Overnight Volatility Processes with Applications of Value at Risk

Abstract
Several parametric volatility models based on high-frequency financial data have been developed. These can capture market dynamics well by adopting realized volatil- ity estimators. However, when applying them to financial applications such as risk management, performance evaluation, and portfolio allocation, we face the nonavail- ability problem of high-frequency trading data during the close-to-open period. Thus, volatility models based on high-frequency data often ignore volatility information from the close-to-open period, which causes undervalued market risk. In this paper, to ac- count for whole-day market dynamics, we propose an overnight volatility process based on It^o  diffusion processes, which have two different instantaneous volatility processes for the open-to-close and close-to-open periods, respectively. Then we discuss how to apply the proposed process to Value at Risk (VaR). We also suggest a quasi-likelihood estimation method to estimate model parameters and establish its asymptotic proper- ties. We then conduct a simulation study to check the finite sample performance of the proposed model, and we apply the proposed model to measure the VaR of the real trading data.