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Estimation of Stochastic Volatility with High and Low Prices

  • Suk Joon Byun KAIST Business School, 85 Hoegiro, Dongdaemun-gu, Seoul, 130-722, Korea
  • Jung-Soon Hyun KAIST Business School, 85 Hoegiro, Dongdaemun-gu, Seoul, 130-722, Korea
  • Woon Jun Sung KAIST Business School, 85 Hoegiro, Dongdaemun-gu, Seoul, 130-722, Korea
This paper suggests stochastic volatility models incorporating both the leverage effect and information on the daily high/low prices of stocks. The leverage effect is measured using open-to-close returns and two distinct intraday data, ranges, defined by the differences between daily high and low log-prices, and extreme prices in order to detect asymmetric volatility behavior. The likelihood-based inferences of Markov Chain Monte Carlo (MCMC) are conducted to estimate parameters and volatility. The simulation study reveals that the proposed model is superior to a traditional stochastic volatility model using returns only but there is little difference between estimators using ranges or high/low prices. Performing an empirical analysis using the E-mini S&P 500 and the Nasdaq 100 Futures, we find strong evidence of the leverage effect even when information of high/low prices is incorporated.

  • Suk Joon Byun
  • Jung-Soon Hyun
  • Woon Jun Sung
This paper suggests stochastic volatility models incorporating both the leverage effect and information on the daily high/low prices of stocks. The leverage effect is measured using open-to-close returns and two distinct intraday data, ranges, defined by the differences between daily high and low log-prices, and extreme prices in order to detect asymmetric volatility behavior. The likelihood-based inferences of Markov Chain Monte Carlo (MCMC) are conducted to estimate parameters and volatility. The simulation study reveals that the proposed model is superior to a traditional stochastic volatility model using returns only but there is little difference between estimators using ranges or high/low prices. Performing an empirical analysis using the E-mini S&P 500 and the Nasdaq 100 Futures, we find strong evidence of the leverage effect even when information of high/low prices is incorporated.