Computation of Volatility in Stochastic Volatility Models with High Frequency Data

2008 ◽  
Author(s):  
Emilio Barucci ◽  
Maria Elvira Elvira Mancino
Keyword(s):  
Stochastic Volatility ◽  
High Frequency ◽  
High Frequency Data ◽  
Frequency Data ◽  
Stochastic Volatility Models ◽  
Volatility Models

COMPUTATION OF VOLATILITY IN STOCHASTIC VOLATILITY MODELS WITH HIGH FREQUENCY DATA

2010 ◽  
Vol 13 (05) ◽  
pp. 767-787 ◽  
Author(s):  
EMILIO BARUCCI ◽  
MARIA ELVIRA MANCINO
Keyword(s):  
Stochastic Volatility ◽  
High Frequency ◽  
Asset Price ◽  
Heston Model ◽  
High Frequency Data ◽  
Monte Carlo Experiment ◽  
Price Model ◽  
Stochastic Volatility Models ◽  
Volatility Models ◽  
Correlation Parameters

We consider general stochastic volatility models driven by continuous Brownian semimartingales, we show that the volatility of the variance and the leverage component (covariance between the asset price and the variance) can be reconstructed pathwise by exploiting Fourier analysis from the observation of the asset price. Specifying parametrically the asset price model we show that the method allows us to compute the parameters of the model. We provide a Monte Carlo experiment to recover the volatility and correlation parameters of the Heston model.

scholarly journals Bayesian Analysis of Intraday Stochastic Volatility Models of High-Frequency Stock Returns with Skew Heavy-Tailed Errors

2021 ◽  
Vol 14 (4) ◽  
pp. 145
Author(s):  
Makoto Nakakita ◽  
Teruo Nakatsuma
Keyword(s):  
Stock Returns ◽  
Stochastic Volatility ◽  
High Frequency ◽  
Stock Price ◽  
Information Criterion ◽  
High Frequency Data ◽  
Return Volatility ◽  
Frequency Data ◽  
Volatility Clustering ◽  
Variance Gamma

Intraday high-frequency data of stock returns exhibit not only typical characteristics (e.g., volatility clustering and the leverage effect) but also a cyclical pattern of return volatility that is known as intraday seasonality. In this paper, we extend the stochastic volatility (SV) model for application with such intraday high-frequency data and develop an efficient Markov chain Monte Carlo (MCMC) sampling algorithm for Bayesian inference of the proposed model. Our modeling strategy is two-fold. First, we model the intraday seasonality of return volatility as a Bernstein polynomial and estimate it along with the stochastic volatility simultaneously. Second, we incorporate skewness and excess kurtosis of stock returns into the SV model by assuming that the error term follows a family of generalized hyperbolic distributions, including variance-gamma and Student’s t distributions. To improve efficiency of MCMC implementation, we apply an ancillarity-sufficiency interweaving strategy (ASIS) and generalized Gibbs sampling. As a demonstration of our new method, we estimate intraday SV models with 1 min return data of a stock price index (TOPIX) and conduct model selection among various specifications with the widely applicable information criterion (WAIC). The result shows that the SV model with the skew variance-gamma error is the best among the candidates.

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