a low sampling frequency. A stochastic differential equation with time varying volatility of the instantaneous log-returns process is simulated, in order to mimic the continuous time diffusion analogue of the discrete time volatility process. The simulations provide evidence that the price range measures are superior to the realized volatility constructed at low sampling frequency. The high-low price range volatility estimator is more accurate than the realized volatility estimator based on five, or less, equidistance points in time. The open-high-low-close price range is more accurate than the realized volatility estimator based on eight, or less, intra-period log-returns

Evaluation of Realized Volatility Predictions from Models with Leptokurtically and Asymmetrically Distributed Forecast Errors

Accurate volatility forecasting is a key determinant for portfolio management, risk management and economic policy. The paper provides evidence that the sum of squared standardized forecast errors is a reliable measure for model evaluation when the predicted variable is the intra-day realized volatility. The forecasting evaluation is valid for standardized forecast errors with leptokurtic distribution as well as with leptokurtic and asymmetric distribution. Additionally, the widely applied forecasting evaluation function, the predicted mean squared error, fails to select the adequate model in the case of models with residuals that are leptokurtically and asymmetrically distributed. Hence, the realized volatility forecasting evaluation should be based on the standardized forecast errors instead of their unstandardized version

Evaluation of Realized Volatility Predictions from Models with Leptokurtically and Asymmetrically Distributed Forecast Errors

Accurate volatility forecasting is a key determinant for portfolio management, risk management and economic policy. The paper provides evidence that the sum of squared standardized forecast errors is a reliable measure for model evaluation when the predicted variable is the intra-day realized volatility. The forecasting evaluation is valid for standardized forecast errors with leptokurtic distribution as well as with leptokurtic and asymmetric distribution. Additionally, the widely applied forecasting evaluation function, the predicted mean squared error, fails to select the adequate model in the case of models with residuals that are leptokurtically and asymmetrically distributed. Hence, the realized volatility forecasting evaluation should be based on the standardized forecast errors instead of their unstandardized version

Evaluating Value-at-Risk Models before and after the Financial Crisis of 2008: International Evidence

Τhis paper focuses on the performance of three alternative Value-at-Risk (VaR) models to provide suitable estimates for measuring and forecasting market risk. The data sample consists of five international developed and emerging stock market indices over the time period from 2004 to 2008. The main research question is related to the performance of widely-accepted and simplified approaches to estimate VaR before and after the financial crisis. VaR is estimated using daily data from UK (FTSE 100), Germany (DAX30), USA (S&P500), Turkey (ISE National 100) and Greece (GRAGENL). Methods adopted to calculate VaR are: 1) EWMA of Riskmetrics, 2) classic GARCH(1,1) model of conditional variance assuming a conditional normally distributed returns and 3) asymmetric GARCH with skewed Student-t distributed standardized innovations. The results indicate that the widely accepted and simplified ARCH framework seems to provide satisfactory forecasts of VaR not only for the pre-2008 period of the financial crisis but also for the period of high volatility of stock market returns. Thus, the blame for financial crisis should not be cast upon quantitative techniques, used to measure and forecast market risk, alone

Rolling-sampled parameters of ARCH and Levy-stable models

In this paper an asymmetric autoregressive conditional heteroskedasticity (ARCH) model and a Levy-stable distribution are applied to some well-known financial indices (DAX30, FTSE20, FTSE100 and SP500), using a rolling sample of constant size, in order to investigate whether the values of the estimated parameters of the models change over time. Although, there are changes in the estimated parameters reflecting that structural properties and trading behaviour alter over time, the ARCH model adequately forecasts the one-day-ahead volatility. A simulation study is run to investigate whether the time variant attitude holds in the case of a generated ARCH data process revealing that even in that case the rolling-sampled parameters are time-varying