# Equilibrium price and optimal insider trading strategy under stochastic liquidity with long memory

## TL;DR

This paper extends the Kyle insider trading model by incorporating long memory in trading volume and stochastic noise volatility, deriving explicit equilibrium strategies and analyzing their effects on price impact and volatility.

## Contribution

It introduces a novel Kyle model with long memory and stochastic volatility, providing explicit solutions for insider strategies and market impact.

## Key findings

- Optimal insider trading strategy exhibits long memory properties.
- Price impact is influenced by fractional noise.
- Price volatility can become excessive due to aggressive trading.

## Abstract

In this paper, the Kyle model of insider trading is extended by characterizing the trading volume with long memory and allowing the noise trading volatility to follow a general stochastic process. Under this newly revised model, the equilibrium conditions are determined, with which the optimal insider trading strategy, price impact and price volatility are obtained explicitly. The volatility of the price volatility appears excessive, which is a result of the fact that a more aggressive trading strategy is chosen by the insider when uninformed volume is higher. The optimal trading strategy turns out to possess the property of long memory, and the price impact is also affected by the fractional noise.