Insider trading at a random deadline with correlation between dynamic asset and stochastic liquidity

Abstract

We propose a generalized continuous-time insider trading model, building upon the frameworks of Caldentey and Stacchetti (2010) and Collin-Dufresne and Fos (2016), with a correlation between the value of a risky asset following an Ornstein-Uhlenbeck-type process and the noise trading volume with volatility characterized by a general stochastic process. And a closed form of the market equilibrium is established, consisting of the insider's trading strategy and the market makers' pricing rule. It shows that at the equilibrium: (i) all of the insider's private information is released at the end of the transaction; (ii) market depth and market liquidity evolve as semi-martingales, respectively; and (iii) the equilibrium price is driven by a bridge process that solves an Ornstein-Uhlenbeck-type SDE. Numerical simulations show that as the correlation coefficient increases, the equilibrium price becomes more informative, leading to a decrease in both the trading intensity and the expected payoff for the insider.