A behavioural finance-based tick-by-tick model for price and volume

We propose a model for jointly predicting stock price and volume at the tick-by-tick level. We model the investors’ preferences by a random utility model that incorporates several important behavioral biases such as the status quo bias, the disposition effect, and loss-aversion. Our model is a logistic regression model with incomplete information; consequently, we are unable to use the maximum likelihood estimation method and have to resort to Markov Chain Monte Carlo (MCMC) to estimate the model parameters. Moreover, the constraint that the volume predicted by the MCMC model exactly match the observed volume vt introduces serial correlation in the stock price. Thus, the standard MCMC methods for calibrating parameters do not work. We develop new modifications of the Metropolis-within-Gibbs method to estimate the parameters in our model. Our primary goal in developing this model is to predict the market impact function and VWAP (volume weighted average price) of individual stocks.