Joint modeling of high-frequency price and duration data

High frequency financial data is irregularly spaced in time. The information content that determines the time between subsequent trades introduces is potentially related to volatility. We introduce a new continuous time model to jointly model stock return and duration between trades. This model include a bivariate Ornstein-Uhlenbeck process for two latent processes: log-volatility of stock returns and log-intensity of the elapsed time between trades. We apply this model to tickby-tick stock price data. We find that volatility and intensity have strong persistence and are contemporaneously positively correlated. A Monte Carlo study points out that more accurate measurement of volatility can be obtain by conditioning on observed duration between trades in addition to conditioning on the returns. ∗Mailing address: Department of Economics, Campus Box 8110, North Carolina State University, Raleigh, 276958110, USA. e-mail: denis [email protected]. Web site: http://www4.ncsu.edu/∼dpellet. †Mailing address: Department of Economics, Campus Box 8110, North Carolina State University, Raleigh, 276958110, USA. e-mail: [email protected]. Web site: http://www4.ncsu.edu/∼hzheng2.