Volatility and quantile forecasts by realized stochastic volatility models with generalized hyperbolic distribution

Abstract

The realized stochastic volatility model of Takahashi, Omori, and Watanabe (2009), which incorporates the asymmetric stochastic volatility model with the realized volatility, is extended with more general form of bias correction in realized volatility and wider class distribution, the generalized hyperbolic skew Student's t-distribution, for financial returns. The extensions make it possible to adjust the bias due to the market microstructure noise and non-trading hours, which possibly depends on the level of the volatility, and to consider the heavy tail and skewness in financial returns. With the Bayesian estimation scheme via Markov chain Monte Carlo method, the model enables us to estimate the parameters in the return distribution and in the model jointly. It also makes it possible to forecast volatility and return quantiles by sampling from their posterior distributions jointly. The model is applied to quantile forecasts of financial returns such as value-at-risk and expected shortfall as well as volatility forecasts and those forecasts are evaluated by several backtesting procedures. Empirical results with SPDR, the S&P 500 exchange-traded fund, show that the heavy tail and skewness of daily returns are important for the model fit and the quantile forecasts but not for the volatility forecasts, and that the additional bias correction improves the quantile forecasts but does not substantially improve the model fit nor the volatility forecasts.

Skew exponential power stochastic volatility model for analysis of skewness, non-normal tails, quantiles and expectiles

“…To summarise, while the large negative returns in the crisis period are explained by the asymmetric return distribution, with θ 1 and θ 2 different from each other or p different from 0.5, it has become less asymmetric and the SV component has come to explain the persistent shock due to the crisis. A similar discussion in the context of the stock returns is found in, e.g., Takahashi et al (2014).…”

“…It is also interesting to consider an extension to a realised stochastic volatility model which jointly models daily returns and the realised volatility (e.g., Takahashi et al 2009Takahashi et al , 2014.…”

Value‐at‐risk under market shifts through highly flexible models

“…The Basel committee further requires daily forecasts of the VaR for returns over a holding period of 10 days (Basel Committee on Banking Supervision, 2006). However, most researchers often predict the 1-day-ahead VaR that corresponds to returns over a holding period of 1 day, since it provides the most reliable measure for model comparison (see, e.g., Ardia & Hoogerheide, 2014;Berger & Missong, 2014;Cheng & Hung, 2011;Dendramis et al, 2014;Nieto & Ruiz, 2016;Takahashi, Watanabe, & Omori, 2016), and because the Basel accords allow the 10-day-ahead VaR to be obtained from shorter period forecasts by using the square-root-of-time rule (Nieto & Ruiz, 2016). 7 7 The square-root-of-time rule, however, can lead to overestimating the VaR under a "realistic" data-generating process for financial returns featuring serial dependence, mean reversion, and heavy tails (Daníelsson & Zigrand, 2006).…”

Gaussian Process Regression Stochastic Volatility Model for Financial Time Series

“…We can also apply different covariance functions besides the most common used squared exponential covariance function to adapt better for specific applications. On the application aspect, we can try to apply this model to forecast tail risk measurements, such as the VaR and expected shortfall [47]. Note: A t-statistic absolute value greater than 1.96 indicates a rejection of the null of equal predictive accuracy at the 0.05 level.…”